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

Percentage Accurate: 91.2% → 92.6%

Time: 9.1s

Alternatives: 11

Speedup: 0.6×

• 29.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+180)
   (/ (* y (/ x a)) 2.0)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = (y * (x / a)) / 2.0;
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+180)
		tmp = Float64(Float64(y * Float64(x / a)) / 2.0);
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+180], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999996e180

   1. Initial program 73.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 99.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 99.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 99.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 77.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(0.5 \cdot y\right)}{a}} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]

      3. *-commutative 99.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\left(y \cdot 0.5\right)} \]

      4. metadata-eval 99.9%

         \[\leadsto \frac{x}{a} \cdot \left(y \cdot \color{blue}{\frac{1}{2}}\right) \]

      5. div-inv 99.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{y}{2}} \]

      6. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   if -4.9999999999999996e180 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. div-sub 91.7%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      2. *-commutative 91.7%

         \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 93.9%

         \[\leadsto \color{blue}{\frac{y \cdot x - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. cancel-sign-sub-inv 93.9%

         \[\leadsto \frac{\color{blue}{y \cdot x + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      5. *-commutative 93.9%

         \[\leadsto \frac{\color{blue}{x \cdot y} + \left(-z \cdot 9\right) \cdot t}{a \cdot 2} \]

      6. fma-define 94.4%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      7. distribute-rgt-neg-in 94.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      8. associate-*r* 94.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      9. distribute-lft-neg-in 94.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      10. *-commutative 94.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      11. distribute-rgt-neg-in 94.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      12. metadata-eval 94.4%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{\left(z \cdot t\right) \cdot -4.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-41)
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 1e-30)
     (/ (* (* z t) -4.5) a)
     (if (<= (* x y) 5e+123) (/ (* x y) (* a 2.0)) (* x (/ (* y 0.5) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = ((z * t) * -4.5) / a;
	} else if ((x * y) <= 5e+123) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-2d-41)) then
        tmp = x / (a * (2.0d0 / y))
    else if ((x * y) <= 1d-30) then
        tmp = ((z * t) * (-4.5d0)) / a
    else if ((x * y) <= 5d+123) then
        tmp = (x * y) / (a * 2.0d0)
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = ((z * t) * -4.5) / a;
	} else if ((x * y) <= 5e+123) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = x / (a * (2.0 / y))
	elif (x * y) <= 1e-30:
		tmp = ((z * t) * -4.5) / a
	elif (x * y) <= 5e+123:
		tmp = (x * y) / (a * 2.0)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(Float64(Float64(z * t) * -4.5) / a);
	elseif (Float64(x * y) <= 5e+123)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = x / (a * (2.0 / y));
	elseif ((x * y) <= 1e-30)
		tmp = ((z * t) * -4.5) / a;
	elseif ((x * y) <= 5e+123)
		tmp = (x * y) / (a * 2.0);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(N[(N[(z * t), $MachinePrecision] * -4.5), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+123], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 87.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 74.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 74.3%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{0.5 \cdot y}}} \]

      2. un-div-inv 74.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{0.5 \cdot y}}} \]

      3. *-commutative 74.9%

         \[\leadsto \frac{x}{\frac{a}{\color{blue}{y \cdot 0.5}}} \]

   7. Applied egg-rr 74.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} \]
   8. Step-by-step derivation

      1. clear-num 74.2%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{y \cdot 0.5}{a}}}} \]

      2. *-commutative 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{0.5 \cdot y}}{a}}} \]

      3. metadata-eval 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{2}} \cdot y}{a}}} \]

      4. associate-/r/ 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{\frac{2}{y}}}}{a}}} \]

      5. associate-/l/ 74.3%

         \[\leadsto \frac{x}{\frac{1}{\color{blue}{\frac{1}{a \cdot \frac{2}{y}}}}} \]

      6. remove-double-div 74.9%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \frac{2}{y}}} \]

      7. *-commutative 74.9%

         \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   9. Applied egg-rr 74.9%

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 79.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 79.3%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 84.6%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t \cdot z}{a}} \]

      2. *-commutative 84.6%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} \]

      3. associate-*l/ 84.6%

         \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} \]

   7. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} \]

   if 1e-30 < (*.f64 x y) < 4.99999999999999974e123

   1. Initial program 93.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if 4.99999999999999974e123 < (*.f64 x y)

   1. Initial program 81.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 79.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 79.1%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 79.1%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 79.1%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{\left(z \cdot t\right) \cdot -4.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-41)
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 1e-30)
     (* -4.5 (/ (* z t) a))
     (if (<= (* x y) 5e+123) (/ (* x y) (* a 2.0)) (* x (/ (* y 0.5) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+123) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-2d-41)) then
        tmp = x / (a * (2.0d0 / y))
    else if ((x * y) <= 1d-30) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d+123) then
        tmp = (x * y) / (a * 2.0d0)
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+123) {
		tmp = (x * y) / (a * 2.0);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = x / (a * (2.0 / y))
	elif (x * y) <= 1e-30:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e+123:
		tmp = (x * y) / (a * 2.0)
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e+123)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = x / (a * (2.0 / y));
	elseif ((x * y) <= 1e-30)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e+123)
		tmp = (x * y) / (a * 2.0);
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+123], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 87.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 74.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 74.3%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{0.5 \cdot y}}} \]

      2. un-div-inv 74.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{0.5 \cdot y}}} \]

      3. *-commutative 74.9%

         \[\leadsto \frac{x}{\frac{a}{\color{blue}{y \cdot 0.5}}} \]

   7. Applied egg-rr 74.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} \]
   8. Step-by-step derivation

      1. clear-num 74.2%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{y \cdot 0.5}{a}}}} \]

      2. *-commutative 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{0.5 \cdot y}}{a}}} \]

      3. metadata-eval 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{2}} \cdot y}{a}}} \]

      4. associate-/r/ 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{\frac{2}{y}}}}{a}}} \]

      5. associate-/l/ 74.3%

         \[\leadsto \frac{x}{\frac{1}{\color{blue}{\frac{1}{a \cdot \frac{2}{y}}}}} \]

      6. remove-double-div 74.9%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \frac{2}{y}}} \]

      7. *-commutative 74.9%

         \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   9. Applied egg-rr 74.9%

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 1e-30 < (*.f64 x y) < 4.99999999999999974e123

   1. Initial program 93.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.0%

      \[\leadsto \frac{\color{blue}{x \cdot y}}{a \cdot 2} \]

   if 4.99999999999999974e123 < (*.f64 x y)

   1. Initial program 81.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 79.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 79.1%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 79.1%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 79.1%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-41)
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 1e-30)
     (* -4.5 (/ (* z t) a))
     (if (<= (* x y) 5e+123) (/ 0.5 (/ a (* x y))) (* x (/ (* y 0.5) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+123) {
		tmp = 0.5 / (a / (x * y));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-2d-41)) then
        tmp = x / (a * (2.0d0 / y))
    else if ((x * y) <= 1d-30) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d+123) then
        tmp = 0.5d0 / (a / (x * y))
    else
        tmp = x * ((y * 0.5d0) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+123) {
		tmp = 0.5 / (a / (x * y));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = x / (a * (2.0 / y))
	elif (x * y) <= 1e-30:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e+123:
		tmp = 0.5 / (a / (x * y))
	else:
		tmp = x * ((y * 0.5) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e+123)
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = x / (a * (2.0 / y));
	elseif ((x * y) <= 1e-30)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e+123)
		tmp = 0.5 / (a / (x * y));
	else
		tmp = x * ((y * 0.5) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+123], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 87.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 74.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 74.3%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{0.5 \cdot y}}} \]

      2. un-div-inv 74.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{0.5 \cdot y}}} \]

      3. *-commutative 74.9%

         \[\leadsto \frac{x}{\frac{a}{\color{blue}{y \cdot 0.5}}} \]

   7. Applied egg-rr 74.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} \]
   8. Step-by-step derivation

      1. clear-num 74.2%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{y \cdot 0.5}{a}}}} \]

      2. *-commutative 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{0.5 \cdot y}}{a}}} \]

      3. metadata-eval 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{2}} \cdot y}{a}}} \]

      4. associate-/r/ 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{\frac{2}{y}}}}{a}}} \]

      5. associate-/l/ 74.3%

         \[\leadsto \frac{x}{\frac{1}{\color{blue}{\frac{1}{a \cdot \frac{2}{y}}}}} \]

      6. remove-double-div 74.9%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \frac{2}{y}}} \]

      7. *-commutative 74.9%

         \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   9. Applied egg-rr 74.9%

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 1e-30 < (*.f64 x y) < 4.99999999999999974e123

   1. Initial program 93.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 93.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 93.4%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 93.4%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 93.4%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 93.4%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 93.4%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 93.4%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

   6. Simplified 93.4%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 57.9%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]

   if 4.99999999999999974e123 < (*.f64 x y)

   1. Initial program 81.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 73.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 73.8%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 79.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 79.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 79.1%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 79.1%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 79.1%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* y 0.5) a))))
   (if (<= (* x y) -2e-41)
     t_1
     (if (<= (* x y) 1e-30)
       (* -4.5 (/ (* z t) a))
       (if (<= (* x y) 5e+123) (/ 0.5 (/ a (* x y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = t_1;
	} else if ((x * y) <= 1e-30) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+123) {
		tmp = 0.5 / (a / (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * 0.5d0) / a)
    if ((x * y) <= (-2d-41)) then
        tmp = t_1
    else if ((x * y) <= 1d-30) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 5d+123) then
        tmp = 0.5d0 / (a / (x * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y * 0.5) / a);
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = t_1;
	} else if ((x * y) <= 1e-30) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 5e+123) {
		tmp = 0.5 / (a / (x * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y * 0.5) / a)
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = t_1
	elif (x * y) <= 1e-30:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 5e+123:
		tmp = 0.5 / (a / (x * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 5e+123)
		tmp = Float64(0.5 / Float64(a / Float64(x * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y * 0.5) / a);
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = t_1;
	elseif ((x * y) <= 1e-30)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 5e+123)
		tmp = 0.5 / (a / (x * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+123], N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41 or 4.99999999999999974e123 < (*.f64 x y)

   1. Initial program 85.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 76.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 76.2%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 76.2%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 76.2%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 1e-30 < (*.f64 x y) < 4.99999999999999974e123

   1. Initial program 93.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 93.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 93.4%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 93.4%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 93.4%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 93.4%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 93.4%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 93.4%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 93.4%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

   6. Simplified 93.4%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

   7. Taylor expanded in x around inf 57.9%

      \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+123}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{\left(z \cdot t\right) \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-41)
   (/ x (* a (/ 2.0 y)))
   (if (<= (* x y) 1e-30) (/ (* (* z t) -4.5) a) (/ (* y (/ x a)) 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = ((z * t) * -4.5) / a;
	} else {
		tmp = (y * (x / a)) / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-2d-41)) then
        tmp = x / (a * (2.0d0 / y))
    else if ((x * y) <= 1d-30) then
        tmp = ((z * t) * (-4.5d0)) / a
    else
        tmp = (y * (x / a)) / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-41) {
		tmp = x / (a * (2.0 / y));
	} else if ((x * y) <= 1e-30) {
		tmp = ((z * t) * -4.5) / a;
	} else {
		tmp = (y * (x / a)) / 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-41:
		tmp = x / (a * (2.0 / y))
	elif (x * y) <= 1e-30:
		tmp = ((z * t) * -4.5) / a
	else:
		tmp = (y * (x / a)) / 2.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-41)
		tmp = Float64(x / Float64(a * Float64(2.0 / y)));
	elseif (Float64(x * y) <= 1e-30)
		tmp = Float64(Float64(Float64(z * t) * -4.5) / a);
	else
		tmp = Float64(Float64(y * Float64(x / a)) / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-41)
		tmp = x / (a * (2.0 / y));
	elseif ((x * y) <= 1e-30)
		tmp = ((z * t) * -4.5) / a;
	else
		tmp = (y * (x / a)) / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-41], N[(x / N[(a * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-30], N[(N[(N[(z * t), $MachinePrecision] * -4.5), $MachinePrecision] / a), $MachinePrecision], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000001e-41

   1. Initial program 87.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 74.3%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 74.3%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. clear-num 74.3%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{a}{0.5 \cdot y}}} \]

      2. un-div-inv 74.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{0.5 \cdot y}}} \]

      3. *-commutative 74.9%

         \[\leadsto \frac{x}{\frac{a}{\color{blue}{y \cdot 0.5}}} \]

   7. Applied egg-rr 74.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y \cdot 0.5}}} \]
   8. Step-by-step derivation

      1. clear-num 74.2%

         \[\leadsto \frac{x}{\color{blue}{\frac{1}{\frac{y \cdot 0.5}{a}}}} \]

      2. *-commutative 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{0.5 \cdot y}}{a}}} \]

      3. metadata-eval 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{2}} \cdot y}{a}}} \]

      4. associate-/r/ 74.2%

         \[\leadsto \frac{x}{\frac{1}{\frac{\color{blue}{\frac{1}{\frac{2}{y}}}}{a}}} \]

      5. associate-/l/ 74.3%

         \[\leadsto \frac{x}{\frac{1}{\color{blue}{\frac{1}{a \cdot \frac{2}{y}}}}} \]

      6. remove-double-div 74.9%

         \[\leadsto \frac{x}{\color{blue}{a \cdot \frac{2}{y}}} \]

      7. *-commutative 74.9%

         \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   9. Applied egg-rr 74.9%

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{y} \cdot a}} \]

   if -2.00000000000000001e-41 < (*.f64 x y) < 1e-30

   1. Initial program 98.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 79.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 79.3%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
   6. Step-by-step derivation

      1. associate-*r/ 84.6%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t \cdot z}{a}} \]

      2. *-commutative 84.6%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} \]

      3. associate-*l/ 84.6%

         \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} \]

   7. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} \]

   if 1e-30 < (*.f64 x y)

   1. Initial program 86.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 65.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 65.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 65.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 65.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 65.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 67.4%

         \[\leadsto \color{blue}{\frac{x \cdot \left(0.5 \cdot y\right)}{a}} \]

      2. associate-*l/ 68.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]

      3. *-commutative 68.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\left(y \cdot 0.5\right)} \]

      4. metadata-eval 68.9%

         \[\leadsto \frac{x}{a} \cdot \left(y \cdot \color{blue}{\frac{1}{2}}\right) \]

      5. div-inv 68.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{y}{2}} \]

      6. associate-*r/ 68.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   7. Applied egg-rr 68.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{a \cdot \frac{2}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-30}:\\ \;\;\;\;\frac{\left(z \cdot t\right) \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+180)
   (/ (* y (/ x a)) 2.0)
   (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = (y * (x / a)) / 2.0;
	} else {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-5d+180)) then
        tmp = (y * (x / a)) / 2.0d0
    else
        tmp = ((x * y) - (t * (z * 9.0d0))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = (y * (x / a)) / 2.0;
	} else {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+180:
		tmp = (y * (x / a)) / 2.0
	else:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+180)
		tmp = Float64(Float64(y * Float64(x / a)) / 2.0);
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+180)
		tmp = (y * (x / a)) / 2.0;
	else
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+180], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999996e180

   1. Initial program 73.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 99.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 99.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 99.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 77.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(0.5 \cdot y\right)}{a}} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]

      3. *-commutative 99.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\left(y \cdot 0.5\right)} \]

      4. metadata-eval 99.9%

         \[\leadsto \frac{x}{a} \cdot \left(y \cdot \color{blue}{\frac{1}{2}}\right) \]

      5. div-inv 99.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{y}{2}} \]

      6. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   if -4.9999999999999996e180 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + t \cdot \left(z \cdot -9\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+180)
   (/ (* y (/ x a)) 2.0)
   (/ 0.5 (/ a (+ (* x y) (* t (* z -9.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = (y * (x / a)) / 2.0;
	} else {
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-5d+180)) then
        tmp = (y * (x / a)) / 2.0d0
    else
        tmp = 0.5d0 / (a / ((x * y) + (t * (z * (-9.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+180) {
		tmp = (y * (x / a)) / 2.0;
	} else {
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+180:
		tmp = (y * (x / a)) / 2.0
	else:
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+180)
		tmp = Float64(Float64(y * Float64(x / a)) / 2.0);
	else
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) + Float64(t * Float64(z * -9.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+180)
		tmp = (y * (x / a)) / 2.0;
	else
		tmp = 0.5 / (a / ((x * y) + (t * (z * -9.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+180], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.9999999999999996e180

   1. Initial program 73.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 99.7%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 99.7%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 99.7%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 77.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(0.5 \cdot y\right)}{a}} \]

      2. associate-*l/ 99.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]

      3. *-commutative 99.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\left(y \cdot 0.5\right)} \]

      4. metadata-eval 99.9%

         \[\leadsto \frac{x}{a} \cdot \left(y \cdot \color{blue}{\frac{1}{2}}\right) \]

      5. div-inv 99.9%

         \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{y}{2}} \]

      6. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot y}{2}} \]

   if -4.9999999999999996e180 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 93.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}}} \]

      2. inv-pow 93.2%

         \[\leadsto \color{blue}{{\left(\frac{a \cdot 2}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1}} \]

      3. *-commutative 93.2%

         \[\leadsto {\left(\frac{\color{blue}{2 \cdot a}}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}^{-1} \]

      4. associate-/l* 93.2%

         \[\leadsto {\color{blue}{\left(2 \cdot \frac{a}{x \cdot y - \left(z \cdot 9\right) \cdot t}\right)}}^{-1} \]

      5. fma-neg 93.6%

         \[\leadsto {\left(2 \cdot \frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}\right)}^{-1} \]

      6. *-commutative 93.6%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, -\color{blue}{t \cdot \left(z \cdot 9\right)}\right)}\right)}^{-1} \]

      7. distribute-rgt-neg-in 93.6%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right)}\right)}^{-1} \]

      8. distribute-rgt-neg-in 93.6%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right)}\right)}^{-1} \]

      9. metadata-eval 93.6%

         \[\leadsto {\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right)}\right)}^{-1} \]

   4. Applied egg-rr 93.6%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 93.6%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      2. associate-/r* 93.6%

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]

      3. metadata-eval 93.6%

         \[\leadsto \frac{\color{blue}{0.5}}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}} \]

   6. Simplified 93.6%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}}} \]
   7. Step-by-step derivation

      1. fma-undefine 93.2%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + t \cdot \left(z \cdot -9\right)}}} \]

   8. Applied egg-rr 93.2%

      \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + t \cdot \left(z \cdot -9\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+180}:\\ \;\;\;\;\frac{y \cdot \frac{x}{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + t \cdot \left(z \cdot -9\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+82} \lor \neg \left(x \leq 2.1 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.35e+82) (not (<= x 2.1e-59)))
   (* x (/ (* y 0.5) a))
   (* -4.5 (/ (* z t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.35e+82) || !(x <= 2.1e-59)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x <= (-1.35d+82)) .or. (.not. (x <= 2.1d-59))) then
        tmp = x * ((y * 0.5d0) / a)
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.35e+82) || !(x <= 2.1e-59)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.35e+82) or not (x <= 2.1e-59):
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.35e+82) || !(x <= 2.1e-59))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.35e+82) || ~((x <= 2.1e-59)))
		tmp = x * ((y * 0.5) / a);
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.35e+82], N[Not[LessEqual[x, 2.1e-59]], $MachinePrecision]], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35e82 or 2.09999999999999997e-59 < x

   1. Initial program 83.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} \cdot 0.5} \]

      2. associate-/l* 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \frac{y}{a}\right)} \cdot 0.5 \]

      3. associate-*r* 69.1%

         \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]

      4. *-commutative 69.1%

         \[\leadsto x \cdot \color{blue}{\left(0.5 \cdot \frac{y}{a}\right)} \]

      5. associate-*r/ 69.1%

         \[\leadsto x \cdot \color{blue}{\frac{0.5 \cdot y}{a}} \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{x \cdot \frac{0.5 \cdot y}{a}} \]

   if -1.35e82 < x < 2.09999999999999997e-59

   1. Initial program 99.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+82} \lor \neg \left(x \leq 2.1 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{+42}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a 2.6e+42) (* -4.5 (/ (* z t) a)) (* -4.5 (* t (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.6e+42) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= 2.6d+42) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 2.6e+42) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= 2.6e+42:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 2.6e+42)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 2.6e+42)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, 2.6e+42], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.5999999999999999e42

   1. Initial program 94.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 50.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 2.5999999999999999e42 < a

   1. Initial program 79.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 50.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* 56.1%

         \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

   5. Simplified 56.1%

      \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{+42}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = (-4.5d0) * (t * (z / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

def code(x, y, z, t, a):
	return -4.5 * (t * (z / a))

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t * Float64(z / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.6%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 50.2%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
4. Step-by-step derivation

   1. associate-/l* 49.5%

      \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

5. Simplified 49.5%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]
6. Add Preprocessing

Developer Target 1: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))