Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.7% → 97.2%

Time: 8.0s

Alternatives: 14

Speedup: 1.0×

• 63.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\cosh x \cdot \frac{y}{x}}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))

C

double code(double x, double y, double z) {
	return (cosh(x) * (y / x)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (cosh(x) * (y / x)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (Math.cosh(x) * (y / x)) / z;
}

Python

def code(x, y, z):
	return (math.cosh(x) * (y / x)) / z

Julia

function code(x, y, z)
	return Float64(Float64(cosh(x) * Float64(y / x)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (cosh(x) * (y / x)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\cosh x \cdot \frac{y}{x}}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* (cosh x) (/ y x)) z))

C

double code(double x, double y, double z) {
	return (cosh(x) * (y / x)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (cosh(x) * (y / x)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (Math.cosh(x) * (y / x)) / z;
}

Python

def code(x, y, z):
	return (math.cosh(x) * (y / x)) / z

Julia

function code(x, y, z)
	return Float64(Float64(cosh(x) * Float64(y / x)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (cosh(x) * (y / x)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cosh x \cdot \frac{y}{x}\\ \mathbf{if}\;t_0 \leq 4 \cdot 10^{+49}:\\ \;\;\;\;\frac{t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x}{\frac{\cosh x}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cosh x) (/ y x))))
   (if (<= t_0 4e+49) (/ t_0 z) (/ y (/ x (/ (cosh x) z))))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) * (y / x);
	double tmp;
	if (t_0 <= 4e+49) {
		tmp = t_0 / z;
	} else {
		tmp = y / (x / (cosh(x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cosh(x) * (y / x)
    if (t_0 <= 4d+49) then
        tmp = t_0 / z
    else
        tmp = y / (x / (cosh(x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(x) * (y / x);
	double tmp;
	if (t_0 <= 4e+49) {
		tmp = t_0 / z;
	} else {
		tmp = y / (x / (Math.cosh(x) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) * (y / x)
	tmp = 0
	if t_0 <= 4e+49:
		tmp = t_0 / z
	else:
		tmp = y / (x / (math.cosh(x) / z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) * Float64(y / x))
	tmp = 0.0
	if (t_0 <= 4e+49)
		tmp = Float64(t_0 / z);
	else
		tmp = Float64(y / Float64(x / Float64(cosh(x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) * (y / x);
	tmp = 0.0;
	if (t_0 <= 4e+49)
		tmp = t_0 / z;
	else
		tmp = y / (x / (cosh(x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 4e+49], N[(t$95$0 / z), $MachinePrecision], N[(y / N[(x / N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < 3.99999999999999979e49

   1. Initial program 97.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]

   if 3.99999999999999979e49 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 68.4%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 94.2%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 83.5%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 83.5%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 83.5%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 83.5%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 83.5%

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

      1. clear-num 83.5%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{x \cdot z}{\cosh x}}} \]

      2. un-div-inv 83.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{x \cdot z}{\cosh x}}} \]

      3. associate-/l* 99.9%

         \[\leadsto \frac{y}{\color{blue}{\frac{x}{\frac{\cosh x}{z}}}} \]

   5. Applied egg-rr 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq 4 \cdot 10^{+49}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x}{\frac{\cosh x}{z}}}\\ \end{array} \]

Alternative 2: 87.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot z\right)}{z \cdot \frac{z}{x}} \cdot \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.5e+167)
   (* (/ (* y (* x z)) (* z (/ z x))) (/ 0.5 x))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+167) {
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x);
	} else {
		tmp = y * (cosh(x) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-7.5d+167)) then
        tmp = ((y * (x * z)) / (z * (z / x))) * (0.5d0 / x)
    else
        tmp = y * (cosh(x) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.5e+167) {
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x);
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.5e+167:
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x)
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.5e+167)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) / Float64(z * Float64(z / x))) * Float64(0.5 / x));
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.5e+167)
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x);
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.5e+167], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4999999999999995e167

   1. Initial program 50.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 50.0%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 50.0%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 50.0%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 50.0%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 45.5%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 45.5%

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

      2. associate-/l* 39.0%

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

      3. *-commutative 39.0%

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

      4. associate-/r* 39.0%

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

   6. Simplified 39.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 39.0%

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

      2. +-commutative 39.0%

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

      3. associate-*r/ 39.0%

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

      4. frac-add 40.4%

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

      5. *-commutative 40.4%

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

      6. *-commutative 40.4%

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

   8. Applied egg-rr 40.4%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 40.4%

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

      2. associate-*r* 40.4%

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

      3. *-commutative 40.4%

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

      4. distribute-rgt-out 40.4%

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

      5. associate-*l* 40.5%

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

      6. associate-*l* 60.5%

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

   10. Simplified 60.5%

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

   11. Taylor expanded in x around inf 63.7%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
   12. Step-by-step derivation

       1. *-commutative 63.7%

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

       2. *-commutative 63.7%

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

       3. times-frac 83.5%

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

   13. Applied egg-rr 83.5%

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

   if -7.4999999999999995e167 < x

   1. Initial program 89.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 95.7%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 92.1%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 92.1%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 92.1%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 92.1%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 92.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot z\right)}{z \cdot \frac{z}{x}} \cdot \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 3: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y}{\frac{x}{\frac{\cosh x}{z}}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ y (/ x (/ (cosh x) z))))

C

double code(double x, double y, double z) {
	return y / (x / (cosh(x) / z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y / (x / (cosh(x) / z))
end function

Java

public static double code(double x, double y, double z) {
	return y / (x / (Math.cosh(x) / z));
}

Python

def code(x, y, z):
	return y / (x / (math.cosh(x) / z))

Julia

function code(x, y, z)
	return Float64(y / Float64(x / Float64(cosh(x) / z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = y / (x / (cosh(x) / z));
end

Wolfram

code[x_, y_, z_] := N[(y / N[(x / N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

   \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
2. Step-by-step derivation

   1. associate-*r/ 96.2%

      \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

   2. associate-/l/ 87.2%

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

   3. associate-*l/ 87.2%

      \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

   4. *-commutative 87.2%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

   5. *-commutative 87.2%

      \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

3. Simplified 87.2%

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

   1. clear-num 87.2%

      \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{x \cdot z}{\cosh x}}} \]

   2. un-div-inv 87.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{x \cdot z}{\cosh x}}} \]

   3. associate-/l* 96.6%

      \[\leadsto \frac{y}{\color{blue}{\frac{x}{\frac{\cosh x}{z}}}} \]

5. Applied egg-rr 96.6%

   \[\leadsto \color{blue}{\frac{y}{\frac{x}{\frac{\cosh x}{z}}}} \]

6. Final simplification 96.6%

   \[\leadsto \frac{y}{\frac{x}{\frac{\cosh x}{z}}} \]

Alternative 4: 68.7% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{t_0 \cdot 0.5}{z \cdot z}\\ \mathbf{elif}\;x \leq 125000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{y \cdot 0.5}{x} \cdot \frac{x \cdot z}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x \cdot z} \cdot \frac{t_0}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))))
   (if (<= x -1.2e+40)
     (/ (* t_0 0.5) (* z z))
     (if (<= x 125000.0)
       (* y (+ (* 0.5 (/ x z)) (/ (/ 1.0 x) z)))
       (if (<= x 2.8e+127)
         (* (/ (* y 0.5) x) (/ (* x z) (* z (/ z x))))
         (* (/ 0.5 (* x z)) (/ t_0 (/ z x))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (x <= -1.2e+40) {
		tmp = (t_0 * 0.5) / (z * z);
	} else if (x <= 125000.0) {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	} else if (x <= 2.8e+127) {
		tmp = ((y * 0.5) / x) * ((x * z) / (z * (z / x)));
	} else {
		tmp = (0.5 / (x * z)) * (t_0 / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x * z)
    if (x <= (-1.2d+40)) then
        tmp = (t_0 * 0.5d0) / (z * z)
    else if (x <= 125000.0d0) then
        tmp = y * ((0.5d0 * (x / z)) + ((1.0d0 / x) / z))
    else if (x <= 2.8d+127) then
        tmp = ((y * 0.5d0) / x) * ((x * z) / (z * (z / x)))
    else
        tmp = (0.5d0 / (x * z)) * (t_0 / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (x <= -1.2e+40) {
		tmp = (t_0 * 0.5) / (z * z);
	} else if (x <= 125000.0) {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	} else if (x <= 2.8e+127) {
		tmp = ((y * 0.5) / x) * ((x * z) / (z * (z / x)));
	} else {
		tmp = (0.5 / (x * z)) * (t_0 / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	tmp = 0
	if x <= -1.2e+40:
		tmp = (t_0 * 0.5) / (z * z)
	elif x <= 125000.0:
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z))
	elif x <= 2.8e+127:
		tmp = ((y * 0.5) / x) * ((x * z) / (z * (z / x)))
	else:
		tmp = (0.5 / (x * z)) * (t_0 / (z / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (x <= -1.2e+40)
		tmp = Float64(Float64(t_0 * 0.5) / Float64(z * z));
	elseif (x <= 125000.0)
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(Float64(1.0 / x) / z)));
	elseif (x <= 2.8e+127)
		tmp = Float64(Float64(Float64(y * 0.5) / x) * Float64(Float64(x * z) / Float64(z * Float64(z / x))));
	else
		tmp = Float64(Float64(0.5 / Float64(x * z)) * Float64(t_0 / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	tmp = 0.0;
	if (x <= -1.2e+40)
		tmp = (t_0 * 0.5) / (z * z);
	elseif (x <= 125000.0)
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	elseif (x <= 2.8e+127)
		tmp = ((y * 0.5) / x) * ((x * z) / (z * (z / x)));
	else
		tmp = (0.5 / (x * z)) * (t_0 / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+40], N[(N[(t$95$0 * 0.5), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 125000.0], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+127], N[(N[(N[(y * 0.5), $MachinePrecision] / x), $MachinePrecision] * N[(N[(x * z), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2e40

   1. Initial program 65.2%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 63.0%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 63.0%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 63.0%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 63.0%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 39.5%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 39.5%

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

      2. associate-/l* 33.2%

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

      3. *-commutative 33.2%

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

      4. associate-/r* 33.2%

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

   6. Simplified 33.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 33.2%

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

      2. +-commutative 33.2%

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

      3. associate-*r/ 33.2%

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

      4. frac-add 42.0%

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

      5. *-commutative 42.0%

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

      6. *-commutative 42.0%

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

   8. Applied egg-rr 42.0%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 42.0%

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

      2. associate-*r* 42.0%

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

      3. *-commutative 42.0%

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

      4. distribute-rgt-out 42.0%

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

      5. associate-*l* 42.1%

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

      6. associate-*l* 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in x around inf 59.4%

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

   12. Taylor expanded in x around 0 55.2%

       \[\leadsto \frac{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}{\color{blue}{{z}^{2}}} \]
   13. Step-by-step derivation

       1. unpow2 55.2%

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

   14. Simplified 55.2%

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

   if -1.2e40 < x < 125000

   1. Initial program 92.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 92.8%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 93.5%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 93.5%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 93.5%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 93.5%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 88.2%

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{z \cdot x} + 0.5 \cdot \frac{x}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-/l/ 88.3%

         \[\leadsto y \cdot \left(\color{blue}{\frac{\frac{1}{x}}{z}} + 0.5 \cdot \frac{x}{z}\right) \]

      2. +-commutative 88.3%

         \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   6. Simplified 88.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   if 125000 < x < 2.8000000000000002e127

   1. Initial program 96.9%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 96.9%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 96.9%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 96.9%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 96.9%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 34.1%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 34.1%

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

      2. associate-/l* 40.1%

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

      3. *-commutative 40.1%

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

      4. associate-/r* 40.1%

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

   6. Simplified 40.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 40.1%

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

      2. +-commutative 40.1%

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

      3. associate-*r/ 40.1%

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

      4. frac-add 45.0%

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

      5. *-commutative 45.0%

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

      6. *-commutative 45.0%

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

   8. Applied egg-rr 45.0%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 45.0%

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

      2. associate-*r* 45.0%

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

      3. *-commutative 45.0%

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

      4. distribute-rgt-out 45.0%

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

      5. associate-*l* 45.0%

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

      6. associate-*l* 50.7%

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

   10. Simplified 50.7%

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

   11. Taylor expanded in x around inf 50.7%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 50.7%

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

       2. times-frac 60.5%

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

       3. *-commutative 60.5%

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

   13. Applied egg-rr 60.5%

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

   if 2.8000000000000002e127 < x

   1. Initial program 69.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 85.7%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 85.7%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 85.7%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 85.7%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 50.2%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 50.2%

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

      2. associate-/l* 59.0%

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

      3. *-commutative 59.0%

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

      4. associate-/r* 59.0%

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

   6. Simplified 59.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 59.0%

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

      2. +-commutative 59.0%

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

      3. associate-*r/ 59.0%

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

      4. frac-add 58.3%

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

      5. *-commutative 58.3%

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

      6. *-commutative 58.3%

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

   8. Applied egg-rr 58.3%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 58.3%

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

      2. associate-*r* 58.3%

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

      3. *-commutative 58.3%

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

      4. distribute-rgt-out 58.3%

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

      5. associate-*l* 58.3%

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

      6. associate-*l* 65.3%

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

   10. Simplified 65.3%

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

   11. Taylor expanded in x around inf 65.3%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 58.3%

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

       2. *-commutative 58.3%

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

       3. times-frac 69.4%

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

   13. Applied egg-rr 69.4%

       \[\leadsto \color{blue}{\frac{0.5}{z \cdot x} \cdot \frac{y \cdot \left(z \cdot x\right)}{\frac{z}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot z\right)\right) \cdot 0.5}{z \cdot z}\\ \mathbf{elif}\;x \leq 125000:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{y \cdot 0.5}{x} \cdot \frac{x \cdot z}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x \cdot z} \cdot \frac{y \cdot \left(x \cdot z\right)}{\frac{z}{x}}\\ \end{array} \]

Alternative 5: 74.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+39} \lor \neg \left(x \leq 125000\right):\\ \;\;\;\;\frac{y \cdot 0.5}{z \cdot \frac{z}{x}} \cdot \frac{x \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.4e+39) (not (<= x 125000.0)))
   (* (/ (* y 0.5) (* z (/ z x))) (/ (* x z) x))
   (* y (+ (* 0.5 (/ x z)) (/ (/ 1.0 x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e+39) || !(x <= 125000.0)) {
		tmp = ((y * 0.5) / (z * (z / x))) * ((x * z) / x);
	} else {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3.4d+39)) .or. (.not. (x <= 125000.0d0))) then
        tmp = ((y * 0.5d0) / (z * (z / x))) * ((x * z) / x)
    else
        tmp = y * ((0.5d0 * (x / z)) + ((1.0d0 / x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.4e+39) || !(x <= 125000.0)) {
		tmp = ((y * 0.5) / (z * (z / x))) * ((x * z) / x);
	} else {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.4e+39) or not (x <= 125000.0):
		tmp = ((y * 0.5) / (z * (z / x))) * ((x * z) / x)
	else:
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.4e+39) || !(x <= 125000.0))
		tmp = Float64(Float64(Float64(y * 0.5) / Float64(z * Float64(z / x))) * Float64(Float64(x * z) / x));
	else
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(Float64(1.0 / x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.4e+39) || ~((x <= 125000.0)))
		tmp = ((y * 0.5) / (z * (z / x))) * ((x * z) / x);
	else
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.4e+39], N[Not[LessEqual[x, 125000.0]], $MachinePrecision]], N[(N[(N[(y * 0.5), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3999999999999999e39 or 125000 < x

   1. Initial program 75.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 80.0%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 80.0%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 80.0%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 80.0%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 41.8%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 41.8%

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

      2. associate-/l* 44.1%

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

      3. *-commutative 44.1%

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

      4. associate-/r* 44.1%

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

   6. Simplified 44.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 44.1%

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

      2. +-commutative 44.1%

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

      3. associate-*r/ 44.1%

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

      4. frac-add 48.5%

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

      5. *-commutative 48.5%

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

      6. *-commutative 48.5%

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

   8. Applied egg-rr 48.5%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 48.5%

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

      2. associate-*r* 48.5%

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

      3. *-commutative 48.5%

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

      4. distribute-rgt-out 48.5%

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

      5. associate-*l* 48.5%

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

      6. associate-*l* 58.3%

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

   10. Simplified 58.3%

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

   11. Taylor expanded in x around inf 59.1%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 59.1%

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

       2. *-commutative 59.1%

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

       3. times-frac 62.9%

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

       4. *-commutative 62.9%

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

   13. Applied egg-rr 62.9%

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

   if -3.3999999999999999e39 < x < 125000

   1. Initial program 92.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 92.8%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 93.5%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 93.5%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 93.5%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 93.5%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 93.5%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 88.2%

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{z \cdot x} + 0.5 \cdot \frac{x}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-/l/ 88.3%

         \[\leadsto y \cdot \left(\color{blue}{\frac{\frac{1}{x}}{z}} + 0.5 \cdot \frac{x}{z}\right) \]

      2. +-commutative 88.3%

         \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   6. Simplified 88.3%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+39} \lor \neg \left(x \leq 125000\right):\\ \;\;\;\;\frac{y \cdot 0.5}{z \cdot \frac{z}{x}} \cdot \frac{x \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \end{array} \]

Alternative 6: 78.2% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -21500000 \lor \neg \left(x \leq 125000\right):\\ \;\;\;\;\frac{y \cdot \left(x \cdot z\right)}{z \cdot \frac{z}{x}} \cdot \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -21500000.0) (not (<= x 125000.0)))
   (* (/ (* y (* x z)) (* z (/ z x))) (/ 0.5 x))
   (* y (+ (* 0.5 (/ x z)) (/ (/ 1.0 x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -21500000.0) || !(x <= 125000.0)) {
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x);
	} else {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-21500000.0d0)) .or. (.not. (x <= 125000.0d0))) then
        tmp = ((y * (x * z)) / (z * (z / x))) * (0.5d0 / x)
    else
        tmp = y * ((0.5d0 * (x / z)) + ((1.0d0 / x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -21500000.0) || !(x <= 125000.0)) {
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x);
	} else {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -21500000.0) or not (x <= 125000.0):
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x)
	else:
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -21500000.0) || !(x <= 125000.0))
		tmp = Float64(Float64(Float64(y * Float64(x * z)) / Float64(z * Float64(z / x))) * Float64(0.5 / x));
	else
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(Float64(1.0 / x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -21500000.0) || ~((x <= 125000.0)))
		tmp = ((y * (x * z)) / (z * (z / x))) * (0.5 / x);
	else
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -21500000.0], N[Not[LessEqual[x, 125000.0]], $MachinePrecision]], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15e7 or 125000 < x

   1. Initial program 75.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 80.6%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 80.6%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 80.6%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 80.6%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 42.1%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 42.1%

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

      2. associate-/l* 44.3%

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

      3. *-commutative 44.3%

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

      4. associate-/r* 44.3%

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

   6. Simplified 44.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 44.3%

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

      2. +-commutative 44.3%

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

      3. associate-*r/ 44.3%

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

      4. frac-add 48.6%

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

      5. *-commutative 48.6%

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

      6. *-commutative 48.6%

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

   8. Applied egg-rr 48.6%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 48.6%

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

      2. associate-*r* 48.6%

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

      3. *-commutative 48.6%

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

      4. distribute-rgt-out 48.6%

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

      5. associate-*l* 48.6%

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

      6. associate-*l* 58.1%

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

   10. Simplified 58.1%

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

   11. Taylor expanded in x around inf 58.9%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
   12. Step-by-step derivation

       1. *-commutative 58.9%

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

       2. *-commutative 58.9%

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

       3. times-frac 70.0%

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

   13. Applied egg-rr 70.0%

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

   if -2.15e7 < x < 125000

   1. Initial program 92.6%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 92.6%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 93.3%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 93.3%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 93.3%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 93.3%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 89.3%

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{z \cdot x} + 0.5 \cdot \frac{x}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-/l/ 89.4%

         \[\leadsto y \cdot \left(\color{blue}{\frac{\frac{1}{x}}{z}} + 0.5 \cdot \frac{x}{z}\right) \]

      2. +-commutative 89.4%

         \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   6. Simplified 89.4%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -21500000 \lor \neg \left(x \leq 125000\right):\\ \;\;\;\;\frac{y \cdot \left(x \cdot z\right)}{z \cdot \frac{z}{x}} \cdot \frac{0.5}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \end{array} \]

Alternative 7: 67.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{t_0 \cdot 0.5}{z \cdot z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x \cdot z} \cdot \frac{t_0}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))))
   (if (<= x -3.4e+39)
     (/ (* t_0 0.5) (* z z))
     (if (<= x 1.2e+121)
       (* y (+ (* 0.5 (/ x z)) (/ (/ 1.0 x) z)))
       (* (/ 0.5 (* x z)) (/ t_0 (/ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (x <= -3.4e+39) {
		tmp = (t_0 * 0.5) / (z * z);
	} else if (x <= 1.2e+121) {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	} else {
		tmp = (0.5 / (x * z)) * (t_0 / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x * z)
    if (x <= (-3.4d+39)) then
        tmp = (t_0 * 0.5d0) / (z * z)
    else if (x <= 1.2d+121) then
        tmp = y * ((0.5d0 * (x / z)) + ((1.0d0 / x) / z))
    else
        tmp = (0.5d0 / (x * z)) * (t_0 / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (x <= -3.4e+39) {
		tmp = (t_0 * 0.5) / (z * z);
	} else if (x <= 1.2e+121) {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	} else {
		tmp = (0.5 / (x * z)) * (t_0 / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	tmp = 0
	if x <= -3.4e+39:
		tmp = (t_0 * 0.5) / (z * z)
	elif x <= 1.2e+121:
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z))
	else:
		tmp = (0.5 / (x * z)) * (t_0 / (z / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (x <= -3.4e+39)
		tmp = Float64(Float64(t_0 * 0.5) / Float64(z * z));
	elseif (x <= 1.2e+121)
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(Float64(1.0 / x) / z)));
	else
		tmp = Float64(Float64(0.5 / Float64(x * z)) * Float64(t_0 / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	tmp = 0.0;
	if (x <= -3.4e+39)
		tmp = (t_0 * 0.5) / (z * z);
	elseif (x <= 1.2e+121)
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	else
		tmp = (0.5 / (x * z)) * (t_0 / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e+39], N[(N[(t$95$0 * 0.5), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+121], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / N[(x * z), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3999999999999999e39

   1. Initial program 65.2%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 63.0%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 63.0%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 63.0%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 63.0%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 39.5%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 39.5%

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

      2. associate-/l* 33.2%

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

      3. *-commutative 33.2%

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

      4. associate-/r* 33.2%

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

   6. Simplified 33.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 33.2%

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

      2. +-commutative 33.2%

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

      3. associate-*r/ 33.2%

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

      4. frac-add 42.0%

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

      5. *-commutative 42.0%

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

      6. *-commutative 42.0%

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

   8. Applied egg-rr 42.0%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 42.0%

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

      2. associate-*r* 42.0%

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

      3. *-commutative 42.0%

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

      4. distribute-rgt-out 42.0%

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

      5. associate-*l* 42.1%

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

      6. associate-*l* 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in x around inf 59.4%

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

   12. Taylor expanded in x around 0 55.2%

       \[\leadsto \frac{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}{\color{blue}{{z}^{2}}} \]
   13. Step-by-step derivation

       1. unpow2 55.2%

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

   14. Simplified 55.2%

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

   if -3.3999999999999999e39 < x < 1.2e121

   1. Initial program 93.4%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 94.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 94.1%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 94.0%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 94.0%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 94.0%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 79.8%

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{z \cdot x} + 0.5 \cdot \frac{x}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-/l/ 79.9%

         \[\leadsto y \cdot \left(\color{blue}{\frac{\frac{1}{x}}{z}} + 0.5 \cdot \frac{x}{z}\right) \]

      2. +-commutative 79.9%

         \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   6. Simplified 79.9%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   if 1.2e121 < x

   1. Initial program 71.1%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 86.7%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 86.7%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 86.7%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 86.7%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 51.4%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 51.4%

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

      2. associate-/l* 59.6%

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

      3. *-commutative 59.6%

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

      4. associate-/r* 59.6%

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

   6. Simplified 59.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 59.6%

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

      2. +-commutative 59.6%

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

      3. associate-*r/ 59.6%

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

      4. frac-add 59.0%

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

      5. *-commutative 59.0%

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

      6. *-commutative 59.0%

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

   8. Applied egg-rr 59.0%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 59.0%

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

      2. associate-*r* 59.0%

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

      3. *-commutative 59.0%

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

      4. distribute-rgt-out 59.0%

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

      5. associate-*l* 59.0%

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

      6. associate-*l* 67.6%

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

   10. Simplified 67.6%

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

   11. Taylor expanded in x around inf 67.6%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
   12. Step-by-step derivation

       1. associate-*r* 59.0%

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

       2. *-commutative 59.0%

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

       3. times-frac 69.3%

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

   13. Applied egg-rr 69.3%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot z\right)\right) \cdot 0.5}{z \cdot z}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x \cdot z} \cdot \frac{y \cdot \left(x \cdot z\right)}{\frac{z}{x}}\\ \end{array} \]

Alternative 8: 68.7% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -960 \lor \neg \left(x \leq 125000\right):\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot z\right)\right) \cdot 0.5}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -960.0) (not (<= x 125000.0)))
   (/ (* (* y (* x z)) 0.5) (* z z))
   (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -960.0) || !(x <= 125000.0)) {
		tmp = ((y * (x * z)) * 0.5) / (z * z);
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-960.0d0)) .or. (.not. (x <= 125000.0d0))) then
        tmp = ((y * (x * z)) * 0.5d0) / (z * z)
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -960.0) || !(x <= 125000.0)) {
		tmp = ((y * (x * z)) * 0.5) / (z * z);
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -960.0) or not (x <= 125000.0):
		tmp = ((y * (x * z)) * 0.5) / (z * z)
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -960.0) || !(x <= 125000.0))
		tmp = Float64(Float64(Float64(y * Float64(x * z)) * 0.5) / Float64(z * z));
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -960.0) || ~((x <= 125000.0)))
		tmp = ((y * (x * z)) * 0.5) / (z * z);
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -960.0], N[Not[LessEqual[x, 125000.0]], $MachinePrecision]], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -960 or 125000 < x

   1. Initial program 76.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 80.8%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 80.8%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 80.8%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 80.8%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 41.8%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 41.8%

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

      2. associate-/l* 44.0%

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

      3. *-commutative 44.0%

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

      4. associate-/r* 44.0%

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

   6. Simplified 44.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 44.0%

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

      2. +-commutative 44.0%

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

      3. associate-*r/ 44.0%

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

      4. frac-add 48.3%

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

      5. *-commutative 48.3%

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

      6. *-commutative 48.3%

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

   8. Applied egg-rr 48.3%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 48.3%

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

      2. associate-*r* 48.3%

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

      3. *-commutative 48.3%

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

      4. distribute-rgt-out 48.3%

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

      5. associate-*l* 48.3%

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

      6. associate-*l* 57.7%

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

   10. Simplified 57.7%

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

   11. Taylor expanded in x around inf 58.4%

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

   12. Taylor expanded in x around 0 54.0%

       \[\leadsto \frac{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}{\color{blue}{{z}^{2}}} \]
   13. Step-by-step derivation

       1. unpow2 54.0%

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

   14. Simplified 54.0%

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

   if -960 < x < 125000

   1. Initial program 92.5%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 92.5%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 93.3%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 93.2%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 93.2%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 93.2%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 89.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -960 \lor \neg \left(x \leq 125000\right):\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot z\right)\right) \cdot 0.5}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 9: 67.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot z\right)\right) \cdot 0.5}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e+39)
   (/ (* (* y (* x z)) 0.5) (* z z))
   (* y (+ (* 0.5 (/ x z)) (/ (/ 1.0 x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+39) {
		tmp = ((y * (x * z)) * 0.5) / (z * z);
	} else {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.2d+39)) then
        tmp = ((y * (x * z)) * 0.5d0) / (z * z)
    else
        tmp = y * ((0.5d0 * (x / z)) + ((1.0d0 / x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e+39) {
		tmp = ((y * (x * z)) * 0.5) / (z * z);
	} else {
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e+39:
		tmp = ((y * (x * z)) * 0.5) / (z * z)
	else:
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e+39)
		tmp = Float64(Float64(Float64(y * Float64(x * z)) * 0.5) / Float64(z * z));
	else
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(Float64(1.0 / x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e+39)
		tmp = ((y * (x * z)) * 0.5) / (z * z);
	else
		tmp = y * ((0.5 * (x / z)) + ((1.0 / x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e+39], N[(N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999997e39

   1. Initial program 65.2%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 63.0%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 63.0%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 63.0%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 63.0%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 39.5%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   5. Step-by-step derivation

      1. +-commutative 39.5%

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

      2. associate-/l* 33.2%

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

      3. *-commutative 33.2%

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

      4. associate-/r* 33.2%

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

   6. Simplified 33.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}} \]
   7. Step-by-step derivation

      1. associate-/l/ 33.2%

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

      2. +-commutative 33.2%

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

      3. associate-*r/ 33.2%

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

      4. frac-add 42.0%

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

      5. *-commutative 42.0%

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

      6. *-commutative 42.0%

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

   8. Applied egg-rr 42.0%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{z}{x} + \left(x \cdot z\right) \cdot \left(0.5 \cdot y\right)}{\left(x \cdot z\right) \cdot \frac{z}{x}}} \]
   9. Step-by-step derivation

      1. +-commutative 42.0%

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

      2. associate-*r* 42.0%

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

      3. *-commutative 42.0%

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

      4. distribute-rgt-out 42.0%

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

      5. associate-*l* 42.1%

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

      6. associate-*l* 57.2%

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

   10. Simplified 57.2%

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

   11. Taylor expanded in x around inf 59.4%

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

   12. Taylor expanded in x around 0 55.2%

       \[\leadsto \frac{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}{\color{blue}{{z}^{2}}} \]
   13. Step-by-step derivation

       1. unpow2 55.2%

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

   14. Simplified 55.2%

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

   if -4.1999999999999997e39 < x

   1. Initial program 88.7%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 95.3%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 92.5%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 92.4%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 92.4%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 92.4%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 75.5%

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{z \cdot x} + 0.5 \cdot \frac{x}{z}\right)} \]
   5. Step-by-step derivation

      1. associate-/l/ 75.5%

         \[\leadsto y \cdot \left(\color{blue}{\frac{\frac{1}{x}}{z}} + 0.5 \cdot \frac{x}{z}\right) \]

      2. +-commutative 75.5%

         \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]

   6. Simplified 75.5%

      \[\leadsto y \cdot \color{blue}{\left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot z\right)\right) \cdot 0.5}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{\frac{1}{x}}{z}\right)\\ \end{array} \]

Alternative 10: 67.0% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (not (<= x 1.4))) (* 0.5 (* y (/ x z))) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 1.4)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.45d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = 0.5d0 * (y * (x / z))
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 1.4)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45) or not (x <= 1.4):
		tmp = 0.5 * (y * (x / z))
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45) || !(x <= 1.4))
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((x <= 1.4)))
		tmp = 0.5 * (y * (x / z));
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 1.3999999999999999 < x

   1. Initial program 76.2%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]

   2. Taylor expanded in x around 0 40.6%

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

   3. Taylor expanded in x around inf 40.6%

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

      1. associate-*r/ 43.4%

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

   5. Simplified 43.4%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 93.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 93.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 93.8%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 93.7%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 93.7%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 93.7%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 92.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 11: 67.1% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45)
   (* 0.5 (/ (* x y) z))
   (if (<= x 1.4) (/ y (* x z)) (* 0.5 (* y (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45) {
		tmp = 0.5 * ((x * y) / z);
	} else if (x <= 1.4) {
		tmp = y / (x * z);
	} else {
		tmp = 0.5 * (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d0)) then
        tmp = 0.5d0 * ((x * y) / z)
    else if (x <= 1.4d0) then
        tmp = y / (x * z)
    else
        tmp = 0.5d0 * (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45) {
		tmp = 0.5 * ((x * y) / z);
	} else if (x <= 1.4) {
		tmp = y / (x * z);
	} else {
		tmp = 0.5 * (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45:
		tmp = 0.5 * ((x * y) / z)
	elif x <= 1.4:
		tmp = y / (x * z)
	else:
		tmp = 0.5 * (y * (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45)
		tmp = Float64(0.5 * Float64(Float64(x * y) / z));
	elseif (x <= 1.4)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45)
		tmp = 0.5 * ((x * y) / z);
	elseif (x <= 1.4)
		tmp = y / (x * z);
	else
		tmp = 0.5 * (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45], N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999996

   1. Initial program 68.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]

   2. Taylor expanded in x around 0 38.4%

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

   3. Taylor expanded in x around inf 38.4%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 93.0%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 93.0%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 93.8%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 93.7%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 93.7%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 93.7%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 92.8%

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

   if 1.3999999999999999 < x

   1. Initial program 81.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]

   2. Taylor expanded in x around 0 42.0%

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

   3. Taylor expanded in x around inf 42.0%

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

      1. associate-*r/ 50.5%

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

   5. Simplified 50.5%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 12: 57.8% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-65} \lor \neg \left(y \leq 5.5 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e-65) (not (<= y 5.5e-21))) (/ (/ y z) x) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-65) || !(y <= 5.5e-21)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1d-65)) .or. (.not. (y <= 5.5d-21))) then
        tmp = (y / z) / x
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-65) || !(y <= 5.5e-21)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e-65) or not (y <= 5.5e-21):
		tmp = (y / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e-65) || !(y <= 5.5e-21))
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e-65) || ~((y <= 5.5e-21)))
		tmp = (y / z) / x;
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e-65], N[Not[LessEqual[y, 5.5e-21]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999923e-66 or 5.49999999999999977e-21 < y

   1. Initial program 92.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 93.6%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 90.3%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 90.3%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 90.3%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 90.3%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 53.0%

      \[\leadsto y \cdot \color{blue}{\frac{1}{z \cdot x}} \]
   5. Step-by-step derivation

      1. div-inv 53.0%

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

      2. associate-/r* 62.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{z}}{x}} \]

   6. Applied egg-rr 62.8%

      \[\leadsto \color{blue}{\frac{\frac{y}{z}}{x}} \]

   if -9.99999999999999923e-66 < y < 5.49999999999999977e-21

   1. Initial program 74.9%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.1%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 83.6%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 83.6%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 83.6%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 83.6%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 45.5%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x}} \]
   5. Step-by-step derivation

      1. *-commutative 45.5%

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

      2. associate-/r* 51.8%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} \]

   6. Simplified 51.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-65} \lor \neg \left(y \leq 5.5 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 13: 52.0% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 4.2e-64) (/ (/ y x) z) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.2e-64) {
		tmp = (y / x) / z;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 4.2d-64) then
        tmp = (y / x) / z
    else
        tmp = y / (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.2e-64) {
		tmp = (y / x) / z;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4.2e-64:
		tmp = (y / x) / z
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4.2e-64)
		tmp = Float64(Float64(y / x) / z);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4.2e-64)
		tmp = (y / x) / z;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4.2e-64], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.20000000000000023e-64

   1. Initial program 87.8%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 91.4%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 91.3%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 91.3%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 91.3%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 48.7%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x}} \]
   5. Step-by-step derivation

      1. *-commutative 48.7%

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

      2. associate-/r* 52.7%

         \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} \]

   6. Simplified 52.7%

      \[\leadsto \color{blue}{\frac{\frac{y}{x}}{z}} \]

   if 4.20000000000000023e-64 < z

   1. Initial program 76.2%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Step-by-step derivation

      1. associate-*r/ 87.1%

         \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      2. associate-/l/ 76.9%

         \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

      3. associate-*l/ 76.9%

         \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

      4. *-commutative 76.9%

         \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

      5. *-commutative 76.9%

         \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

   4. Taylor expanded in x around 0 51.6%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 14: 50.3% accurate, 21.4× speedup

Math

\[\begin{array}{l} \\ \frac{y}{x \cdot z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ y (* x z)))

C

double code(double x, double y, double z) {
	return y / (x * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y / (x * z)
end function

Java

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

Python

def code(x, y, z):
	return y / (x * z)

Julia

function code(x, y, z)
	return Float64(y / Float64(x * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = y / (x * z);
end

Wolfram

code[x_, y_, z_] := N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

   \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
2. Step-by-step derivation

   1. associate-*r/ 96.2%

      \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

   2. associate-/l/ 87.2%

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}} \]

   3. associate-*l/ 87.2%

      \[\leadsto \color{blue}{\frac{\cosh x}{z \cdot x} \cdot y} \]

   4. *-commutative 87.2%

      \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{z \cdot x}} \]

   5. *-commutative 87.2%

      \[\leadsto y \cdot \frac{\cosh x}{\color{blue}{x \cdot z}} \]

3. Simplified 87.2%

   \[\leadsto \color{blue}{y \cdot \frac{\cosh x}{x \cdot z}} \]

4. Taylor expanded in x around 0 49.5%

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

5. Final simplification 49.5%

   \[\leadsto \frac{y}{x \cdot z} \]

Developer target: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (/ y z) x) (cosh x))))
   (if (< y -4.618902267687042e-52)
     t_0
     (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / z) / x) * cosh(x)
    if (y < (-4.618902267687042d-52)) then
        tmp = t_0
    else if (y < 1.038530535935153d-39) then
        tmp = ((cosh(x) * y) / x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * Math.cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((Math.cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / z) / x) * math.cosh(x)
	tmp = 0
	if y < -4.618902267687042e-52:
		tmp = t_0
	elif y < 1.038530535935153e-39:
		tmp = ((math.cosh(x) * y) / x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / z) / x) * cosh(x))
	tmp = 0.0
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = Float64(Float64(Float64(cosh(x) * y) / x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / z) / x) * cosh(x);
	tmp = 0.0;
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = ((cosh(x) * y) / x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] * N[Cosh[x], $MachinePrecision]), $MachinePrecision]}, If[Less[y, -4.618902267687042e-52], t$95$0, If[Less[y, 1.038530535935153e-39], N[(N[(N[(N[Cosh[x], $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023262 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))