Merge branch 'exprMerge' of gitlab.mpi-sws.org:jbard/FloVer into exprMerge

testcases/smalltest/BallBeam.scala

+import daisy.lang._
+import Real._
+
+
+object BallBeam {
+
+  // s1 <1, 16, 14>, s2, s3, s4: <1, 16, 15>
+  def ballbeam(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(0 <= s1 && s1 <= 1 && -0.5 <= s2 && s2 <= 0.5 && 0 <= s3 && s3 <= 0.5 && 0 <= s4 && s4 <= 0.5)
+    (-1828.6) * s1 + (-1028.6) * s2 + (-2008.0) * s3 + (-104.0) * s4
+  }
+
+
+
+}

testcases/smalltest/Bicycle.scala

+import daisy.lang._
+import Real._
+
+
+object Bicycle {
+
+  // s1, s2, s3, y1: <1, 16, 14>, [-1, 1]
+  def out1(s1: Real, s2: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1)
+    (-3.025300) * s1 + (-12.608900) * s2
+  }
+
+  def state1(s1: Real, s2: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= y1 && y1 <= 1)
+    (0.961270) * s1 + (-0.095962) * s2 + (0.013200) * y1
+  }
+
+  def state2(s1: Real, s2: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= y1 && y1 <= 1)
+    (-0.058217) * s1 + (0.727430) * s2 + (0.102100) * y1
+  }
+
+
+}
\ No newline at end of file

testcases/smalltest/Bsplines.scala

+
+import daisy.lang._
+import Real._
+
+/**
+  Equation and initial ranges from:
+  L. Zhang, Y. Zhang, and W. Zhou. Tradeoff between Approximation Accuracy and
+  Complexity for Range Analysis using Affine Arithmetic.
+*/
+object Bsplines {
+
+  def bspline0(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    (1 - u) * (1 - u) * (1 - u) / 6.0
+  } ensuring (res => 0 <= res && res <= 0.17 && res +/- 1e-15)
+  // proven in paper: [-0.05, 0.17]
+
+  def bspline1(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    (3 * u*u*u - 6 * u*u + 4) / 6.0
+  } ensuring (res => 0.16 <= res && res <= 0.7 && res +/- 1e-15)
+  // in paper [-0.05, 0.98]
+
+  def bspline2(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    (-3 * u*u*u  + 3*u*u + 3*u + 1) / 6.0
+  } ensuring (res => 0.16 <= res && res <= 0.7 && res +/- 1e-15)
+  // in paper [-0.02, 0.89]
+
+  def bspline3(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    -u*u*u / 6.0
+  } ensuring (res => -0.17 <= res && res <= 0.0 && res +/- 1e-15)
+  // in paper [-0.17, 0.05]
+
+}

testcases/smalltest/Floudas.scala

+
+
+import daisy.lang._
+import Real._
+
+/*
+  Real2Float
+
+  Optimization problems
+  A Collection of Test Problems for
+  Constrained Global Optimization Algorithms,
+  Floudas, Pardalos 1990
+
+*/
+object Floudas {
+
+
+
+  def floudas26(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real,
+    x7: Real, x8: Real, x9: Real, x10: Real): Real = {
+    require(0 <= x1 && x1 <= 1 && 0 <= x2 && x2 <= 1 && 0 <= x3 && x3 <= 1 && 0 <= x4 && x4 <= 1 &&
+      0 <= x5 && x5 <= 1 && 0 <= x6 && x6 <= 1 && 0 <= x7 && x7 <= 1 && 0 <= x8 && x8 <= 1 &&
+      0 <= x9 && x9 <= 1 && 0 <= x10 && x10 <= 1 &&
+      2 * x1 +6*x2 +1*x3 +0*x4 +3*x5 + 3*x6 +2*x7 +6*x8 +2*x9+2*x10 - 4  >= 0 &&
+      22-(6*x1 -5*x2 +8*x3 -3*x4 +0*x5+1*x6 +3*x7 +8*x8 +9*x9-3*x10)>= 0 &&
+      -(5*x1 +6*x2 +5*x3 +3*x4 +8*x5 -8*x6 +9*x7 +2*x8 +0*x9-9*x10) - 6 >= 0 &&
+      -(9*x1 +5*x2 +0*x3 -9*x4 +1*x5 -8*x6 +3*x7 -9*x8 -9*x9-3*x10) - 23 >= 0 &&
+      -(-(8*x1) +7*x2 -4*x3 -5*x4 -9*x5 +1*x6 -7*x7 -1*x8 +3*x9-2*x10) - 12 >= 0)
+
+    48*x1 + 42*x2 + 48*x3 + 45*x4 + 44*x5 + 41*x6 + 47*x7 + 42*x8 + 45*x9 + 46*x10 -
+      50*(x1*x1 + x2*x2 + x3*x3 + x4*x4 + x5*x5 + x6*x6 + x7*x7 + x8*x8 + x9*x9 + x10*x10)
+
+  }// 5.15e-13
+
+  def floudas33(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real): Real = {
+    require(0 <= x1 && x1 <= 6 && 0 <= x2 && x2 <= 6 && 1 <= x3 && x3 <= 5 &&
+      0 <= x4 && x4 <= 6 && 1 <= x5 && x5 <= 5 && 0 <= x6 && x6 <= 10 &&
+      (x3 -3)*(x3 -3) + x4 - 4 >= 0 &&
+      (x5 -3)*(x5 -3) + x6 - 4 >= 0 &&
+      2 - x1 + 3 * x2 >= 0 &&
+      2 + x1 - x2 >= 0 &&
+      6 - x1 - x2 >= 0 &&
+      x1 + x2 - 2 >= 0)
+
+    - (25 * (x1 -2)*(x1 -2)) - (x2 -2)* (x2 -2) - (x3 -1)*(x3 -1) -
+      (x4 -4)*(x4 -4) - (x5 - 1)*(x5 - 1) - (x6 - 4)* (x6 - 4)
+  } //5.81e–13
+
+  def floudas34(x1: Real, x2: Real, x3: Real): Real = {
+    require(0 <= x1 && x1 <= 2 && 0 <= x2 && x2 <= 2 && 0 <= x3 && x3 <= 3 &&
+      4 - x1 - x2 - x3 >= 0 &&
+      6 - 3 * x2 - x3 >= 0 &&
+      2*x1 - 0.75 - 2*x3 + 4*x1*x1 - 4*x1*x2 + 4*x1*x3 + 2*x2*x2 - 2*x2*x3 + 2*x3*x3 >= 0)
+
+    -2 * x1 + x2 - x3
+
+  } //2.67e - 15
+
+  def floudas46(x1: Real, x2: Real): Real = {
+    require(0 <= x1 && x1 <= 3 && 0 <= x2 && x2 <= 4 &&
+      2 * x1*x1*x1*x1 - 8 * x1*x1*x1 + 8 * x1* x1 - x2 >= 0 &&
+      4 * x1*x1*x1*x1 - 32 * x1*x1*x1 + 88 * x1*x1 - 96*x1 + 36 - x2 >= 0)
+
+    -x1 - x2
+  } //1.38e–15
+
+  def floudas47(x1: Real, x2: Real): Real = {
+    require(0 <= x1 && x1 <= 2 && 0 <= x2 && x2 <= 3 &&
+      -2 * x1*x1*x1*x1 + 2 - x2 >= 0)
+
+    -12*x1 -7*x2 +x2 *x2
+
+  } //1.01e–14
+
+
+  // from FPTaylor github
+  def floudas1(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real): Real = {
+    require(0 <= x1 && x1 <= 6 && 0 <= x2 && x2 <= 6 && 1 <= x3 && x3 <= 5 &&
+      0 <= x4 && x4 <= 6 && 1 <= x5 && x5 <= 5 && 0 <= x6 && x6 <= 10 &&
+      (x3 - 3) * (x3 - 3) + x4 - 4 >= 0 && (x5 - 3) * (x5 - 3) + x6 - 4 >= 0 &&
+      2 - x1 + 3 * x2 >= 0 &&  2 + x1 - x2 >= 0 &&  6 - x1 - x2 >= 0 && x1 + x2 - 2 >= 0)
+
+    -25 * ((x1 - 2) * (x1 - 2)) - ((x2 - 2) * (x2 - 2)) - ((x3 - 1) * (x3 - 1)) -
+      ((x4 - 4) * (x4 - 4)) - ((x5 - 1) * (x5 - 1)) - ((x6 - 4) * (x6 - 4))
+  }
+
+}
+

testcases/smalltest/InvertedPendulum.scala

+import daisy.lang._
+import Real._
+
+
+object InvertedPendulum {
+
+  // s1: <1, 16, 9>  s2: <1, 16, 11>   s3,s4: <1, 16, 15>
+  def out(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(-50 <= s1 && s1 <= 50 && -10 <= s2 && s2 <= 10 && -0.785 <= s3 && s3 <= 0.785 && -0.785 <= s4 && s4 <= 0.785)
+
+    1.0000 * s1 + 1.6567 * s2 + (-18.6854) * s3 + (-3.4594) * s4
+  }
+
+
+
+}

testcases/smalltest/Kepler.scala

+
+import daisy.lang._
+import Real._
+
+/*
+  These benchmarks were used by the Real2Float tool,
+  and come from the proof of the Kepler conjecture
+  Introduction to the flyspec project, T.C. Hales, Dagstuhl 2006
+*/
+object Kepler {
+
+  //15 operations
+  def kepler0(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real): Real = {
+    require(4 <= x1 && x1 <= 6.36 && 4 <= x2 && x2 <= 6.36 && 4 <= x3 && x3 <= 6.36 &&
+      4 <= x4 && x4 <= 6.36 && 4 <= x5 && x5 <= 6.36 && 4 <= x6 && x6 <= 6.36)
+
+    val t = ((-1 * x1) + x2 + x3 - x4 + x5 + x6)
+    x2 * x5 + x3 * x6 - x2 * x3 - x5 * x6 + x1 * t
+
+  } // 1.15e-15
+
+  //24 operations
+  def kepler1(x1: Real, x2: Real, x3: Real, x4: Real): Real = {
+    require(4 <= x1 && x1 <= 6.36 && 4 <= x2 && x2 <= 6.36 && 4 <= x3 && x3 <= 6.36 &&
+      4 <= x4 && x4 <= 6.36)
+
+    val t = ((-1 * x1) + x2 + x3 - x4)
+
+    x1 * x4 * t + x2 * (x1 - x2 + x3 + x4) + x3 * (x1 + x2 - x3 + x4) -
+      x2 * x3 * x4 - x1 * x3 - x1 * x2 - x4
+
+  } // 4.50e–13
+
+  //36 operations
+  def kepler2(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real): Real = {
+    require(4 <= x1 && x1 <= 6.36 && 4 <= x2 && x2 <= 6.36 && 4 <= x3 && x3 <= 6.36 &&
+      4 <= x4 && x4 <= 6.36 && 4 <= x5 && x5 <= 6.36 && 4 <= x6 && x6 <= 6.36)
+
+      val t = ((-1 * x1) + x2 + x3 - x4 + x5 + x6)
+      val t2 = (x1 - x2 + x3 + x4 - x5 + x6)
+
+      x1 * x4 * t + x2 * x5 * t2 +
+        x3* x6 * (x1 + x2 - x3 + x4 + x5 - x6) - x2 * x3 * x4 -
+          x1* x3* x5 - x1 * x2 * x6 - x4 * x5 * x6
+
+  } //2.08e–12
+}

testcases/smalltest/Science.scala

+
+
+import daisy.lang._
+import Real._
+
+
+
+object Science {
+
+  def verhulst(r: Real, K: Real, x: Real): Real = {
+    require(r >= 4.0 && r <= 4.0 && K >= 1.11 && K <= 1.11 && 0.1 <= x && x <= 0.3)
+
+    (r*x) / (1 + (x/K))
+
+  }
+
+  def predatorPrey(r: Real, K: Real, x: Real): Real = {
+    require(r >= 4.0 && r <= 4.0 && K >= 1.11 && K <= 1.11 && 0.1 <= x && x <= 0.3)
+
+    (r*x*x) / (1 + (x/K)*(x/K))
+
+  }
+
+  def carbonGas(T: Real, a: Real, b: Real, N: Real, p: Real, V: Real): Real = {
+    require(T >= 300 && T <= 300 && a >= 0.401 && a <= 0.401 && b >= 42.7e-6 && b <= 42.7e-6 && N >= 1000 && N <= 1000 &&
+    p >= 3.5e7 && p <= 3.5e7 && 0.1 < V && V < 0.5)
+
+    val k: Real = 1.3806503e-23
+    (p + a * (N / V) * (N / V)) * (V - N * b) - k * N * T
+
+  }
+
+}
\ No newline at end of file

testcases/smalltest/Traincar1.scala

+
+import daisy.lang._
+import Real._
+
+object Traincar1 {
+
+  // y1, y2: <1, 30, 16>    s1, s2, s3: <1, 30, 25>
+  def out1(s0: Real, s1: Real, s2: Real) = {
+    require(0 <= s0 && s0 <= 4.6 && 0 <= s1 && s1 <= 10 && 0 <= s2 && s2 <= 10)
+    (-3.795323e2) * s0 + (-5.443608e2) * s1 + 92.729 * s2 + 4.5165916241610748e3
+  }
+
+  def state1(s0: Real, s1: Real, s2: Real, y0: Real, y1: Real) = {
+    require(0 <= s0 && s0 <= 4.6 && 0 <= s1 && s1 <= 10 && 0 <= s2 && s2 <= 10 &&
+      0 <= y0 && y0 <= 10 && 0 <= y1 && y1 <= 10)
+    (9.9992292212695999e-01)*s0+ (6.7987387059578006e-02)*s1+ (-5.7849982690687002e-02)*s2 +
+      (-6.7093068270769995e-02)*y0 + (5.6868444245656999e-02)*y1+ (1.93109421e-07)*4.5165916241610748e+03
+  }
+
+  def state2(s0: Real, s1: Real, s2: Real, y0: Real, y1: Real) = {
+    require(0 <= s0 && s0 <= 4.6 && 0 <= s1 && s1 <= 10 && 0 <= s2 && s2 <= 10 &&
+      0 <= y0 && y0 <= 10 && 0 <= y1 && y1 <= 10)
+    (-2.1755689728790001e-03)*s0+ (9.8343791204296505e-01)*s1+ (2.6908497812900001e-03)*s2 +
+      (1.3497550507479000e-02)*y0 + (-2.1628302791680000e-03)*y1+ (5.615999103e-06)*4.5165916241610748e+03
+  }
+
+  def state3(s0: Real, s1: Real, s2: Real, y0: Real, y1: Real) = {
+    require(0 <= s0 && s0 <= 4.6 && 0 <= s1 && s1 <= 10 && 0 <= s2 && s2 <= 10 &&
+      0 <= y0 && y0 <= 10 && 0 <= y1 && y1 <= 10)
+    (7.5141305955000001e-05)*s0+ (2.4840831806619999e-03)*s1+ (9.9188004018882503e-01)*s2 + (-2.4770170720600001e-03)*y0 +
+     (8.1097048460159991e-03)*y1+ (7.060315e-09)*4.5165916241610748e+03
+  }
+
+
+}
\ No newline at end of file

testcases/testsmt/BallBeam.scala

+import daisy.lang._
+import Real._
+
+
+object BallBeam {
+
+  // s1 <1, 16, 14>, s2, s3, s4: <1, 16, 15>
+  def ballbeam(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(0 <= s1 && s1 <= 1 && -0.5 <= s2 && s2 <= 0.5 && 0 <= s3 && s3 <= 0.5 && 0 <= s4 && s4 <= 0.5)
+    (-1828.6) * s1 + (-1028.6) * s2 + (-2008.0) * s3 + (-104.0) * s4
+  }
+
+
+
+}

testcases/testsmt/BatchProcessor.scala

+
+import daisy.lang._
+import Real._
+
+
+object BatchProcessor {
+
+  // s1, s2, s3, s4, y1, y2: <1, 16, 11>
+  def out1(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(-10 <= s1 && s1 <= 10 && -10 <= s2 && s2 <= 10 && -10 <= s3 && s3 <= 10 && -10 <= s4 && s4 <= 10)
+    (-0.0429) * s1 + (-0.9170) * s2 + (-0.3299) * s3 + (-0.8206) * s4
+  }
+
+  def out2(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(-10 <= s1 && s1 <= 10 && -10 <= s2 && s2 <= 10 && -10 <= s3 && s3 <= 10 && -10 <= s4 && s4 <= 10)
+    2.4908 * s1 + 0.0751 * s2 + 1.7481 * s3 + (-1.1433) * s4
+  }
+
+  def state1(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real) = {
+    require(-10 <= s1 && s1 <= 10 && -10 <= s2 && s2 <= 10 && -10 <= s3 && s3 <= 10 && -10 <= s4 && s4 <= 10 &&
+      -10 <= y1 && y1 <= 10)
+    0.9670 * s1 + (-0.0019) * s2 + 0.0187 * s3 + (-0.0088) * s4 + 0.0447 * y1
+  }
+
+  def state2(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-10 <= s1 && s1 <= 10 && -10 <= s2 && s2 <= 10 && -10 <= s3 && s3 <= 10 && -10 <= s4 && s4 <= 10 &&
+      -10 <= y1 && y1 <= 10 && -10 <= y2 && y2 <= 10)
+    (-0.0078) * s1 + 0.9052 * s2 + (-0.0181) * s3 + (-0.0392) * s4 + (-0.0003) * y1 + 0.0020 * y2
+    //((0.9052 * s2) + (((s3 * -0.0181) + (-0.0078 * s1)) + (((-0.0392 * s4) + (-0.0003 * y1)) + (0.002 * y2))))
+  }
+
+  def state3(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-10 <= s1 && s1 <= 10 && -10 <= s2 && s2 <= 10 && -10 <= s3 && s3 <= 10 && -10 <= s4 && s4 <= 10 &&
+      -10 <= y1 && y1 <= 10 && -10 <= y2 && y2 <= 10)
+    (-0.0830) * s1 + 0.0222 * s2 + 0.8620 * s3 + 0.0978 * s4 + 0.0170 * y1 + 0.0058 * y2
+  }
+
+  def state4(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-10 <= s1 && s1 <= 10 && -10 <= s2 && s2 <= 10 && -10 <= s3 && s3 <= 10 && -10 <= s4 && s4 <= 10 &&
+      -10 <= y1 && y1 <= 10 && -10 <= y2 && y2 <= 10)
+    (-0.0133) * s1 + 0.0243 * s2 + (-0.0043) * s3 + 0.9824 * s4 + 0.0127 * y1 + 0.0059 * y2
+  }
+}
\ No newline at end of file

testcases/testsmt/BatchReactor.scala

+import daisy.lang._
+import Real._
+
+
+object BatchReactor {
+
+  // s1, s2, s3, s4, y1, y2: <1, 16, 14>
+  def out1(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= s4 && s4 <= 1)
+    (-0.058300) * s1 + (-0.908300) * s2 + (-0.325800) * s3 + (-0.872100) * s4
+  }
+
+  def out2(s1: Real, s2: Real, s3: Real, s4: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= s4 && s4 <= 1)
+    (2.463800) * s1 + (0.050400) * s2 + (1.709900) * s3 + (-1.165300) * s4
+  }
+
+  def state1(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= s4 && s4 <= 1 &&
+      -1 <= y1 && y1 <= 1 && -1 <= y2 && y2 <= 1)
+    (0.934292) * s1 + (0.008415) * s2 + (-0.014106) * s3 + (0.023954) * s4 + (0.077400) * y1 + (-0.010300) * y2
+  }
+
+  def state2(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= s4 && s4 <= 1 &&
+      -1 <= y1 && y1 <= 1 && -1 <= y2 && y2 <= 1)
+    (-0.006769) * s1 + (0.884924) * s2 + (-0.016066) * s3 + (-0.044019) * s4 + (-0.002200) * y1 + (0.022700) * y2
+  }
+
+  def state3(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= s4 && s4 <= 1 &&
+      -1 <= y1 && y1 <= 1 && -1 <= y2 && y2 <= 1)
+    (-0.092148) * s1 + (-0.011039) * s2 + (0.853511) * s3 + (0.107537) * s4 + (0.026700) * y1 + (0.039800) * y2
+  }
+
+  def state4(s1: Real, s2: Real, s3: Real, s4: Real, y1: Real, y2: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= s4 && s4 <= 1 &&
+      -1 <= y1 && y1 <= 1 && -1 <= y2 && y2 <= 1)
+    (-0.036410) * s1 + (0.030194) * s2 + (-0.027155) * s3 + (1.004619) * s4 + (0.035600) * y1 + (0.000100) * y2
+  }
+
+
+
+}
\ No newline at end of file

testcases/testsmt/Bicycle.scala

+import daisy.lang._
+import Real._
+
+
+object Bicycle {
+
+  // s1, s2, s3, y1: <1, 16, 14>, [-1, 1]
+  def out1(s1: Real, s2: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1)
+    (-3.025300) * s1 + (-12.608900) * s2
+  }
+
+  def state1(s1: Real, s2: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= y1 && y1 <= 1)
+    (0.961270) * s1 + (-0.095962) * s2 + (0.013200) * y1
+  }
+
+  def state2(s1: Real, s2: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= y1 && y1 <= 1)
+    (-0.058217) * s1 + (0.727430) * s2 + (0.102100) * y1
+  }
+
+
+}
\ No newline at end of file

testcases/testsmt/Bsplines.scala

+
+import daisy.lang._
+import Real._
+
+/**
+  Equation and initial ranges from:
+  L. Zhang, Y. Zhang, and W. Zhou. Tradeoff between Approximation Accuracy and
+  Complexity for Range Analysis using Affine Arithmetic.
+*/
+object Bsplines {
+
+  def bspline0(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    (1 - u) * (1 - u) * (1 - u) / 6.0
+  } ensuring (res => 0 <= res && res <= 0.17 && res +/- 1e-15)
+  // proven in paper: [-0.05, 0.17]
+
+  def bspline1(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    (3 * u*u*u - 6 * u*u + 4) / 6.0
+  } ensuring (res => 0.16 <= res && res <= 0.7 && res +/- 1e-15)
+  // in paper [-0.05, 0.98]
+
+  def bspline2(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    (-3 * u*u*u  + 3*u*u + 3*u + 1) / 6.0
+  } ensuring (res => 0.16 <= res && res <= 0.7 && res +/- 1e-15)
+  // in paper [-0.02, 0.89]
+
+  def bspline3(u: Real): Real = {
+    require(0 <= u && u <= 1)
+    -u*u*u / 6.0
+  } ensuring (res => -0.17 <= res && res <= 0.0 && res +/- 1e-15)
+  // in paper [-0.17, 0.05]
+
+}

testcases/testsmt/DCMotor.scala

+import daisy.lang._
+import Real._
+
+
+object DCMotor {
+
+  // s1, s2, s3, y1: <1, 16, 14>, [-1, 1]
+  def out1(s1: Real, s2: Real, s3: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1)
+    (-0.112900) * s1 + (-0.021100) * s2 + (-0.009300) * s3
+  }
+
+  def state1(s1: Real, s2: Real, s3: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= y1 && y1 <= 1)
+    (0.960883) * s1 + (0.000949) * s2 + (-0.000004) * s3 + (0.039000) * y1
+  }
+
+  def state2(s1: Real, s2: Real, s3: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= y1 && y1 <= 1)
+    (-0.602449) * s1 + (0.899089) * s2 + (-0.013648) * s3 + (0.370000) * y1
+  }
+
+  def state3(s1: Real, s2: Real, s3: Real, y1: Real) = {
+    require(-1 <= s1 && s1 <= 1 && -1 <= s2 && s2 <= 1 && -1 <= s3 && s3 <= 1 && -1 <= y1 && y1 <= 1)
+    (-0.009134) * s1 + (-0.011434) * s2 + (-0.002232) * s3 + (-0.017500) * y1
+  }
+
+}
\ No newline at end of file

testcases/testsmt/Doppler.scala

+
+
+import daisy.lang._
+import Real._
+
+
+object Doppler {
+
+  def doppler(u: Real, v: Real, T: Real): Real = {
+    require(-100.0 <= u && u <= 100 && 20 <= v && v <= 20000 && -30 <= T && T <= 50 && u + T <= 100)
+
+    val t1 = 331.4 + 0.6 * T
+    (- (t1) *v) / ((t1 + u)*(t1 + u))
+
+  }
+
+
+}

testcases/testsmt/DopplerFMA.scala

+
+
+import daisy.lang._
+import Real._
+
+
+object DopplerFMA {
+
+  def doppler(u: Real, v: Real, T: Real): Real = {
+    require(-100.0 <= u && u <= 100 && 20 <= v && v <= 20000 && -30 <= T && T <= 50)
+
+    val t1 = fma(0.6, T, 331.4)
+    (- (t1) *v) / ((t1 + u)*(t1 + u))
+
+  }
+
+
+}

testcases/testsmt/Floudas.scala

+
+
+import daisy.lang._
+import Real._
+
+/*
+  Real2Float
+
+  Optimization problems
+  A Collection of Test Problems for
+  Constrained Global Optimization Algorithms,
+  Floudas, Pardalos 1990
+
+*/
+object Floudas {
+
+
+
+  def floudas26(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real,
+    x7: Real, x8: Real, x9: Real, x10: Real): Real = {
+    require(0 <= x1 && x1 <= 1 && 0 <= x2 && x2 <= 1 && 0 <= x3 && x3 <= 1 && 0 <= x4 && x4 <= 1 &&
+      0 <= x5 && x5 <= 1 && 0 <= x6 && x6 <= 1 && 0 <= x7 && x7 <= 1 && 0 <= x8 && x8 <= 1 &&
+      0 <= x9 && x9 <= 1 && 0 <= x10 && x10 <= 1 &&
+      2 * x1 +6*x2 +1*x3 +0*x4 +3*x5 + 3*x6 +2*x7 +6*x8 +2*x9+2*x10 - 4  >= 0 &&
+      22-(6*x1 -5*x2 +8*x3 -3*x4 +0*x5+1*x6 +3*x7 +8*x8 +9*x9-3*x10)>= 0 &&
+      -(5*x1 +6*x2 +5*x3 +3*x4 +8*x5 -8*x6 +9*x7 +2*x8 +0*x9-9*x10) - 6 >= 0 &&
+      -(9*x1 +5*x2 +0*x3 -9*x4 +1*x5 -8*x6 +3*x7 -9*x8 -9*x9-3*x10) - 23 >= 0 &&
+      -(-(8*x1) +7*x2 -4*x3 -5*x4 -9*x5 +1*x6 -7*x7 -1*x8 +3*x9-2*x10) - 12 >= 0)
+
+    48*x1 + 42*x2 + 48*x3 + 45*x4 + 44*x5 + 41*x6 + 47*x7 + 42*x8 + 45*x9 + 46*x10 -
+      50*(x1*x1 + x2*x2 + x3*x3 + x4*x4 + x5*x5 + x6*x6 + x7*x7 + x8*x8 + x9*x9 + x10*x10)
+
+  }// 5.15e-13
+
+  def floudas33(x1: Real, x2: Real, x3: Real, x4: Real, x5: Real, x6: Real): Real = {
+    require(0 <= x1 && x1 <= 6 && 0 <= x2 && x2 <= 6 && 1 <= x3 && x3 <= 5 &&
+      0 <= x4 && x4 <= 6 && 1 <= x5 && x5 <= 5 && 0 <= x6 && x6 <= 10 &&
+      (x3 -3)*(x3 -3) + x4 - 4 >= 0 &&
+      (x5 -3)*(x5 -3) + x6 - 4 >= 0 &&
+      2 - x1 + 3 * x2 >= 0 &&
+      2 + x1 - x2 >= 0 &&
+      6 - x1 - x2 >= 0 &&
+      x1 + x2 - 2 >= 0)
+
+    - (25 * (x1 -2)*(x1 -2)) - (x2 -2)* (x2 -2) - (x3 -1)*(x3 -1) -
+      (x4 -4)*(x4 -4) - (x5 - 1)*(x5 - 1) - (x6 - 4)* (x6 - 4)
+  } //5.81e–13
+
+  def floudas34(x1: Real, x2: Real, x3: Real): Real = {
+    require(0 <= x1 && x1 <= 2 && 0 <= x2 && x2 <= 2 && 0 <= x3 && x3 <= 3 &&
+      4 - x1 - x2 - x3 >= 0 &&
+      6 - 3 * x2 - x3 >= 0 &&
+      2*x1 - 0.75 - 2*x3 + 4*x1*x1 - 4*x1*x2 + 4*x1*x3 + 2*x2*x2 - 2*x2*x3 + 2*x3*x3 >= 0)
+
+    -2 * x1 + x2 - x3
+
+  } //2.67e - 15
+
+  def floudas46(x1: Real, x2: Real): Real = {
+    require(0 <= x1 && x1 <= 3 && 0 <= x2 && x2 <= 4 &&
+      2 * x1*x1*x1*x1 - 8 * x1*x1*x1 + 8 * x1* x1 - x2 >= 0 &&
+      4 * x1*x1*x1*x1 - 32 * x1*x1*x1 + 88 * x1*x1 - 96*x1 + 36 - x2 >= 0)
+
+    -x1 - x2
+  } //1.38e–15
+
+  def floudas47(x1: Real, x2: Real): Real = {
+    require(0 <= x1 && x1 <= 2 && 0 <= x2 && x2 <= 3 &&
+      -2 * x1*x1*x1*x1 + 2 - x2 >= 0)