Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, K

Percentage Accurate: 70.0% → 74.6%

Time: 15.9s

Alternatives: 14

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 74.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 5 \cdot 10^{+17}:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(\sin \left(\mathsf{fma}\left(\frac{z}{3}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot 1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 5e+17)
     (-
      (*
       t_1
       (fma
        (sin (fma (/ z 3.0) t (/ (PI) 2.0)))
        (cos y)
        (* (sin (/ (* t z) 3.0)) (sin y))))
      (/ a (* b 3.0)))
     (- (* t_1 1.0) (/ (/ a 3.0) b)))))

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 5e17

   1. Initial program 80.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      3. cos-diff N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      4. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{3}}\right)\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{z \cdot t}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      13. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      14. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{\color{blue}{-3}}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      15. lower-cos.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \color{blue}{\cos y}, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      16. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      17. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      18. lower-sin.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{z \cdot t}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      20. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      21. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      22. lower-sin.f64 82.9

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \color{blue}{\sin y}\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 82.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\frac{t \cdot z}{-3}\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      2. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{t \cdot z}{-3}\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      3. sin-+PI/2-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\sin \left(\left(\mathsf{neg}\left(\frac{t \cdot z}{-3}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\left(\mathsf{neg}\left(\color{blue}{\frac{t \cdot z}{-3}}\right)\right) + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      5. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\color{blue}{\frac{t \cdot z}{\mathsf{neg}\left(-3\right)}} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      6. metadata-eval N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\frac{t \cdot z}{\color{blue}{3}} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      7. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\frac{\color{blue}{t \cdot z}}{3} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      8. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\frac{\color{blue}{z \cdot t}}{3} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      9. lower-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\sin \left(\frac{z \cdot t}{3} + \frac{\mathsf{PI}\left(\right)}{2}\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      10. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\frac{\color{blue}{t \cdot z}}{3} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      11. associate-/l* N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\color{blue}{t \cdot \frac{z}{3}} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\color{blue}{\frac{z}{3} \cdot t} + \frac{\mathsf{PI}\left(\right)}{2}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \color{blue}{\left(\mathsf{fma}\left(\frac{z}{3}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      14. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\mathsf{fma}\left(\color{blue}{\frac{z}{3}}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      15. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\mathsf{fma}\left(\frac{z}{3}, t, \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right)\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      16. lower-PI.f64 83.4

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(\mathsf{fma}\left(\frac{z}{3}, t, \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right)\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   6. Applied rewrites 83.4%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\sin \left(\mathsf{fma}\left(\frac{z}{3}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   if 5e17 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 50.2%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 74.3

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 74.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

      3. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

      4. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      6. lower-/.f64 74.4

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

   7. Applied rewrites 74.4%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 74.7%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 74.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 5 \cdot 10^{+17}:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\mathsf{fma}\left(\frac{z}{-3}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot \sin y\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot 1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 5e+17)
     (-
      (*
       t_1
       (fma
        (cos (/ (* t z) -3.0))
        (cos y)
        (* (cos (fma (/ z -3.0) t (/ (PI) 2.0))) (sin y))))
      (/ a (* b 3.0)))
     (- (* t_1 1.0) (/ (/ a 3.0) b)))))

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 5e17

   1. Initial program 80.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      3. cos-diff N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      4. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{3}}\right)\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{z \cdot t}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      13. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      14. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{\color{blue}{-3}}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      15. lower-cos.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \color{blue}{\cos y}, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      16. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      17. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      18. lower-sin.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{z \cdot t}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      20. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      21. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      22. lower-sin.f64 82.9

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \color{blue}{\sin y}\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 82.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. lift-sin.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{t \cdot z}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      2. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \color{blue}{\left(\frac{t \cdot z}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      3. metadata-eval N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{\color{blue}{\mathsf{neg}\left(-3\right)}}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      4. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \color{blue}{\left(\mathsf{neg}\left(\frac{t \cdot z}{-3}\right)\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      5. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\mathsf{neg}\left(\color{blue}{\frac{t \cdot z}{-3}}\right)\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      6. sin-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\left(\mathsf{neg}\left(\sin \left(\frac{t \cdot z}{-3}\right)\right)\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      7. cos-+PI/2-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\cos \left(\frac{t \cdot z}{-3} + \frac{\mathsf{PI}\left(\right)}{2}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      8. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\cos \left(\frac{t \cdot z}{-3} + \frac{\mathsf{PI}\left(\right)}{2}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      9. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\color{blue}{\frac{t \cdot z}{-3}} + \frac{\mathsf{PI}\left(\right)}{2}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      10. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\frac{\color{blue}{t \cdot z}}{-3} + \frac{\mathsf{PI}\left(\right)}{2}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      11. associate-/l* N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\color{blue}{t \cdot \frac{z}{-3}} + \frac{\mathsf{PI}\left(\right)}{2}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\color{blue}{\frac{z}{-3} \cdot t} + \frac{\mathsf{PI}\left(\right)}{2}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      13. lower-fma.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \color{blue}{\left(\mathsf{fma}\left(\frac{z}{-3}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      14. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\mathsf{fma}\left(\color{blue}{\frac{z}{-3}}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      15. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\mathsf{fma}\left(\frac{z}{-3}, t, \color{blue}{\frac{\mathsf{PI}\left(\right)}{2}}\right)\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      16. lower-PI.f64 83.1

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \cos \left(\mathsf{fma}\left(\frac{z}{-3}, t, \frac{\color{blue}{\mathsf{PI}\left(\right)}}{2}\right)\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   6. Applied rewrites 83.1%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\cos \left(\mathsf{fma}\left(\frac{z}{-3}, t, \frac{\mathsf{PI}\left(\right)}{2}\right)\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   if 5e17 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 50.2%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 74.3

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 74.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

      3. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

      4. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      6. lower-/.f64 74.4

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

   7. Applied rewrites 74.4%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 74.7%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-0.3333333333333333 \cdot t\right) \cdot z\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \leq 10^{+41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2 \cdot b, \mathsf{fma}\left(\sin t\_1, -\sin y, \cos t\_1 \cdot \cos y\right) \cdot \sqrt{x}, -0.3333333333333333 \cdot a\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot 1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* -0.3333333333333333 t) z)) (t_2 (* 2.0 (sqrt x))))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))) 1e+41)
     (/
      (fma
       (* 2.0 b)
       (* (fma (sin t_1) (- (sin y)) (* (cos t_1) (cos y))) (sqrt x))
       (* -0.3333333333333333 a))
      b)
     (- (* t_2 1.0) (/ (/ a 3.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-0.3333333333333333 * t) * z;
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))) <= 1e+41) {
		tmp = fma((2.0 * b), (fma(sin(t_1), -sin(y), (cos(t_1) * cos(y))) * sqrt(x)), (-0.3333333333333333 * a)) / b;
	} else {
		tmp = (t_2 * 1.0) - ((a / 3.0) / b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-0.3333333333333333 * t) * z)
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0))) <= 1e+41)
		tmp = Float64(fma(Float64(2.0 * b), Float64(fma(sin(t_1), Float64(-sin(y)), Float64(cos(t_1) * cos(y))) * sqrt(x)), Float64(-0.3333333333333333 * a)) / b);
	else
		tmp = Float64(Float64(t_2 * 1.0) - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-0.3333333333333333 * t), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+41], N[(N[(N[(2.0 * b), $MachinePrecision] * N[(N[(N[Sin[t$95$1], $MachinePrecision] * (-N[Sin[y], $MachinePrecision]) + N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(t$95$2 * 1.0), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 1.00000000000000001e41

   1. Initial program 75.6%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{2 \cdot \left(\left(b \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot \sqrt{x}\right) - \frac{1}{3} \cdot a}{b}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 \cdot \left(\left(b \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot \sqrt{x}\right) - \frac{1}{3} \cdot a}{b}} \]

   5. Applied rewrites 75.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(2 \cdot b, \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right) \cdot \sqrt{x}, -0.3333333333333333 \cdot a\right)}{b}} \]
   6. Step-by-step derivation

   7. Applied rewrites 78.2%

      \[\leadsto \frac{\mathsf{fma}\left(2 \cdot b, \mathsf{fma}\left(\sin \left(\left(-0.3333333333333333 \cdot t\right) \cdot z\right), -\sin y, \cos \left(\left(-0.3333333333333333 \cdot t\right) \cdot z\right) \cdot \cos y\right) \cdot \sqrt{x}, -0.3333333333333333 \cdot a\right)}{b} \]

   if 1.00000000000000001e41 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 61.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 80.8

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 80.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

      3. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

      4. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      6. lower-/.f64 80.9

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

   7. Applied rewrites 80.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 81.3%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \leq 10^{+41}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(\mathsf{fma}\left(\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right), \cos y, \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right) \cdot \sin y\right) \cdot b\right) \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot a\right)}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot 1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (- (* t_1 (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))) 1e+41)
     (/
      (fma
       (*
        (*
         (fma
          (cos (* -0.3333333333333333 (* t z)))
          (cos y)
          (* (sin (* (* t z) 0.3333333333333333)) (sin y)))
         b)
        (sqrt x))
       2.0
       (* -0.3333333333333333 a))
      b)
     (- (* t_1 1.0) (/ (/ a 3.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (((t_1 * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))) <= 1e+41) {
		tmp = fma(((fma(cos((-0.3333333333333333 * (t * z))), cos(y), (sin(((t * z) * 0.3333333333333333)) * sin(y))) * b) * sqrt(x)), 2.0, (-0.3333333333333333 * a)) / b;
	} else {
		tmp = (t_1 * 1.0) - ((a / 3.0) / b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0))) <= 1e+41)
		tmp = Float64(fma(Float64(Float64(fma(cos(Float64(-0.3333333333333333 * Float64(t * z))), cos(y), Float64(sin(Float64(Float64(t * z) * 0.3333333333333333)) * sin(y))) * b) * sqrt(x)), 2.0, Float64(-0.3333333333333333 * a)) / b);
	else
		tmp = Float64(Float64(t_1 * 1.0) - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+41], N[(N[(N[(N[(N[(N[Cos[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[y], $MachinePrecision] + N[(N[Sin[N[(N[(t * z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 2.0 + N[(-0.3333333333333333 * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(t$95$1 * 1.0), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 1.00000000000000001e41

   1. Initial program 75.6%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      3. cos-diff N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      4. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{3}}\right)\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{z \cdot t}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      13. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      14. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{\color{blue}{-3}}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      15. lower-cos.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \color{blue}{\cos y}, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      16. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      17. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      18. lower-sin.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{z \cdot t}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      20. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      21. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      22. lower-sin.f64 78.8

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \color{blue}{\sin y}\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 78.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]

   5. Taylor expanded in b around 0

      \[\leadsto \color{blue}{\frac{2 \cdot \left(\left(b \cdot \left(\cos y \cdot \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right) + \sin y \cdot \sin \left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot \sqrt{x}\right) - \frac{1}{3} \cdot a}{b}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 \cdot \left(\left(b \cdot \left(\cos y \cdot \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right) + \sin y \cdot \sin \left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \cdot \sqrt{x}\right) - \frac{1}{3} \cdot a}{b}} \]

   7. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\left(\mathsf{fma}\left(\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right), \cos y, \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right) \cdot \sin y\right) \cdot b\right) \cdot \sqrt{x}, 2, -0.3333333333333333 \cdot a\right)}{b}} \]

   if 1.00000000000000001e41 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 61.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 80.8

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 80.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

      3. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

      4. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      6. lower-/.f64 80.9

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

   7. Applied rewrites 80.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 81.3%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 76.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.94:\\ \;\;\;\;t\_2 \cdot \mathsf{fma}\left(\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2} + y\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))) (t_2 (* 2.0 (sqrt x))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.94)
     (-
      (*
       t_2
       (fma
        (cos (* -0.3333333333333333 (* t z)))
        (cos y)
        (* (sin (/ (* t z) 3.0)) (sin y))))
      t_1)
     (- (* t_2 (sin (+ (/ (PI) 2.0) y))) t_1))))

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.93999999999999995

   1. Initial program 71.6%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      3. cos-diff N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      4. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{3}}\right)\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{z \cdot t}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      13. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      14. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{\color{blue}{-3}}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      15. lower-cos.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \color{blue}{\cos y}, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      16. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      17. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      18. lower-sin.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{z \cdot t}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      20. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      21. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      22. lower-sin.f64 75.0

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \color{blue}{\sin y}\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 75.0%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]

   5. Taylor expanded in z around inf

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      3. lower-*.f64 75.2

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(-0.3333333333333333 \cdot \color{blue}{\left(t \cdot z\right)}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   7. Applied rewrites 75.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)}, \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

   if 0.93999999999999995 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 66.8%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 84.9

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 84.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 85.0%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sin \left(\frac{\mathsf{PI}\left(\right)}{2} + y\right) - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 71.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-52} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-135}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (or (<= t_1 -5e-52) (not (<= t_1 2e-135)))
     (- (* (* 2.0 (sqrt x)) 1.0) (/ (/ a 3.0) b))
     (* (* (sqrt x) 2.0) (cos (fma -0.3333333333333333 (* t z) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if ((t_1 <= -5e-52) || !(t_1 <= 2e-135)) {
		tmp = ((2.0 * sqrt(x)) * 1.0) - ((a / 3.0) / b);
	} else {
		tmp = (sqrt(x) * 2.0) * cos(fma(-0.3333333333333333, (t * z), y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if ((t_1 <= -5e-52) || !(t_1 <= 2e-135))
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * 1.0) - Float64(Float64(a / 3.0) / b));
	else
		tmp = Float64(Float64(sqrt(x) * 2.0) * cos(fma(-0.3333333333333333, Float64(t * z), y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-52], N[Not[LessEqual[t$95$1, 2e-135]], $MachinePrecision]], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -5e-52 or 2.0000000000000001e-135 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 79.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 91.8

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 91.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

      3. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

      4. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      6. lower-/.f64 91.8

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

   7. Applied rewrites 91.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 88.7%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]

   if -5e-52 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 2.0000000000000001e-135

   1. Initial program 52.4%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-2 \cdot \left(\sqrt{x} \cdot \left(\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left(\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right) \cdot -2} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot {\left(\sqrt{-1}\right)}^{2}\right)} \cdot -2 \]

      3. unpow2 N/A

         \[\leadsto \left(\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot \color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)}\right) \cdot -2 \]

      4. rem-square-sqrt N/A

         \[\leadsto \left(\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot \color{blue}{-1}\right) \cdot -2 \]

      5. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot \left(-1 \cdot -2\right)} \]

      6. metadata-eval N/A

         \[\leadsto \left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) \cdot \color{blue}{2} \]

      7. *-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)} \]

      8. associate-*r* N/A

         \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)} \]

      9. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)} \]

      10. *-commutative N/A

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right)} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right)} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \]

      12. lower-sqrt.f64 N/A

          \[\leadsto \left(\color{blue}{\sqrt{x}} \cdot 2\right) \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \]

      13. lower-cos.f64 N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \color{blue}{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)} \]

      14. cancel-sign-sub-inv N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \cos \color{blue}{\left(y + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(t \cdot z\right)\right)} \]

      15. distribute-lft-neg-in N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      16. +-commutative N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \cos \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right) + y\right)} \]

      17. distribute-lft-neg-in N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(t \cdot z\right)} + y\right) \]

      18. metadata-eval N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\color{blue}{\frac{-1}{3}} \cdot \left(t \cdot z\right) + y\right) \]

      19. lower-fma.f64 N/A

          \[\leadsto \left(\sqrt{x} \cdot 2\right) \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\frac{-1}{3}, t \cdot z, y\right)\right)} \]

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -5 \cdot 10^{-52} \lor \neg \left(\frac{a}{b \cdot 3} \leq 2 \cdot 10^{-135}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-52} \lor \neg \left(t\_1 \leq 10^{-131}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\cos y\right) \cdot \sqrt{x}\right) \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (or (<= t_1 -5e-52) (not (<= t_1 1e-131)))
     (- (* (* 2.0 (sqrt x)) 1.0) (/ (/ a 3.0) b))
     (* (* (- (cos y)) (sqrt x)) -2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if ((t_1 <= -5e-52) || !(t_1 <= 1e-131)) {
		tmp = ((2.0 * sqrt(x)) * 1.0) - ((a / 3.0) / b);
	} else {
		tmp = (-cos(y) * sqrt(x)) * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (b * 3.0d0)
    if ((t_1 <= (-5d-52)) .or. (.not. (t_1 <= 1d-131))) then
        tmp = ((2.0d0 * sqrt(x)) * 1.0d0) - ((a / 3.0d0) / b)
    else
        tmp = (-cos(y) * sqrt(x)) * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if ((t_1 <= -5e-52) || !(t_1 <= 1e-131)) {
		tmp = ((2.0 * Math.sqrt(x)) * 1.0) - ((a / 3.0) / b);
	} else {
		tmp = (-Math.cos(y) * Math.sqrt(x)) * -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	tmp = 0
	if (t_1 <= -5e-52) or not (t_1 <= 1e-131):
		tmp = ((2.0 * math.sqrt(x)) * 1.0) - ((a / 3.0) / b)
	else:
		tmp = (-math.cos(y) * math.sqrt(x)) * -2.0
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if ((t_1 <= -5e-52) || !(t_1 <= 1e-131))
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * 1.0) - Float64(Float64(a / 3.0) / b));
	else
		tmp = Float64(Float64(Float64(-cos(y)) * sqrt(x)) * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (b * 3.0);
	tmp = 0.0;
	if ((t_1 <= -5e-52) || ~((t_1 <= 1e-131)))
		tmp = ((2.0 * sqrt(x)) * 1.0) - ((a / 3.0) / b);
	else
		tmp = (-cos(y) * sqrt(x)) * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-52], N[Not[LessEqual[t$95$1, 1e-131]], $MachinePrecision]], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(N[((-N[Cos[y], $MachinePrecision]) * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -5e-52 or 9.9999999999999999e-132 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 79.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 92.2

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 92.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

      3. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

      4. associate-/r* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

      6. lower-/.f64 92.3

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

   7. Applied rewrites 92.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
   9. Step-by-step derivation

   10. Applied rewrites 89.1%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]

   if -5e-52 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 9.9999999999999999e-132

   1. Initial program 51.9%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      3. cos-diff N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      4. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y} + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      5. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3} \]

      6. cos-neg-rev N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      7. lower-cos.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\color{blue}{\cos \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      8. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{3}}\right)\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      9. distribute-neg-frac2 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      10. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \color{blue}{\left(\frac{z \cdot t}{\mathsf{neg}\left(3\right)}\right)}, \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      11. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{z \cdot t}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      12. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      13. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{\color{blue}{t \cdot z}}{\mathsf{neg}\left(3\right)}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      14. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{\color{blue}{-3}}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      15. lower-cos.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \color{blue}{\cos y}, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3} \]

      16. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      17. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y}\right) - \frac{a}{b \cdot 3} \]

      18. lower-sin.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \color{blue}{\sin \left(\frac{z \cdot t}{3}\right)} \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      19. lift-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{z \cdot t}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      20. *-commutative N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      21. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{\color{blue}{t \cdot z}}{3}\right) \cdot \sin y\right) - \frac{a}{b \cdot 3} \]

      22. lower-sin.f64 55.6

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \color{blue}{\sin y}\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 55.6%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\frac{t \cdot z}{-3}\right), \cos y, \sin \left(\frac{t \cdot z}{3}\right) \cdot \sin y\right)} - \frac{a}{b \cdot 3} \]

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-2 \cdot \left(\sqrt{x} \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(\cos y \cdot \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right) + \sin y \cdot \sin \left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(\cos y \cdot \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right) + \sin y \cdot \sin \left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right) \cdot -2} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left({\left(\sqrt{-1}\right)}^{2} \cdot \left(\cos y \cdot \cos \left(\frac{-1}{3} \cdot \left(t \cdot z\right)\right) + \sin y \cdot \sin \left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right) \cdot -2} \]

   7. Applied rewrites 54.9%

      \[\leadsto \color{blue}{\left(\left(-\sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right), \cos y, \sin \left(\left(t \cdot z\right) \cdot 0.3333333333333333\right) \cdot \sin y\right)\right) \cdot -2} \]

   8. Taylor expanded in z around 0

      \[\leadsto \left(-1 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \cdot -2 \]
   9. Step-by-step derivation

   10. Applied rewrites 50.4%

       \[\leadsto \left(\left(-\cos y\right) \cdot \sqrt{x}\right) \cdot -2 \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -5 \cdot 10^{-52} \lor \neg \left(\frac{a}{b \cdot 3} \leq 10^{-131}\right):\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\cos y\right) \cdot \sqrt{x}\right) \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{a}{3}}{b} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ (/ a 3.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - ((a / 3.0) / b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - ((a / 3.0d0) / b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - ((a / 3.0) / b);
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - ((a / 3.0) / b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(Float64(a / 3.0) / b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - ((a / 3.0) / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

   3. *-commutative N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

   4. associate-/r* N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   5. lower-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   6. lower-/.f64 77.1

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

7. Applied rewrites 77.1%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]
8. Add Preprocessing

Alternative 9: 76.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Add Preprocessing

Alternative 10: 76.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \frac{a}{b}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (* 2.0 (cos y)) (sqrt x) (* -0.3333333333333333 (/ a b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((2.0 * cos(y)), sqrt(x), (-0.3333333333333333 * (a / b)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(2.0 * cos(y)), sqrt(x), Float64(-0.3333333333333333 * Float64(a / b)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Sqrt[x], $MachinePrecision] + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right)} \cdot \frac{a}{b} \]

   2. fp-cancel-sign-sub-inv N/A

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \frac{-1}{3} \cdot \frac{a}{b}} \]

   3. *-commutative N/A

      \[\leadsto 2 \cdot \color{blue}{\left(\cos y \cdot \sqrt{x}\right)} + \frac{-1}{3} \cdot \frac{a}{b} \]

   4. associate-*r* N/A

      \[\leadsto \color{blue}{\left(2 \cdot \cos y\right) \cdot \sqrt{x}} + \frac{-1}{3} \cdot \frac{a}{b} \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, \frac{-1}{3} \cdot \frac{a}{b}\right)} \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \cos y}, \sqrt{x}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   7. lower-cos.f64 N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\cos y}, \sqrt{x}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   8. lower-sqrt.f64 N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \color{blue}{\sqrt{x}}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}}\right) \]

   10. lower-/.f64 77.0

       \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}}\right) \]

5. Applied rewrites 77.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]
6. Add Preprocessing

Alternative 11: 65.3% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) 1.0) (/ (/ a 3.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * 1.0) - ((a / 3.0) / b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * 1.0d0) - ((a / 3.0d0) / b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * 1.0) - ((a / 3.0) / b);
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * 1.0) - ((a / 3.0) / b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * 1.0) - Float64(Float64(a / 3.0) / b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * 1.0) - ((a / 3.0) / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{b \cdot 3}} \]

   3. *-commutative N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{\color{blue}{3 \cdot b}} \]

   4. associate-/r* N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   5. lower-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

   6. lower-/.f64 77.1

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{a}{3}}}{b} \]

7. Applied rewrites 77.1%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{3}}{b}} \]

8. Taylor expanded in y around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
9. Step-by-step derivation

10. Applied rewrites 69.8%

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{\frac{a}{3}}{b} \]
11. Add Preprocessing

Alternative 12: 65.3% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) 1.0) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * 1.0) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * 1.0d0) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * 1.0) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * 1.0) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * 1.0) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * 1.0) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 1.0), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

6. Taylor expanded in y around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{a}{b \cdot 3} \]
7. Step-by-step derivation

8. Applied rewrites 69.7%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot 1 - \frac{a}{b \cdot 3} \]
9. Add Preprocessing

Alternative 13: 65.2% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-0.3333333333333333, \frac{a}{b}, \sqrt{x} \cdot 2\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma -0.3333333333333333 (/ a b) (* (sqrt x) 2.0)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(-0.3333333333333333, (a / b), (sqrt(x) * 2.0));
}

Julia

function code(x, y, z, t, a, b)
	return fma(-0.3333333333333333, Float64(a / b), Float64(sqrt(x) * 2.0))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision] + N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{\left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. fp-cancel-sub-sign-inv N/A

      \[\leadsto \color{blue}{\left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

   2. metadata-eval N/A

      \[\leadsto \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) + \color{blue}{\frac{-1}{3}} \cdot \frac{a}{b} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b} + \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right)} \]

   4. associate-*r/ N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{3} \cdot a}{b}} + \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   5. associate-*l/ N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{3}}{b} \cdot a} + \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \frac{\color{blue}{\frac{-1}{3} \cdot 1}}{b} \cdot a + \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   7. associate-*r/ N/A

      \[\leadsto \color{blue}{\left(\frac{-1}{3} \cdot \frac{1}{b}\right)} \cdot a + \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   8. metadata-eval N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right)} \cdot \frac{1}{b}\right) \cdot a + \left(\frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   9. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{1}{b}, a, \frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right)} \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{3}} \cdot \frac{1}{b}, a, \frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   11. associate-*r/ N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{-1}{3} \cdot 1}{b}}, a, \frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   12. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{3}}}{b}, a, \frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

   13. lower-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{-1}{3}}{b}}, a, \frac{2}{3} \cdot \left(\left(t \cdot \left(z \cdot \sin y\right)\right) \cdot \sqrt{x}\right) + 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right) \]

5. Applied rewrites 60.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-0.3333333333333333}{b}, a, \sqrt{x} \cdot \mathsf{fma}\left(0.6666666666666666 \cdot \left(\sin y \cdot z\right), t, \cos y \cdot 2\right)\right)} \]

6. Taylor expanded in y around 0

   \[\leadsto \frac{-1}{3} \cdot \frac{a}{b} + \color{blue}{2 \cdot \sqrt{x}} \]
7. Step-by-step derivation

8. Applied rewrites 69.7%

   \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \color{blue}{\frac{a}{b}}, \sqrt{x} \cdot 2\right) \]
9. Add Preprocessing

Alternative 14: 50.5% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (-0.3333333333333333d0) * (a / b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Python

def code(x, y, z, t, a, b):
	return -0.3333333333333333 * (a / b)

Julia

function code(x, y, z, t, a, b)
	return Float64(-0.3333333333333333 * Float64(a / b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.3%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

   2. lower-/.f64 53.8

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

5. Applied rewrites 53.8%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Add Preprocessing

Developer Target 1: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t\_3 \cdot \cos \left(\frac{1}{y} - t\_1\right) - t\_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t\_1\right) \cdot t\_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ 0.3333333333333333 z) t))
        (t_2 (/ (/ a 3.0) b))
        (t_3 (* 2.0 (sqrt x))))
   (if (< z -1.3793337487235141e+129)
     (- (* t_3 (cos (- (/ 1.0 y) t_1))) t_2)
     (if (< z 3.516290613555987e+106)
       (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) t_2)
       (- (* (cos (- y t_1)) t_3) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (0.3333333333333333d0 / z) / t
    t_2 = (a / 3.0d0) / b
    t_3 = 2.0d0 * sqrt(x)
    if (z < (-1.3793337487235141d+129)) then
        tmp = (t_3 * cos(((1.0d0 / y) - t_1))) - t_2
    else if (z < 3.516290613555987d+106) then
        tmp = ((sqrt(x) * 2.0d0) * cos((y - ((t / 3.0d0) * z)))) - t_2
    else
        tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * Math.cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((Math.sqrt(x) * 2.0) * Math.cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (Math.cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.3333333333333333 / z) / t
	t_2 = (a / 3.0) / b
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if z < -1.3793337487235141e+129:
		tmp = (t_3 * math.cos(((1.0 / y) - t_1))) - t_2
	elif z < 3.516290613555987e+106:
		tmp = ((math.sqrt(x) * 2.0) * math.cos((y - ((t / 3.0) * z)))) - t_2
	else:
		tmp = (math.cos((y - t_1)) * t_3) - ((a / b) / 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.3333333333333333 / z) / t)
	t_2 = Float64(Float64(a / 3.0) / b)
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (z < -1.3793337487235141e+129)
		tmp = Float64(Float64(t_3 * cos(Float64(Float64(1.0 / y) - t_1))) - t_2);
	elseif (z < 3.516290613555987e+106)
		tmp = Float64(Float64(Float64(sqrt(x) * 2.0) * cos(Float64(y - Float64(Float64(t / 3.0) * z)))) - t_2);
	else
		tmp = Float64(Float64(cos(Float64(y - t_1)) * t_3) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.3333333333333333 / z) / t;
	t_2 = (a / 3.0) / b;
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (z < -1.3793337487235141e+129)
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	elseif (z < 3.516290613555987e+106)
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	else
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.3333333333333333 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.3793337487235141e+129], N[(N[(t$95$3 * N[Cos[N[(N[(1.0 / y), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[z, 3.516290613555987e+106], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(y - N[(N[(t / 3.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))