Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 85.0% → 96.4%

Time: 9.2s

Alternatives: 11

Speedup: 1.0×

• 64.7% 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: 85.0% 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: 96.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / cosh(x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-*l/ 86.0%

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

3. Simplified 86.0%

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

   1. clear-num 86.0%

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

   2. frac-times 98.4%

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

   3. *-un-lft-identity 98.4%

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

6. Applied egg-rr 98.4%

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

7. Final simplification 98.4%

   \[\leadsto \frac{y}{x \cdot \frac{z}{\cosh x}} \]
8. Add Preprocessing

Alternative 2: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{z} \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4e-39) (/ y (* z x)) (* (/ (cosh x) z) (/ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e-39) {
		tmp = y / (z * x);
	} else {
		tmp = (cosh(x) / z) * (y / 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) :: tmp
    if (x <= 4d-39) then
        tmp = y / (z * x)
    else
        tmp = (cosh(x) / z) * (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e-39) {
		tmp = y / (z * x);
	} else {
		tmp = (Math.cosh(x) / z) * (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4e-39:
		tmp = y / (z * x)
	else:
		tmp = (math.cosh(x) / z) * (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4e-39)
		tmp = Float64(y / Float64(z * x));
	else
		tmp = Float64(Float64(cosh(x) / z) * Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4e-39)
		tmp = y / (z * x);
	else
		tmp = (cosh(x) / z) * (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4e-39], N[(y / N[(z * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.99999999999999972e-39

   1. Initial program 91.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 70.0%

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

   if 3.99999999999999972e-39 < x

   1. Initial program 74.6%

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

      1. associate-*l/ 74.7%

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

   3. Simplified 74.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{z} \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-*l/ 86.0%

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

3. Simplified 86.0%

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

   1. clear-num 86.0%

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

   2. frac-times 98.4%

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

   3. *-un-lft-identity 98.4%

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

6. Applied egg-rr 98.4%

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

   1. associate-*l/ 92.2%

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

   2. associate-/l* 98.4%

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

   3. associate-/l* 96.2%

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

   4. *-commutative 96.2%

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

   5. associate-/l* 90.4%

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

   6. associate-/r/ 98.3%

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

8. Applied egg-rr 98.3%

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

9. Final simplification 98.3%

   \[\leadsto y \cdot \frac{\frac{\cosh x}{x}}{z} \]
10. Add Preprocessing

Alternative 4: 66.8% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{1}{z \cdot x}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y (+ (* 0.5 (/ x z)) (/ 1.0 (* z x)))))

C

double code(double x, double y, double z) {
	return y * ((0.5 * (x / z)) + (1.0 / (z * x)));
}

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 * ((0.5d0 * (x / z)) + (1.0d0 / (z * x)))
end function

Java

public static double code(double x, double y, double z) {
	return y * ((0.5 * (x / z)) + (1.0 / (z * x)));
}

Python

def code(x, y, z):
	return y * ((0.5 * (x / z)) + (1.0 / (z * x)))

Julia

function code(x, y, z)
	return Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(1.0 / Float64(z * x))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * ((0.5 * (x / z)) + (1.0 / (z * x)));
end

Wolfram

code[x_, y_, z_] := N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

   1. associate-*l/ 86.0%

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

3. Simplified 86.0%

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

   1. clear-num 86.0%

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

   2. frac-times 98.4%

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

   3. *-un-lft-identity 98.4%

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

6. Applied egg-rr 98.4%

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

   1. associate-*l/ 92.2%

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

   2. associate-/l* 98.4%

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

   3. associate-/l* 96.2%

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

   4. *-commutative 96.2%

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

   5. associate-/l* 90.4%

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

   6. associate-/r/ 98.3%

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

8. Applied egg-rr 98.3%

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

9. Taylor expanded in x around 0 71.7%

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

10. Final simplification 71.7%

    \[\leadsto y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{1}{z \cdot x}\right) \]
11. Add Preprocessing

Alternative 5: 56.4% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4) {
		tmp = y / (z * x);
	} else {
		tmp = 0.5 * (x / (z / y));
	}
	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 <= 1.4d0) then
        tmp = y / (z * x)
    else
        tmp = 0.5d0 * (x / (z / y))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1.3999999999999999

   1. Initial program 91.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.8%

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

   if 1.3999999999999999 < x

   1. Initial program 70.6%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 37.0%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. associate-/l* 31.5%

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

   6. Simplified 31.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{z}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.4% accurate, 8.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4) {
		tmp = y / (z * x);
	} else {
		tmp = x * (y * (0.5 / 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 <= 1.4d0) then
        tmp = y / (z * x)
    else
        tmp = x * (y * (0.5d0 / z))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1.3999999999999999

   1. Initial program 91.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.8%

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

   if 1.3999999999999999 < x

   1. Initial program 70.6%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 37.0%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. *-commutative 37.0%

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

      2. *-commutative 37.0%

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

      3. associate-*l/ 37.0%

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

      4. associate-/l* 37.0%

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

   6. Simplified 37.0%

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

      1. div-inv 37.0%

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

      2. clear-num 37.0%

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

      3. *-commutative 37.0%

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

      4. associate-*l* 31.5%

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

   8. Applied egg-rr 31.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.5% accurate, 8.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4) {
		tmp = y / (z * x);
	} else {
		tmp = (0.5 / z) * (y * 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) :: tmp
    if (x <= 1.4d0) then
        tmp = y / (z * x)
    else
        tmp = (0.5d0 / z) * (y * x)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1.3999999999999999

   1. Initial program 91.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.8%

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

   if 1.3999999999999999 < x

   1. Initial program 70.6%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 37.0%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. *-commutative 37.0%

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

      2. *-commutative 37.0%

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

      3. associate-*l/ 37.0%

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

      4. associate-/l* 37.0%

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

   6. Simplified 37.0%

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

      1. clear-num 37.0%

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

      2. associate-/r/ 37.0%

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

      3. clear-num 37.0%

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

      4. *-commutative 37.0%

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

   8. Applied egg-rr 37.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{z} \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{z}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4) {
		tmp = y / (z * x);
	} else {
		tmp = y * ((x * 0.5) / 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 <= 1.4d0) then
        tmp = y / (z * x)
    else
        tmp = y * ((x * 0.5d0) / z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 1.3999999999999999

   1. Initial program 91.7%

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

      1. associate-*l/ 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 71.8%

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

   if 1.3999999999999999 < x

   1. Initial program 70.6%

      \[\frac{\cosh x \cdot \frac{y}{x}}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 37.0%

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

   4. Taylor expanded in x around inf 37.0%

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

      1. *-commutative 37.0%

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

      2. *-commutative 37.0%

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

      3. associate-*l/ 37.0%

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

      4. associate-/l* 37.0%

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

   6. Simplified 37.0%

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

      1. associate-/r/ 37.0%

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

      2. *-commutative 37.0%

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

      3. associate-*l/ 42.6%

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

      4. associate-/r/ 31.5%

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

      5. *-commutative 31.5%

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

      6. associate-*r/ 31.5%

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

      7. associate-/r/ 42.6%

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

      8. *-commutative 42.6%

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

   8. Applied egg-rr 42.6%

      \[\leadsto \color{blue}{\frac{x \cdot 0.5}{z} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 8.9× speedup

Math

\[\begin{array}{l} \\ \frac{-y}{\frac{z}{x \cdot -0.5 - \frac{1}{x}}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- y) (/ z (- (* x -0.5) (/ 1.0 x)))))

C

double code(double x, double y, double z) {
	return -y / (z / ((x * -0.5) - (1.0 / x)));
}

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 / (z / ((x * (-0.5d0)) - (1.0d0 / x)))
end function

Java

public static double code(double x, double y, double z) {
	return -y / (z / ((x * -0.5) - (1.0 / x)));
}

Python

def code(x, y, z):
	return -y / (z / ((x * -0.5) - (1.0 / x)))

Julia

function code(x, y, z)
	return Float64(Float64(-y) / Float64(z / Float64(Float64(x * -0.5) - Float64(1.0 / x))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = -y / (z / ((x * -0.5) - (1.0 / x)));
end

Wolfram

code[x_, y_, z_] := N[((-y) / N[(z / N[(N[(x * -0.5), $MachinePrecision] - N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

   1. associate-*l/ 86.0%

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

3. Simplified 86.0%

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

   1. clear-num 86.0%

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

   2. frac-times 98.4%

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

   3. *-un-lft-identity 98.4%

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

6. Applied egg-rr 98.4%

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

   1. associate-*l/ 92.2%

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

   2. associate-/l* 98.4%

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

   3. associate-/l* 96.2%

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

   4. *-commutative 96.2%

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

   5. associate-/l* 90.4%

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

   6. associate-/r/ 98.3%

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

8. Applied egg-rr 98.3%

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

9. Taylor expanded in x around 0 71.7%

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

10. Taylor expanded in z around -inf 67.3%

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

    1. mul-1-neg 67.3%

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

    2. associate-/l* 70.6%

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

    3. *-commutative 70.6%

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

12. Simplified 70.6%

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

13. Final simplification 70.6%

    \[\leadsto \frac{-y}{\frac{z}{x \cdot -0.5 - \frac{1}{x}}} \]
14. Add Preprocessing

Alternative 10: 55.2% accurate, 10.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.8e-80) (/ (/ y z) x) (/ y (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.8e-80) {
		tmp = (y / z) / x;
	} else {
		tmp = y / (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) :: tmp
    if (z <= 3.8d-80) then
        tmp = (y / z) / x
    else
        tmp = y / (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.8e-80) {
		tmp = (y / z) / x;
	} else {
		tmp = y / (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.8e-80:
		tmp = (y / z) / x
	else:
		tmp = y / (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.8e-80)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(y / Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.8e-80)
		tmp = (y / z) / x;
	else
		tmp = y / (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.8e-80], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.79999999999999967e-80

   1. Initial program 86.3%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 52.3%

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

      1. clear-num 52.3%

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

      2. associate-/r/ 52.3%

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

      3. *-commutative 52.3%

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

   7. Applied egg-rr 52.3%

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

      1. associate-*l/ 52.3%

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

      2. *-un-lft-identity 52.3%

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

      3. associate-/r* 55.4%

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

   9. Applied egg-rr 55.4%

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

   if 3.79999999999999967e-80 < z

   1. Initial program 85.4%

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

      1. associate-*l/ 85.3%

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

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 61.5%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.8% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

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 / (z * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

   1. associate-*l/ 86.0%

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

3. Simplified 86.0%

   \[\leadsto \color{blue}{\frac{\cosh x}{z} \cdot \frac{y}{x}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 55.0%

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

6. Final simplification 55.0%

   \[\leadsto \frac{y}{z \cdot x} \]
7. Add Preprocessing

Developer target: 97.1% accurate, 0.9× 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 2024024 
(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))