Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.3% → 97.7%

Time: 8.6s

Alternatives: 15

Speedup: 1.0×

• 63.8% 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: 84.3% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{if}\;t_0 \leq 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* (cosh x) (/ y x)) z)))
   (if (<= t_0 1e+101) t_0 (/ (* y (/ (cosh x) z)) x))))

C

double code(double x, double y, double z) {
	double t_0 = (cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= 1e+101) {
		tmp = t_0;
	} else {
		tmp = (y * (cosh(x) / 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 = (cosh(x) * (y / x)) / z
    if (t_0 <= 1d+101) then
        tmp = t_0
    else
        tmp = (y * (cosh(x) / z)) / x
    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)) / z;
	double tmp;
	if (t_0 <= 1e+101) {
		tmp = t_0;
	} else {
		tmp = (y * (Math.cosh(x) / z)) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cosh(x) * (y / x)) / z
	tmp = 0
	if t_0 <= 1e+101:
		tmp = t_0
	else:
		tmp = (y * (math.cosh(x) / z)) / x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cosh(x) * Float64(y / x)) / z)
	tmp = 0.0
	if (t_0 <= 1e+101)
		tmp = t_0;
	else
		tmp = Float64(Float64(y * Float64(cosh(x) / z)) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (cosh(x) * (y / x)) / z;
	tmp = 0.0;
	if (t_0 <= 1e+101)
		tmp = t_0;
	else
		tmp = (y * (cosh(x) / z)) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+101], t$95$0, N[(N[(y * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 9.9999999999999998e100

   1. Initial program 97.1%

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

   if 9.9999999999999998e100 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 68.1%

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

      1. *-commutative 68.1%

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

      2. associate-*r/ 68.8%

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

   3. Simplified 68.8%

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

      1. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 10^{+101}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{z}}{x}\\ \end{array} \]

Alternative 2: 83.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{\cosh x}{x \cdot z}\\ t_1 := \frac{z}{x \cdot y}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+165}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot t_1 + z \cdot 0.5}{z \cdot t_1}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+174}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot 0.5\right) \cdot \left(x \cdot z\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ (cosh x) (* x z)))) (t_1 (/ z (* x y))))
   (if (<= x -1.65e+165)
     (/ (+ (* (/ y x) t_1) (* z 0.5)) (* z t_1))
     (if (<= x -3.2e-153)
       t_0
       (if (<= x 3.8e-186)
         (/ (/ y z) x)
         (if (<= x 6.5e+174)
           t_0
           (/ (* (* y 0.5) (* x z)) (* x (* z (/ z x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (cosh(x) / (x * z));
	double t_1 = z / (x * y);
	double tmp;
	if (x <= -1.65e+165) {
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1);
	} else if (x <= -3.2e-153) {
		tmp = t_0;
	} else if (x <= 3.8e-186) {
		tmp = (y / z) / x;
	} else if (x <= 6.5e+174) {
		tmp = t_0;
	} else {
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (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) :: t_1
    real(8) :: tmp
    t_0 = y * (cosh(x) / (x * z))
    t_1 = z / (x * y)
    if (x <= (-1.65d+165)) then
        tmp = (((y / x) * t_1) + (z * 0.5d0)) / (z * t_1)
    else if (x <= (-3.2d-153)) then
        tmp = t_0
    else if (x <= 3.8d-186) then
        tmp = (y / z) / x
    else if (x <= 6.5d+174) then
        tmp = t_0
    else
        tmp = ((y * 0.5d0) * (x * z)) / (x * (z * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (Math.cosh(x) / (x * z));
	double t_1 = z / (x * y);
	double tmp;
	if (x <= -1.65e+165) {
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1);
	} else if (x <= -3.2e-153) {
		tmp = t_0;
	} else if (x <= 3.8e-186) {
		tmp = (y / z) / x;
	} else if (x <= 6.5e+174) {
		tmp = t_0;
	} else {
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (math.cosh(x) / (x * z))
	t_1 = z / (x * y)
	tmp = 0
	if x <= -1.65e+165:
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1)
	elif x <= -3.2e-153:
		tmp = t_0
	elif x <= 3.8e-186:
		tmp = (y / z) / x
	elif x <= 6.5e+174:
		tmp = t_0
	else:
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(cosh(x) / Float64(x * z)))
	t_1 = Float64(z / Float64(x * y))
	tmp = 0.0
	if (x <= -1.65e+165)
		tmp = Float64(Float64(Float64(Float64(y / x) * t_1) + Float64(z * 0.5)) / Float64(z * t_1));
	elseif (x <= -3.2e-153)
		tmp = t_0;
	elseif (x <= 3.8e-186)
		tmp = Float64(Float64(y / z) / x);
	elseif (x <= 6.5e+174)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(y * 0.5) * Float64(x * z)) / Float64(x * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (cosh(x) / (x * z));
	t_1 = z / (x * y);
	tmp = 0.0;
	if (x <= -1.65e+165)
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1);
	elseif (x <= -3.2e-153)
		tmp = t_0;
	elseif (x <= 3.8e-186)
		tmp = (y / z) / x;
	elseif (x <= 6.5e+174)
		tmp = t_0;
	else
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.65e+165], N[(N[(N[(N[(y / x), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(z * 0.5), $MachinePrecision]), $MachinePrecision] / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-153], t$95$0, If[LessEqual[x, 3.8e-186], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 6.5e+174], t$95$0, N[(N[(N[(y * 0.5), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6499999999999999e165

   1. Initial program 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*r/ 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around 0 63.1%

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

      1. +-commutative 63.1%

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

      2. associate-/l* 48.6%

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

      3. *-commutative 48.6%

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

   6. Simplified 48.6%

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

      1. clear-num 48.6%

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

      2. un-div-inv 48.6%

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

   8. Applied egg-rr 48.6%

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

      1. +-commutative 48.6%

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

      2. associate-/r* 48.6%

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

      3. frac-add 48.5%

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

      4. associate-/l/ 48.5%

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

      5. associate-/l/ 66.6%

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

   10. Applied egg-rr 66.6%

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

   if -1.6499999999999999e165 < x < -3.1999999999999999e-153 or 3.79999999999999974e-186 < x < 6.5000000000000001e174

   1. Initial program 86.7%

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

      1. associate-*r/ 93.9%

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

      2. associate-/l/ 85.7%

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

      3. associate-*l/ 86.3%

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

      4. *-commutative 86.3%

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

      5. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   if -3.1999999999999999e-153 < x < 3.79999999999999974e-186

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*r/ 91.5%

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

   3. Simplified 91.5%

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

      1. associate-*l/ 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in x around 0 96.8%

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

   if 6.5000000000000001e174 < x

   1. Initial program 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*r/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in x around 0 53.2%

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

      1. +-commutative 53.2%

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

      2. associate-/l* 50.6%

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

      3. *-commutative 50.6%

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

   6. Simplified 50.6%

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

      1. +-commutative 50.6%

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

      2. *-commutative 50.6%

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

      3. associate-*r/ 50.6%

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

      4. frac-add 42.7%

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

      5. *-commutative 42.7%

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

      6. *-commutative 42.7%

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

   8. Applied egg-rr 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-*r* 42.7%

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

      3. *-commutative 42.7%

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

      4. distribute-rgt-out 42.7%

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

      5. associate-*l* 42.7%

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

      6. associate-*l* 72.9%

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

   10. Simplified 72.9%

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

   11. Taylor expanded in x around inf 72.9%

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

       1. associate-*r* 72.9%

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

       2. *-commutative 72.9%

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

   13. Simplified 72.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+165}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \frac{z}{x \cdot y} + z \cdot 0.5}{z \cdot \frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-153}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot 0.5\right) \cdot \left(x \cdot z\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \]

Alternative 3: 87.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+60} \lor \neg \left(z \leq 1.42 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e+60) (not (<= z 1.42e+56)))
   (* (/ y x) (/ (cosh x) z))
   (* (cosh x) (/ (/ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+60) || !(z <= 1.42e+56)) {
		tmp = (y / x) * (cosh(x) / z);
	} else {
		tmp = cosh(x) * ((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 <= (-4.8d+60)) .or. (.not. (z <= 1.42d+56))) then
        tmp = (y / x) * (cosh(x) / z)
    else
        tmp = cosh(x) * ((y / z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e+60) || !(z <= 1.42e+56)) {
		tmp = (y / x) * (Math.cosh(x) / z);
	} else {
		tmp = Math.cosh(x) * ((y / z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e+60) or not (z <= 1.42e+56):
		tmp = (y / x) * (math.cosh(x) / z)
	else:
		tmp = math.cosh(x) * ((y / z) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e+60) || !(z <= 1.42e+56))
		tmp = Float64(Float64(y / x) * Float64(cosh(x) / z));
	else
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e+60) || ~((z <= 1.42e+56)))
		tmp = (y / x) * (cosh(x) / z);
	else
		tmp = cosh(x) * ((y / z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e+60], N[Not[LessEqual[z, 1.42e+56]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e60 or 1.42e56 < z

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-*r/ 82.0%

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

   3. Simplified 82.0%

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

   if -4.8e60 < z < 1.42e56

   1. Initial program 85.3%

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

      1. associate-*r/ 85.3%

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

      2. associate-/l/ 84.0%

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

      3. associate-/r* 95.7%

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

   3. Simplified 95.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+60} \lor \neg \left(z \leq 1.42 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 4: 82.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+170}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot 0.5\right) \cdot \left(x \cdot z\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7e+170)
   (* (cosh x) (/ (/ y z) x))
   (/ (* (* y 0.5) (* x z)) (* x (* z (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e+170) {
		tmp = cosh(x) * ((y / z) / x);
	} else {
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (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 (x <= 7d+170) then
        tmp = cosh(x) * ((y / z) / x)
    else
        tmp = ((y * 0.5d0) * (x * z)) / (x * (z * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e+170) {
		tmp = Math.cosh(x) * ((y / z) / x);
	} else {
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7e+170:
		tmp = math.cosh(x) * ((y / z) / x)
	else:
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7e+170)
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	else
		tmp = Float64(Float64(Float64(y * 0.5) * Float64(x * z)) / Float64(x * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7e+170)
		tmp = cosh(x) * ((y / z) / x);
	else
		tmp = ((y * 0.5) * (x * z)) / (x * (z * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7e+170], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * 0.5), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.00000000000000011e170

   1. Initial program 86.4%

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

      1. associate-*r/ 81.4%

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

      2. associate-/l/ 78.1%

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

      3. associate-/r* 86.4%

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

   3. Simplified 86.4%

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

   if 7.00000000000000011e170 < x

   1. Initial program 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*r/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in x around 0 53.2%

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

      1. +-commutative 53.2%

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

      2. associate-/l* 50.6%

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

      3. *-commutative 50.6%

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

   6. Simplified 50.6%

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

      1. +-commutative 50.6%

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

      2. *-commutative 50.6%

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

      3. associate-*r/ 50.6%

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

      4. frac-add 42.7%

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

      5. *-commutative 42.7%

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

      6. *-commutative 42.7%

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

   8. Applied egg-rr 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-*r* 42.7%

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

      3. *-commutative 42.7%

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

      4. distribute-rgt-out 42.7%

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

      5. associate-*l* 42.7%

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

      6. associate-*l* 72.9%

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

   10. Simplified 72.9%

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

   11. Taylor expanded in x around inf 72.9%

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

       1. associate-*r* 72.9%

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

       2. *-commutative 72.9%

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

   13. Simplified 72.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{+170}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot 0.5\right) \cdot \left(x \cdot z\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \]

Alternative 5: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

   1. *-commutative 83.5%

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

   2. associate-*r/ 83.8%

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

3. Simplified 83.8%

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

   1. associate-*l/ 96.3%

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

5. Applied egg-rr 96.3%

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

6. Final simplification 96.3%

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

Alternative 6: 69.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-14} \lor \neg \left(y \leq 1.45 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{0.5}{\frac{z}{x \cdot y}} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-14) (not (<= y 1.45e+72)))
   (+ (/ 0.5 (/ z (* x y))) (/ y (* x z)))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-14) || !(y <= 1.45e+72)) {
		tmp = (0.5 / (z / (x * y))) + (y / (x * z));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / 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 <= (-4d-14)) .or. (.not. (y <= 1.45d+72))) then
        tmp = (0.5d0 / (z / (x * y))) + (y / (x * z))
    else
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-14) || !(y <= 1.45e+72)) {
		tmp = (0.5 / (z / (x * y))) + (y / (x * z));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-14) or not (y <= 1.45e+72):
		tmp = (0.5 / (z / (x * y))) + (y / (x * z))
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-14) || !(y <= 1.45e+72))
		tmp = Float64(Float64(0.5 / Float64(z / Float64(x * y))) + Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e-14) || ~((y <= 1.45e+72)))
		tmp = (0.5 / (z / (x * y))) + (y / (x * z));
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-14], N[Not[LessEqual[y, 1.45e+72]], $MachinePrecision]], N[(N[(0.5 / N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e-14 or 1.45000000000000009e72 < y

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*r/ 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 68.7%

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

      3. *-commutative 68.7%

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

   6. Simplified 68.7%

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

      1. clear-num 68.7%

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

      2. un-div-inv 68.7%

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

   8. Applied egg-rr 68.7%

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

   9. Taylor expanded in z around 0 80.1%

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

   if -4e-14 < y < 1.45000000000000009e72

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 57.1%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-14} \lor \neg \left(y \leq 1.45 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{0.5}{\frac{z}{x \cdot y}} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 7: 73.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-18} \lor \neg \left(y \leq 1.45 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{0.5}{\frac{z}{x \cdot y}} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + y \cdot \frac{x \cdot 0.5}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e-18) (not (<= y 1.45e+72)))
   (+ (/ 0.5 (/ z (* x y))) (/ y (* x z)))
   (+ (/ (/ y x) z) (* y (/ (* x 0.5) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-18) || !(y <= 1.45e+72)) {
		tmp = (0.5 / (z / (x * y))) + (y / (x * z));
	} else {
		tmp = ((y / x) / z) + (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 ((y <= (-3.1d-18)) .or. (.not. (y <= 1.45d+72))) then
        tmp = (0.5d0 / (z / (x * y))) + (y / (x * z))
    else
        tmp = ((y / x) / z) + (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 ((y <= -3.1e-18) || !(y <= 1.45e+72)) {
		tmp = (0.5 / (z / (x * y))) + (y / (x * z));
	} else {
		tmp = ((y / x) / z) + (y * ((x * 0.5) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e-18) or not (y <= 1.45e+72):
		tmp = (0.5 / (z / (x * y))) + (y / (x * z))
	else:
		tmp = ((y / x) / z) + (y * ((x * 0.5) / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e-18) || !(y <= 1.45e+72))
		tmp = Float64(Float64(0.5 / Float64(z / Float64(x * y))) + Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(y * Float64(Float64(x * 0.5) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e-18) || ~((y <= 1.45e+72)))
		tmp = (0.5 / (z / (x * y))) + (y / (x * z));
	else
		tmp = ((y / x) / z) + (y * ((x * 0.5) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e-18], N[Not[LessEqual[y, 1.45e+72]], $MachinePrecision]], N[(N[(0.5 / N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(y * N[(N[(x * 0.5), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000007e-18 or 1.45000000000000009e72 < y

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*r/ 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in x around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 68.7%

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

      3. *-commutative 68.7%

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

   6. Simplified 68.7%

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

      1. clear-num 68.7%

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

      2. un-div-inv 68.7%

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

   8. Applied egg-rr 68.7%

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

   9. Taylor expanded in z around 0 80.1%

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

   if -3.10000000000000007e-18 < y < 1.45000000000000009e72

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r/ 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in x around 0 46.7%

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

      1. +-commutative 46.7%

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

      2. associate-/l* 50.0%

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

      3. *-commutative 50.0%

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

   6. Simplified 50.0%

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

      1. *-un-lft-identity 50.0%

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

      2. div-inv 50.0%

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

      3. times-frac 46.7%

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

   8. Applied egg-rr 46.7%

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

   9. Taylor expanded in y around 0 51.0%

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

       1. distribute-lft-in 51.0%

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

       2. *-commutative 51.0%

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

       3. associate-*r/ 51.4%

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

       4. *-rgt-identity 51.4%

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

       5. associate-/r* 61.8%

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

       6. associate-*r/ 61.8%

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

       7. *-commutative 61.8%

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

   11. Simplified 61.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-18} \lor \neg \left(y \leq 1.45 \cdot 10^{+72}\right):\\ \;\;\;\;\frac{0.5}{\frac{z}{x \cdot y}} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + y \cdot \frac{x \cdot 0.5}{z}\\ \end{array} \]

Alternative 8: 61.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (not (<= x 9.5e-8)))
   (* 0.5 (* x (/ y z)))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 9.5e-8)) {
		tmp = 0.5 * (x * (y / z));
	} 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 ((x <= (-1.45d0)) .or. (.not. (x <= 9.5d-8))) then
        tmp = 0.5d0 * (x * (y / z))
    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 ((x <= -1.45) || !(x <= 9.5e-8)) {
		tmp = 0.5 * (x * (y / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45) or not (x <= 9.5e-8):
		tmp = 0.5 * (x * (y / z))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45) || !(x <= 9.5e-8))
		tmp = Float64(0.5 * Float64(x * Float64(y / z)));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((x <= 9.5e-8)))
		tmp = 0.5 * (x * (y / z));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45], N[Not[LessEqual[x, 9.5e-8]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 9.50000000000000036e-8 < x

   1. Initial program 77.8%

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

   2. Taylor expanded in x around 0 38.6%

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

   3. Taylor expanded in y around 0 38.6%

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

   4. Taylor expanded in x around inf 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-*r/ 28.8%

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

   6. Simplified 28.8%

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

   if -1.44999999999999996 < x < 9.50000000000000036e-8

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 89.7%

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

   3. Simplified 89.7%

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

      1. associate-*l/ 92.2%

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

   5. Applied egg-rr 92.2%

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

   6. Taylor expanded in x around 0 92.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 9: 65.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \frac{0.5}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (not (<= x 9.5e-8)))
   (* y (/ 0.5 (/ z x)))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 9.5e-8)) {
		tmp = y * (0.5 / (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 ((x <= (-1.45d0)) .or. (.not. (x <= 9.5d-8))) then
        tmp = y * (0.5d0 / (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 ((x <= -1.45) || !(x <= 9.5e-8)) {
		tmp = y * (0.5 / (z / x));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45) or not (x <= 9.5e-8):
		tmp = y * (0.5 / (z / x))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45) || !(x <= 9.5e-8))
		tmp = Float64(y * Float64(0.5 / Float64(z / x)));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((x <= 9.5e-8)))
		tmp = y * (0.5 / (z / x));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45], N[Not[LessEqual[x, 9.5e-8]], $MachinePrecision]], N[(y * N[(0.5 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 9.50000000000000036e-8 < x

   1. Initial program 77.8%

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

   2. Taylor expanded in x around 0 38.6%

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

   3. Taylor expanded in y around 0 38.6%

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

   4. Taylor expanded in x around inf 38.6%

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

      1. associate-*r/ 38.6%

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

      2. associate-*r* 38.6%

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

      3. associate-*r/ 33.7%

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

      4. *-commutative 33.7%

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

      5. associate-*r* 33.7%

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

      6. associate-*r/ 33.7%

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

      7. associate-/l* 33.7%

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

   6. Simplified 33.7%

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

   if -1.44999999999999996 < x < 9.50000000000000036e-8

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 89.7%

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

   3. Simplified 89.7%

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

      1. associate-*l/ 92.2%

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

   5. Applied egg-rr 92.2%

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

   6. Taylor expanded in x around 0 92.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot \frac{0.5}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 10: 65.6% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (not (<= x 9.5e-8)))
   (* (* x y) (/ 0.5 z))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 9.5e-8)) {
		tmp = (x * y) * (0.5 / z);
	} 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 ((x <= (-1.45d0)) .or. (.not. (x <= 9.5d-8))) then
        tmp = (x * y) * (0.5d0 / z)
    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 ((x <= -1.45) || !(x <= 9.5e-8)) {
		tmp = (x * y) * (0.5 / z);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45) or not (x <= 9.5e-8):
		tmp = (x * y) * (0.5 / z)
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45) || !(x <= 9.5e-8))
		tmp = Float64(Float64(x * y) * Float64(0.5 / z));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((x <= 9.5e-8)))
		tmp = (x * y) * (0.5 / z);
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45], N[Not[LessEqual[x, 9.5e-8]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] * N[(0.5 / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 9.50000000000000036e-8 < x

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-*r/ 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 38.6%

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

      1. +-commutative 38.6%

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

      2. associate-/l* 32.3%

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

      3. *-commutative 32.3%

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

   6. Simplified 32.3%

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

      1. *-un-lft-identity 32.3%

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

      2. div-inv 32.3%

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

      3. times-frac 38.6%

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

   8. Applied egg-rr 38.6%

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

   9. Taylor expanded in x around inf 38.6%

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

       1. metadata-eval 38.6%

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

       2. times-frac 38.6%

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

       3. *-commutative 38.6%

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

       4. times-frac 38.6%

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

       5. /-rgt-identity 38.6%

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

   11. Simplified 38.6%

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

   if -1.44999999999999996 < x < 9.50000000000000036e-8

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 89.7%

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

   3. Simplified 89.7%

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

      1. associate-*l/ 92.2%

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

   5. Applied egg-rr 92.2%

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

   6. Taylor expanded in x around 0 92.2%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 9.5 \cdot 10^{-8}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 11: 65.5% accurate, 9.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y * ((x * 0.5) + (1.0 / 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 * 0.5d0) + (1.0d0 / x))) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

2. Taylor expanded in x around 0 62.8%

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

3. Taylor expanded in y around 0 62.7%

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

4. Final simplification 62.7%

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

Alternative 12: 65.6% accurate, 9.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((y / x) + (0.5 * (x * y))) / 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) + (0.5d0 * (x * y))) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

2. Taylor expanded in x around 0 62.8%

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

3. Final simplification 62.8%

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

Alternative 13: 52.7% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-12} \lor \neg \left(y \leq 2.95 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e-12) (not (<= y 2.95e+137))) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-12) || !(y <= 2.95e+137)) {
		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 ((y <= (-2d-12)) .or. (.not. (y <= 2.95d+137))) 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 ((y <= -2e-12) || !(y <= 2.95e+137)) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e-12) or not (y <= 2.95e+137):
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e-12) || !(y <= 2.95e+137))
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2e-12) || ~((y <= 2.95e+137)))
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e-12], N[Not[LessEqual[y, 2.95e+137]], $MachinePrecision]], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999996e-12 or 2.95000000000000018e137 < y

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-*r/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around 0 52.9%

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

   if -1.99999999999999996e-12 < y < 2.95000000000000018e137

   1. Initial program 81.1%

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

   2. Taylor expanded in x around 0 48.1%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-12} \lor \neg \left(y \leq 2.95 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 14: 54.9% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.6e+59) (/ y (* x z)) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.6e+59) {
		tmp = y / (x * z);
	} 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 <= (-3.6d+59)) then
        tmp = y / (x * z)
    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 <= -3.6e+59) {
		tmp = y / (x * z);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.6e+59:
		tmp = y / (x * z)
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.6e+59)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.6e+59)
		tmp = y / (x * z);
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.6e+59], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5999999999999999e59

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. associate-*r/ 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around 0 37.1%

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

   if -3.5999999999999999e59 < z

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*r/ 84.3%

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

   3. Simplified 84.3%

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

      1. associate-*l/ 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in x around 0 54.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 15: 49.8% 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 83.5%

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

   1. *-commutative 83.5%

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

   2. associate-*r/ 83.8%

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

3. Simplified 83.8%

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

4. Taylor expanded in x around 0 44.3%

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

5. Final simplification 44.3%

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

Developer target: 96.9% 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 2023230 
(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))