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

Percentage Accurate: 70.6% → 78.2%

Time: 37.4s

Alternatives: 10

Speedup: 1.0×

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: 70.6% 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: 78.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

      2. *-commutative 80.0%

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

      3. associate-/l* 79.8%

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

      4. *-commutative 79.8%

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

   3. Simplified 79.8%

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

   6. Applied egg-rr 80.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\left(z \cdot -0.3333333333333333\right) \cdot t\right) + \left(-\sin y \cdot \sin \left(\left(z \cdot -0.3333333333333333\right) \cdot t\right)\right)\right)} - \frac{a}{3 \cdot b} \]
   7. Step-by-step derivation

      1. fma-define 80.3%

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

      2. *-commutative 80.3%

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

      3. *-commutative 80.3%

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

      4. associate-*l* 80.0%

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

      5. *-commutative 80.0%

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

      6. associate-*r* 80.5%

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

      7. metadata-eval 80.5%

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

      8. distribute-lft-neg-in 80.5%

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

      9. cos-neg 80.5%

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

      10. distribute-rgt-neg-in 80.5%

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

      11. *-commutative 80.5%

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

      12. *-commutative 80.5%

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

      13. associate-*l* 80.3%

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

      14. *-commutative 80.3%

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

      15. associate-*r* 80.4%

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

      16. metadata-eval 80.4%

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

      17. distribute-lft-neg-in 80.4%

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

      18. sin-neg 80.4%

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

      19. remove-double-neg 80.4%

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

   8. Simplified 80.4%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. associate-*l* 0.0%

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

      2. fma-neg 0.0%

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

      3. *-commutative 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

      6. distribute-neg-frac2 0.0%

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

      7. metadata-eval 0.0%

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

      8. distribute-frac-neg 0.0%

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

      9. neg-mul-1 0.0%

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

      10. *-commutative 0.0%

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

      11. times-frac 0.0%

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

      12. metadata-eval 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around 0 67.1%

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

   6. Taylor expanded in y around 0 67.7%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b} + 2 \cdot \sqrt{x}} \]
   7. Step-by-step derivation

      1. +-commutative 67.7%

         \[\leadsto \color{blue}{2 \cdot \sqrt{x} + -0.3333333333333333 \cdot \frac{a}{b}} \]

      2. *-commutative 67.7%

         \[\leadsto \color{blue}{\sqrt{x} \cdot 2} + -0.3333333333333333 \cdot \frac{a}{b} \]

      3. fma-define 67.7%

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

      4. associate-*r/ 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 79.0%

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

Alternative 2: 77.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. associate-*l* 71.0%

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

   2. fma-neg 71.0%

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

   3. *-commutative 71.0%

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

   4. sub-neg 71.0%

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

   5. *-commutative 71.0%

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

   6. distribute-neg-frac2 71.0%

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

   7. metadata-eval 71.0%

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

   8. distribute-frac-neg 71.0%

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

   9. neg-mul-1 71.0%

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

   10. *-commutative 71.0%

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

   11. times-frac 71.3%

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

   12. metadata-eval 71.3%

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

3. Simplified 71.3%

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

5. Taylor expanded in z around 0 77.7%

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

6. Final simplification 77.7%

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

Alternative 3: 77.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (cos(y) * (2.0 * sqrt(x))) - (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 = (cos(y) * (2.0d0 * sqrt(x))) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. associate-/l* 70.7%

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

   4. *-commutative 70.7%

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

3. Simplified 70.7%

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

5. Taylor expanded in z around 0 77.4%

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

6. Final simplification 77.4%

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

Alternative 4: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (cos(y) * (2.0 * sqrt(x))) + (a * (-0.3333333333333333 / 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 = (cos(y) * (2.0d0 * sqrt(x))) + (a * ((-0.3333333333333333d0) / b))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (Math.cos(y) * (2.0 * Math.sqrt(x))) + (a * (-0.3333333333333333 / b));
}

Python

def code(x, y, z, t, a, b):
	return (math.cos(y) * (2.0 * math.sqrt(x))) + (a * (-0.3333333333333333 / b))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (cos(y) * (2.0 * sqrt(x))) + (a * (-0.3333333333333333 / b));
end

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. associate-/l* 70.7%

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

   4. *-commutative 70.7%

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

3. Simplified 70.7%

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

5. Taylor expanded in z around 0 77.4%

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

   1. *-commutative 77.4%

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

   2. frac-2neg 77.4%

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

   3. div-inv 77.4%

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

   4. distribute-rgt-neg-in 77.4%

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

   5. metadata-eval 77.4%

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

   6. metadata-eval 77.4%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \left(-a\right) \cdot \frac{1}{b \cdot \color{blue}{\frac{1}{-0.3333333333333333}}} \]

   7. div-inv 77.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \left(-a\right) \cdot \frac{1}{\color{blue}{\frac{b}{-0.3333333333333333}}} \]

   8. clear-num 77.7%

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

7. Applied egg-rr 77.7%

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

8. Final simplification 77.7%

   \[\leadsto \cos y \cdot \left(2 \cdot \sqrt{x}\right) + a \cdot \frac{-0.3333333333333333}{b} \]
9. Add Preprocessing

Alternative 5: 65.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. associate-*l* 71.0%

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

   2. fma-neg 71.0%

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

   3. *-commutative 71.0%

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

   4. sub-neg 71.0%

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

   5. *-commutative 71.0%

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

   6. distribute-neg-frac2 71.0%

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

   7. metadata-eval 71.0%

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

   8. distribute-frac-neg 71.0%

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

   9. neg-mul-1 71.0%

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

   10. *-commutative 71.0%

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

   11. times-frac 71.3%

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

   12. metadata-eval 71.3%

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

3. Simplified 71.3%

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

5. Taylor expanded in z around 0 77.7%

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

6. Taylor expanded in y around 0 67.9%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b} + 2 \cdot \sqrt{x}} \]
7. Step-by-step derivation

   1. +-commutative 67.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x} + -0.3333333333333333 \cdot \frac{a}{b}} \]

   2. *-commutative 67.9%

      \[\leadsto \color{blue}{\sqrt{x} \cdot 2} + -0.3333333333333333 \cdot \frac{a}{b} \]

   3. fma-define 67.9%

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

   4. associate-*r/ 68.0%

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

8. Simplified 68.0%

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

9. Final simplification 68.0%

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

Alternative 6: 65.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. associate-/l* 70.7%

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

   4. *-commutative 70.7%

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

3. Simplified 70.7%

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

5. Taylor expanded in z around 0 77.4%

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

6. Taylor expanded in y around 0 67.6%

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

   1. *-commutative 67.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot 2} - \frac{a}{3 \cdot b} \]

8. Simplified 67.6%

   \[\leadsto \color{blue}{\sqrt{x} \cdot 2} - \frac{a}{3 \cdot b} \]

9. Final simplification 67.6%

   \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \]
10. Add Preprocessing

Alternative 7: 50.4% accurate, 43.4× 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 71.0%

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

   1. associate-*l* 71.0%

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

   2. fma-neg 71.0%

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

   3. *-commutative 71.0%

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

   4. sub-neg 71.0%

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

   5. *-commutative 71.0%

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

   6. distribute-neg-frac2 71.0%

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

   7. metadata-eval 71.0%

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

   8. distribute-frac-neg 71.0%

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

   9. neg-mul-1 71.0%

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

   10. *-commutative 71.0%

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

   11. times-frac 71.3%

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

   12. metadata-eval 71.3%

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

3. Simplified 71.3%

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

5. Taylor expanded in z around 0 77.7%

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

6. Taylor expanded in a around inf 52.2%

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

7. Final simplification 52.2%

   \[\leadsto -0.3333333333333333 \cdot \frac{a}{b} \]
8. Add Preprocessing

Alternative 8: 50.4% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

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) / (b / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. associate-*l* 71.0%

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

   2. fma-neg 71.0%

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

   3. *-commutative 71.0%

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

   4. sub-neg 71.0%

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

   5. *-commutative 71.0%

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

   6. distribute-neg-frac2 71.0%

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

   7. metadata-eval 71.0%

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

   8. distribute-frac-neg 71.0%

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

   9. neg-mul-1 71.0%

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

   10. *-commutative 71.0%

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

   11. times-frac 71.3%

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

   12. metadata-eval 71.3%

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

3. Simplified 71.3%

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

5. Taylor expanded in z around 0 77.7%

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

6. Taylor expanded in a around inf 52.2%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
7. Step-by-step derivation

   1. clear-num 52.2%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{b}{a}}} \]

   2. un-div-inv 52.2%

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

8. Applied egg-rr 52.2%

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

9. Final simplification 52.2%

   \[\leadsto \frac{-0.3333333333333333}{\frac{b}{a}} \]
10. Add Preprocessing

Alternative 9: 50.5% accurate, 43.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (a * -0.3333333333333333) / 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 = (a * (-0.3333333333333333d0)) / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. associate-*l* 71.0%

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

   2. fma-neg 71.0%

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

   3. *-commutative 71.0%

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

   4. sub-neg 71.0%

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

   5. *-commutative 71.0%

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

   6. distribute-neg-frac2 71.0%

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

   7. metadata-eval 71.0%

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

   8. distribute-frac-neg 71.0%

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

   9. neg-mul-1 71.0%

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

   10. *-commutative 71.0%

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

   11. times-frac 71.3%

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

   12. metadata-eval 71.3%

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

3. Simplified 71.3%

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

5. Taylor expanded in z around 0 77.7%

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

6. Taylor expanded in a around inf 52.2%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
7. Step-by-step derivation

   1. associate-*r/ 52.3%

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

8. Simplified 52.3%

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

9. Final simplification 52.3%

   \[\leadsto \frac{a \cdot -0.3333333333333333}{b} \]
10. Add Preprocessing

Alternative 10: 50.5% accurate, 43.4× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{a}{-3}}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ a -3.0) b))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (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 = (a / (-3.0d0)) / b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (a / -3.0) / b;
}

Python

def code(x, y, z, t, a, b):
	return (a / -3.0) / b

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. associate-/l* 70.7%

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

   4. *-commutative 70.7%

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

3. Simplified 70.7%

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

5. Taylor expanded in z around 0 77.4%

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

   1. *-commutative 77.4%

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

   2. frac-2neg 77.4%

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

   3. div-inv 77.4%

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

   4. distribute-rgt-neg-in 77.4%

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

   5. metadata-eval 77.4%

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

   6. metadata-eval 77.4%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \left(-a\right) \cdot \frac{1}{b \cdot \color{blue}{\frac{1}{-0.3333333333333333}}} \]

   7. div-inv 77.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \left(-a\right) \cdot \frac{1}{\color{blue}{\frac{b}{-0.3333333333333333}}} \]

   8. clear-num 77.7%

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

7. Applied egg-rr 77.7%

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

8. Taylor expanded in a around inf 52.2%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
9. Step-by-step derivation

   1. *-commutative 52.2%

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

   2. metadata-eval 52.2%

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

   3. times-frac 51.9%

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

   4. *-rgt-identity 51.9%

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

   5. *-commutative 51.9%

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

   6. associate-/r* 52.3%

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

10. Simplified 52.3%

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

11. Final simplification 52.3%

    \[\leadsto \frac{\frac{a}{-3}}{b} \]
12. Add Preprocessing

Developer target: 74.7% accurate, 1.0× 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 2024081 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

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