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

Percentage Accurate: 70.5% → 78.3%

Time: 19.7s

Alternatives: 6

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: 70.5% 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: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot -0.3333333333333333\right)\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9999999999999993:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x} \cdot \left(\cos t\_1 \cdot \cos y - \sin t\_1 \cdot \sin y\right), a \cdot \frac{-0.3333333333333333}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right) - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* t -0.3333333333333333))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.9999999999999993)
     (fma
      2.0
      (* (sqrt x) (- (* (cos t_1) (cos y)) (* (sin t_1) (sin y))))
      (* a (/ -0.3333333333333333 b)))
     (- (* (sqrt x) (* 2.0 (cos y))) (/ (/ a 3.0) 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))) <= 0.9999999999999993) {
		tmp = fma(2.0, (sqrt(x) * ((cos(t_1) * cos(y)) - (sin(t_1) * sin(y)))), (a * (-0.3333333333333333 / b)));
	} else {
		tmp = (sqrt(x) * (2.0 * cos(y))) - ((a / 3.0) / b);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t * -0.3333333333333333))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.9999999999999993)
		tmp = fma(2.0, Float64(sqrt(x) * Float64(Float64(cos(t_1) * cos(y)) - Float64(sin(t_1) * sin(y)))), Float64(a * Float64(-0.3333333333333333 / b)));
	else
		tmp = Float64(Float64(sqrt(x) * Float64(2.0 * cos(y))) - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.9999999999999993], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3.0), $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)))) < 0.99999999999999933

   1. Initial program 69.8%

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

   3. Simplified 69.7%

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

      1. fma-undefine 69.7%

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

      2. cos-sum 72.2%

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

   6. Applied egg-rr 72.2%

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

   if 0.99999999999999933 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

      3. *-commutative 65.6%

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

      4. *-commutative 65.6%

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

      5. associate-/l* 65.6%

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

      6. *-commutative 65.6%

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

   3. Simplified 65.6%

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

      1. add-sqr-sqrt 31.2%

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

      2. sqrt-unprod 64.5%

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

      3. div-inv 64.5%

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

      4. metadata-eval 64.5%

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

      5. metadata-eval 64.5%

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

      6. div-inv 64.5%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \sqrt{\left(t \cdot \left(--0.3333333333333333\right)\right) \cdot \color{blue}{\left(t \cdot \frac{1}{3}\right)}}\right) - \frac{a}{3 \cdot b} \]

      7. metadata-eval 64.5%

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

      8. metadata-eval 64.5%

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

      9. swap-sqr 64.5%

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

      10. metadata-eval 64.5%

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

      11. metadata-eval 64.5%

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

      12. metadata-eval 64.5%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right) - \frac{a}{3 \cdot b} \]

      13. metadata-eval 64.5%

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

      14. swap-sqr 64.5%

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

      15. sqrt-unprod 34.3%

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

      16. add-sqr-sqrt 65.6%

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

      17. add-exp-log 34.3%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \color{blue}{e^{\log \left(t \cdot -0.3333333333333333\right)}}\right) - \frac{a}{3 \cdot b} \]

   6. Applied egg-rr 34.3%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \color{blue}{e^{\log \left(t \cdot -0.3333333333333333\right)}}\right) - \frac{a}{3 \cdot b} \]

   7. Taylor expanded in z around 0 85.0%

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

      1. associate-*r* 85.0%

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

      2. *-commutative 85.0%

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

   9. Simplified 85.0%

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

       1. add-sqr-sqrt 84.6%

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

       2. pow2 84.6%

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

       3. pow1/2 84.6%

          \[\leadsto \left({\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

       4. sqrt-pow1 84.6%

          \[\leadsto \left({\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

       5. metadata-eval 84.6%

          \[\leadsto \left({\left({x}^{\color{blue}{0.25}}\right)}^{2} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

   11. Applied egg-rr 84.6%

       \[\leadsto \left(\color{blue}{{\left({x}^{0.25}\right)}^{2}} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]
   12. Step-by-step derivation

       1. pow-pow 85.0%

          \[\leadsto \left(\color{blue}{{x}^{\left(0.25 \cdot 2\right)}} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

       2. metadata-eval 85.0%

          \[\leadsto \left({x}^{\color{blue}{0.5}} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

       3. pow1/2 85.0%

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

       4. associate-*l* 85.0%

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

       5. fmm-def 85.0%

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

   13. Applied egg-rr 85.0%

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

       1. fmm-undef 85.0%

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

       2. associate-/r* 85.0%

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

   15. Simplified 85.0%

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

Alternative 2: 77.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (sqrt(x) * (2.0 * 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 = (sqrt(x) * (2.0d0 * 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 (Math.sqrt(x) * (2.0 * Math.cos(y))) - ((a / 3.0) / b);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.2%

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

   1. *-commutative 68.2%

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

   2. *-commutative 68.2%

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

   3. *-commutative 68.2%

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

   4. *-commutative 68.2%

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

   5. associate-/l* 68.5%

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

   6. *-commutative 68.5%

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

3. Simplified 68.5%

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

   1. add-sqr-sqrt 35.3%

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

   2. sqrt-unprod 57.7%

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

   3. div-inv 57.6%

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

   4. metadata-eval 57.6%

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

   5. metadata-eval 57.6%

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

   6. div-inv 57.5%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \sqrt{\left(t \cdot \left(--0.3333333333333333\right)\right) \cdot \color{blue}{\left(t \cdot \frac{1}{3}\right)}}\right) - \frac{a}{3 \cdot b} \]

   7. metadata-eval 57.5%

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

   8. metadata-eval 57.5%

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

   9. swap-sqr 57.6%

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

   10. metadata-eval 57.6%

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

   11. metadata-eval 57.6%

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

   12. metadata-eval 57.6%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right) - \frac{a}{3 \cdot b} \]

   13. metadata-eval 57.6%

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

   14. swap-sqr 57.5%

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

   15. sqrt-unprod 33.0%

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

   16. add-sqr-sqrt 68.2%

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

   17. add-exp-log 33.3%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \color{blue}{e^{\log \left(t \cdot -0.3333333333333333\right)}}\right) - \frac{a}{3 \cdot b} \]

6. Applied egg-rr 33.3%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \color{blue}{e^{\log \left(t \cdot -0.3333333333333333\right)}}\right) - \frac{a}{3 \cdot b} \]

7. Taylor expanded in z around 0 75.1%

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

   1. associate-*r* 75.1%

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

   2. *-commutative 75.1%

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

9. Simplified 75.1%

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

    1. add-sqr-sqrt 75.0%

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

    2. pow2 75.0%

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

    3. pow1/2 75.0%

       \[\leadsto \left({\left(\sqrt{\color{blue}{{x}^{0.5}}}\right)}^{2} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

    4. sqrt-pow1 75.0%

       \[\leadsto \left({\color{blue}{\left({x}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

    5. metadata-eval 75.0%

       \[\leadsto \left({\left({x}^{\color{blue}{0.25}}\right)}^{2} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

11. Applied egg-rr 75.0%

    \[\leadsto \left(\color{blue}{{\left({x}^{0.25}\right)}^{2}} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]
12. Step-by-step derivation

    1. pow-pow 75.1%

       \[\leadsto \left(\color{blue}{{x}^{\left(0.25 \cdot 2\right)}} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

    2. metadata-eval 75.1%

       \[\leadsto \left({x}^{\color{blue}{0.5}} \cdot 2\right) \cdot \cos y - \frac{a}{3 \cdot b} \]

    3. pow1/2 75.1%

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

    4. associate-*l* 75.1%

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

    5. fmm-def 75.1%

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

13. Applied egg-rr 75.1%

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

    1. fmm-undef 75.1%

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

    2. associate-/r* 75.2%

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

15. Simplified 75.2%

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

Alternative 3: 77.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) + (2.0d0 * (sqrt(x) * cos(y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.2%

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

3. Simplified 68.1%

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

5. Taylor expanded in z around 0 75.2%

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

Alternative 4: 66.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \cdot \frac{a}{b} + 2 \cdot \sqrt{x} \end{array} \]

FPCore

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

C

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

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)) + (2.0d0 * sqrt(x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.2%

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

3. Simplified 68.1%

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

5. Taylor expanded in z around 0 75.2%

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

6. Taylor expanded in y around 0 66.4%

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

   1. *-commutative 66.4%

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

8. Simplified 66.4%

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

9. Final simplification 66.4%

   \[\leadsto -0.3333333333333333 \cdot \frac{a}{b} + 2 \cdot \sqrt{x} \]
10. Add Preprocessing

Alternative 5: 51.5% accurate, 43.4× speedup

Math

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

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(Float64(-0.3333333333333333 * 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[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 68.2%

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

3. Simplified 68.1%

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

5. Taylor expanded in a around inf 48.2%

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

   1. associate-*r/ 48.2%

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

7. Applied egg-rr 48.2%

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

Alternative 6: 51.4% 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 68.2%

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

3. Simplified 68.1%

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

5. Taylor expanded in a around inf 48.2%

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

Developer Target 1: 75.0% 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 2024187 
(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))))