Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.5% → 99.4%

Time: 8.1s

Alternatives: 12

Speedup: 1.0×

• 64.1% 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: 84.5% 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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+180} \lor \neg \left(t_0 \leq 10^{-68}\right):\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* (cosh x) (/ y x)) z)))
   (if (or (<= t_0 -2e+180) (not (<= t_0 1e-68)))
     (/ (/ (* (cosh x) y) z) x)
     (/ (/ y x) z))))

C

double code(double x, double y, double z) {
	double t_0 = (cosh(x) * (y / x)) / z;
	double tmp;
	if ((t_0 <= -2e+180) || !(t_0 <= 1e-68)) {
		tmp = ((cosh(x) * y) / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (cosh(x) * (y / x)) / z
    if ((t_0 <= (-2d+180)) .or. (.not. (t_0 <= 1d-68))) then
        tmp = ((cosh(x) * y) / z) / x
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.cosh(x) * (y / x)) / z;
	double tmp;
	if ((t_0 <= -2e+180) || !(t_0 <= 1e-68)) {
		tmp = ((Math.cosh(x) * y) / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cosh(x) * (y / x)) / z
	tmp = 0
	if (t_0 <= -2e+180) or not (t_0 <= 1e-68):
		tmp = ((math.cosh(x) * y) / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cosh(x) * Float64(y / x)) / z)
	tmp = 0.0
	if ((t_0 <= -2e+180) || !(t_0 <= 1e-68))
		tmp = Float64(Float64(Float64(cosh(x) * y) / z) / x);
	else
		tmp = Float64(Float64(y / x) / z);
	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 <= -2e+180) || ~((t_0 <= 1e-68)))
		tmp = ((cosh(x) * y) / z) / x;
	else
		tmp = (y / x) / z;
	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[Or[LessEqual[t$95$0, -2e+180], N[Not[LessEqual[t$95$0, 1e-68]], $MachinePrecision]], N[(N[(N[(N[Cosh[x], $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < -2e180 or 1.00000000000000007e-68 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 80.2%

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

      1. associate-*r/ 73.3%

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

      2. associate-/r* 76.8%

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

   3. Simplified 76.8%

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

      1. associate-*r/ 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -2e180 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 1.00000000000000007e-68

   1. Initial program 99.8%

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

      1. associate-*r/ 99.8%

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

      2. associate-/r* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around 0 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-/r* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq -2 \cdot 10^{+180} \lor \neg \left(\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 10^{-68}\right):\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 2: 92.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{if}\;t_0 \leq 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* (cosh x) (/ y x)) z)))
   (if (<= t_0 1e-68) t_0 (* (/ (cosh x) x) (/ y z)))))

C

double code(double x, double y, double z) {
	double t_0 = (cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= 1e-68) {
		tmp = t_0;
	} else {
		tmp = (cosh(x) / 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) :: t_0
    real(8) :: tmp
    t_0 = (cosh(x) * (y / x)) / z
    if (t_0 <= 1d-68) then
        tmp = t_0
    else
        tmp = (cosh(x) / x) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= 1e-68) {
		tmp = t_0;
	} else {
		tmp = (Math.cosh(x) / x) * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cosh(x) * (y / x)) / z
	tmp = 0
	if t_0 <= 1e-68:
		tmp = t_0
	else:
		tmp = (math.cosh(x) / x) * (y / z)
	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-68)
		tmp = t_0;
	else
		tmp = Float64(Float64(cosh(x) / x) * Float64(y / z));
	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-68)
		tmp = t_0;
	else
		tmp = (cosh(x) / x) * (y / z);
	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-68], t$95$0, N[(N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 1.00000000000000007e-68

   1. Initial program 95.5%

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

   if 1.00000000000000007e-68 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 71.7%

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

      1. associate-/l* 65.6%

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

   3. Simplified 65.6%

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

      1. associate-/r/ 71.6%

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

      2. frac-times 83.1%

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

      3. *-commutative 83.1%

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

      4. times-frac 93.1%

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

   5. Applied egg-rr 93.1%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 10^{-68}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x} \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 90.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-103} \lor \neg \left(y \leq 5.5 \cdot 10^{-285}\right):\\ \;\;\;\;\frac{\cosh x}{x} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e-103) (not (<= y 5.5e-285)))
   (* (/ (cosh x) x) (/ y z))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-103) || !(y <= 5.5e-285)) {
		tmp = (cosh(x) / x) * (y / z);
	} else {
		tmp = y * (cosh(x) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4d-103)) .or. (.not. (y <= 5.5d-285))) then
        tmp = (cosh(x) / x) * (y / z)
    else
        tmp = y * (cosh(x) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e-103) || !(y <= 5.5e-285)) {
		tmp = (Math.cosh(x) / x) * (y / z);
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e-103) or not (y <= 5.5e-285):
		tmp = (math.cosh(x) / x) * (y / z)
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e-103) || !(y <= 5.5e-285))
		tmp = Float64(Float64(cosh(x) / x) * Float64(y / z));
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e-103) || ~((y <= 5.5e-285)))
		tmp = (cosh(x) / x) * (y / z);
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e-103], N[Not[LessEqual[y, 5.5e-285]], $MachinePrecision]], N[(N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999983e-103 or 5.5000000000000001e-285 < y

   1. Initial program 87.8%

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

      1. associate-/l* 81.4%

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

   3. Simplified 81.4%

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

      1. associate-/r/ 87.7%

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

      2. frac-times 84.7%

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

      3. *-commutative 84.7%

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

      4. times-frac 96.2%

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

   5. Applied egg-rr 96.2%

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

   if -3.99999999999999983e-103 < y < 5.5000000000000001e-285

   1. Initial program 63.9%

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

      1. associate-*r/ 59.9%

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

      2. associate-/r* 75.9%

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

   3. Simplified 75.9%

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

      1. associate-/r* 59.9%

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

      2. associate-*r/ 63.9%

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

      3. add-log-exp 33.6%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      4. *-un-lft-identity 33.6%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      5. log-prod 33.6%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      6. metadata-eval 33.6%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

      7. add-log-exp 63.9%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

      8. associate-*r/ 99.9%

         \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      9. associate-/r* 89.9%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

      10. times-frac 69.0%

          \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

   5. Applied egg-rr 69.0%

      \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. +-lft-identity 69.0%

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

      2. times-frac 89.9%

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

      3. *-rgt-identity 89.9%

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

      4. associate-*r/ 89.8%

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

      5. *-commutative 89.8%

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

      6. associate-/l/ 91.8%

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

      7. associate-*r* 91.8%

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

      8. associate-/l/ 89.8%

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

      9. associate-*r/ 89.8%

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

      10. *-rgt-identity 89.8%

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

      11. *-commutative 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-103} \lor \neg \left(y \leq 5.5 \cdot 10^{-285}\right):\\ \;\;\;\;\frac{\cosh x}{x} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 4: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.5e+246)
   (* y (/ (cosh x) (* x z)))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.5e+246) {
		tmp = y * (cosh(x) / (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 (x <= 4.5d+246) then
        tmp = y * (cosh(x) / (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 (x <= 4.5e+246) {
		tmp = y * (Math.cosh(x) / (x * z));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.5e+246:
		tmp = y * (math.cosh(x) / (x * z))
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4.5e+246)
		tmp = Float64(y * Float64(cosh(x) / 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 (x <= 4.5e+246)
		tmp = y * (cosh(x) / (x * z));
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4.5e+246], N[(y * N[(N[Cosh[x], $MachinePrecision] / 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 x < 4.5e246

   1. Initial program 83.4%

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

      1. associate-*r/ 78.0%

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

      2. associate-/r* 82.0%

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

   3. Simplified 82.0%

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

      1. associate-/r* 78.0%

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

      2. associate-*r/ 83.4%

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

      3. add-log-exp 59.2%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      4. *-un-lft-identity 59.2%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      5. log-prod 59.2%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      6. metadata-eval 59.2%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

      7. add-log-exp 83.4%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

      8. associate-*r/ 94.1%

         \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      9. associate-/r* 88.2%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

      10. times-frac 90.7%

          \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

   5. Applied egg-rr 90.7%

      \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. +-lft-identity 90.7%

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

      2. times-frac 88.2%

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

      3. *-rgt-identity 88.2%

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

      4. associate-*r/ 88.0%

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

      5. *-commutative 88.0%

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

      6. associate-/l/ 90.9%

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

      7. associate-*r* 90.9%

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

      8. associate-/l/ 88.0%

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

      9. associate-*r/ 88.1%

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

      10. *-rgt-identity 88.1%

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

      11. *-commutative 88.1%

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

   7. Simplified 88.1%

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

   if 4.5e246 < x

   1. Initial program 78.6%

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

   2. Taylor expanded in x around 0 79.4%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{+246}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 5: 71.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 0.5 \cdot \left(x \cdot x\right)\\ t_1 := \frac{y}{x} \cdot \frac{t_0}{z}\\ t_2 := \frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \frac{t_0}{x \cdot z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 0.5 (* x x))))
        (t_1 (* (/ y x) (/ t_0 z)))
        (t_2 (/ (- (/ 1.0 x) (* x -0.5)) (/ z y))))
   (if (<= y -1.12e+107)
     t_2
     (if (<= y -5.6e-93)
       t_1
       (if (<= y 2.2e-286)
         (* y (/ t_0 (* x z)))
         (if (<= y 8e+181) t_1 t_2))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (0.5 * (x * x));
	double t_1 = (y / x) * (t_0 / z);
	double t_2 = ((1.0 / x) - (x * -0.5)) / (z / y);
	double tmp;
	if (y <= -1.12e+107) {
		tmp = t_2;
	} else if (y <= -5.6e-93) {
		tmp = t_1;
	} else if (y <= 2.2e-286) {
		tmp = y * (t_0 / (x * z));
	} else if (y <= 8e+181) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 + (0.5d0 * (x * x))
    t_1 = (y / x) * (t_0 / z)
    t_2 = ((1.0d0 / x) - (x * (-0.5d0))) / (z / y)
    if (y <= (-1.12d+107)) then
        tmp = t_2
    else if (y <= (-5.6d-93)) then
        tmp = t_1
    else if (y <= 2.2d-286) then
        tmp = y * (t_0 / (x * z))
    else if (y <= 8d+181) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (0.5 * (x * x));
	double t_1 = (y / x) * (t_0 / z);
	double t_2 = ((1.0 / x) - (x * -0.5)) / (z / y);
	double tmp;
	if (y <= -1.12e+107) {
		tmp = t_2;
	} else if (y <= -5.6e-93) {
		tmp = t_1;
	} else if (y <= 2.2e-286) {
		tmp = y * (t_0 / (x * z));
	} else if (y <= 8e+181) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (0.5 * (x * x))
	t_1 = (y / x) * (t_0 / z)
	t_2 = ((1.0 / x) - (x * -0.5)) / (z / y)
	tmp = 0
	if y <= -1.12e+107:
		tmp = t_2
	elif y <= -5.6e-93:
		tmp = t_1
	elif y <= 2.2e-286:
		tmp = y * (t_0 / (x * z))
	elif y <= 8e+181:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(0.5 * Float64(x * x)))
	t_1 = Float64(Float64(y / x) * Float64(t_0 / z))
	t_2 = Float64(Float64(Float64(1.0 / x) - Float64(x * -0.5)) / Float64(z / y))
	tmp = 0.0
	if (y <= -1.12e+107)
		tmp = t_2;
	elseif (y <= -5.6e-93)
		tmp = t_1;
	elseif (y <= 2.2e-286)
		tmp = Float64(y * Float64(t_0 / Float64(x * z)));
	elseif (y <= 8e+181)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (0.5 * (x * x));
	t_1 = (y / x) * (t_0 / z);
	t_2 = ((1.0 / x) - (x * -0.5)) / (z / y);
	tmp = 0.0;
	if (y <= -1.12e+107)
		tmp = t_2;
	elseif (y <= -5.6e-93)
		tmp = t_1;
	elseif (y <= 2.2e-286)
		tmp = y * (t_0 / (x * z));
	elseif (y <= 8e+181)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y / x), $MachinePrecision] * N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(1.0 / x), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+107], t$95$2, If[LessEqual[y, -5.6e-93], t$95$1, If[LessEqual[y, 2.2e-286], N[(y * N[(t$95$0 / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+181], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999997e107 or 7.9999999999999993e181 < y

   1. Initial program 83.9%

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

   2. Taylor expanded in x around 0 77.0%

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

   3. Taylor expanded in y around -inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. associate-/l* 82.3%

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

      3. *-commutative 82.3%

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

   5. Simplified 82.3%

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

   if -1.11999999999999997e107 < y < -5.59999999999999997e-93 or 2.1999999999999999e-286 < y < 7.9999999999999993e181

   1. Initial program 90.2%

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

      1. associate-*r/ 81.9%

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

      2. associate-/r* 76.2%

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

   3. Simplified 76.2%

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

      1. associate-/r* 81.9%

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

      2. associate-*r/ 90.2%

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

      3. add-log-exp 63.6%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      4. *-un-lft-identity 63.6%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      5. log-prod 63.6%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      6. metadata-eval 63.6%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

      7. add-log-exp 90.2%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

      8. associate-*r/ 97.8%

         \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      9. associate-/r* 83.0%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

      10. times-frac 94.8%

          \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

   5. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. +-lft-identity 94.8%

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

      2. times-frac 83.0%

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

      3. *-rgt-identity 83.0%

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

      4. associate-*r/ 82.8%

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

      5. *-commutative 82.8%

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

      6. associate-/l/ 85.8%

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

      7. associate-*r* 85.8%

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

      8. associate-/l/ 82.8%

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

      9. associate-*r/ 82.8%

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

      10. *-rgt-identity 82.8%

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

      11. *-commutative 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in x around 0 58.6%

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

      1. associate-*r/ 58.6%

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

      2. *-commutative 58.6%

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

      3. frac-add 56.5%

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

      4. *-un-lft-identity 56.5%

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

   10. Applied egg-rr 56.5%

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

   11. Taylor expanded in z around 0 61.3%

       \[\leadsto \color{blue}{\frac{\left(1 + 0.5 \cdot {x}^{2}\right) \cdot y}{z \cdot x}} \]
   12. Step-by-step derivation

       1. times-frac 71.9%

          \[\leadsto \color{blue}{\frac{1 + 0.5 \cdot {x}^{2}}{z} \cdot \frac{y}{x}} \]

       2. unpow2 71.9%

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

   13. Simplified 71.9%

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

   if -5.59999999999999997e-93 < y < 2.1999999999999999e-286

   1. Initial program 64.7%

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

      1. associate-*r/ 59.1%

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

      2. associate-/r* 74.0%

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

   3. Simplified 74.0%

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

      1. associate-/r* 59.1%

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

      2. associate-*r/ 64.7%

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

      3. add-log-exp 33.1%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      4. *-un-lft-identity 33.1%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      5. log-prod 33.1%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      6. metadata-eval 33.1%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

      7. add-log-exp 64.7%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

      8. associate-*r/ 99.9%

         \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      9. associate-/r* 86.9%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

      10. times-frac 69.5%

          \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

   5. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. +-lft-identity 69.5%

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

      2. times-frac 86.9%

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

      3. *-rgt-identity 86.9%

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

      4. associate-*r/ 86.9%

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

      5. *-commutative 86.9%

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

      6. associate-/l/ 90.5%

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

      7. associate-*r* 90.5%

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

      8. associate-/l/ 86.9%

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

      9. associate-*r/ 86.9%

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

      10. *-rgt-identity 86.9%

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

      11. *-commutative 86.9%

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

   7. Simplified 86.9%

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

   8. Taylor expanded in x around 0 62.0%

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

      1. associate-*r/ 62.0%

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

      2. *-commutative 62.0%

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

      3. frac-add 67.0%

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

      4. *-un-lft-identity 67.0%

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

   10. Applied egg-rr 67.0%

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

   11. Taylor expanded in z around 0 72.5%

       \[\leadsto y \cdot \color{blue}{\frac{1 + 0.5 \cdot {x}^{2}}{z \cdot x}} \]
   12. Step-by-step derivation

       1. unpow2 72.5%

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

       2. *-commutative 72.5%

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

   13. Simplified 72.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+107}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{x \cdot z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+181}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{1 + 0.5 \cdot \left(x \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \end{array} \]

Alternative 6: 65.4% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+235}:\\ \;\;\;\;y \cdot \frac{\frac{1}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+235) (* y (/ (/ 1.0 x) z)) (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+235) {
		tmp = y * ((1.0 / 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 (z <= (-4.5d+235)) then
        tmp = y * ((1.0d0 / 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 (z <= -4.5e+235) {
		tmp = y * ((1.0 / x) / z);
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+235:
		tmp = y * ((1.0 / x) / z)
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+235)
		tmp = Float64(y * Float64(Float64(1.0 / 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 (z <= -4.5e+235)
		tmp = y * ((1.0 / x) / z);
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+235], N[(y * N[(N[(1.0 / x), $MachinePrecision] / z), $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 z < -4.5e235

   1. Initial program 71.0%

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

      1. associate-*r/ 66.0%

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

      2. associate-/r* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 85.0%

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

      1. clear-num 84.8%

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

      2. associate-/r/ 85.1%

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

      3. *-commutative 85.1%

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

      4. associate-/r* 85.2%

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

   6. Applied egg-rr 85.2%

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

   if -4.5e235 < z

   1. Initial program 84.1%

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

   2. Taylor expanded in x around 0 63.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+235}:\\ \;\;\;\;y \cdot \frac{\frac{1}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 7: 65.3% accurate, 8.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

   1. associate-*r/ 77.2%

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

   2. associate-/r* 79.5%

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

3. Simplified 79.5%

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

   1. associate-/r* 77.2%

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

   2. associate-*r/ 83.1%

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

   3. add-log-exp 60.2%

      \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

   4. *-un-lft-identity 60.2%

      \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

   5. log-prod 60.2%

      \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

   6. metadata-eval 60.2%

      \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

   7. add-log-exp 83.1%

      \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

   8. associate-*r/ 94.4%

      \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

   9. associate-/r* 85.7%

      \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

   10. times-frac 90.8%

       \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

5. Applied egg-rr 90.8%

   \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
6. Step-by-step derivation

   1. +-lft-identity 90.8%

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

   2. times-frac 85.7%

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

   3. *-rgt-identity 85.7%

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

   4. associate-*r/ 85.6%

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

   5. *-commutative 85.6%

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

   6. associate-/l/ 88.3%

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

   7. associate-*r* 88.3%

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

   8. associate-/l/ 85.6%

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

   9. associate-*r/ 85.6%

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

   10. *-rgt-identity 85.6%

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

   11. *-commutative 85.6%

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

7. Simplified 85.6%

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

8. Taylor expanded in x around 0 65.8%

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

9. Final simplification 65.8%

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

Alternative 8: 67.9% accurate, 8.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

   1. associate-*r/ 77.2%

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

   2. associate-/r* 79.5%

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

3. Simplified 79.5%

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

   1. associate-/r* 77.2%

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

   2. associate-*r/ 83.1%

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

   3. add-log-exp 60.2%

      \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

   4. *-un-lft-identity 60.2%

      \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

   5. log-prod 60.2%

      \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

   6. metadata-eval 60.2%

      \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

   7. add-log-exp 83.1%

      \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

   8. associate-*r/ 94.4%

      \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

   9. associate-/r* 85.7%

      \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

   10. times-frac 90.8%

       \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

5. Applied egg-rr 90.8%

   \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
6. Step-by-step derivation

   1. +-lft-identity 90.8%

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

   2. times-frac 85.7%

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

   3. *-rgt-identity 85.7%

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

   4. associate-*r/ 85.6%

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

   5. *-commutative 85.6%

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

   6. associate-/l/ 88.3%

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

   7. associate-*r* 88.3%

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

   8. associate-/l/ 85.6%

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

   9. associate-*r/ 85.6%

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

   10. *-rgt-identity 85.6%

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

   11. *-commutative 85.6%

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

7. Simplified 85.6%

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

8. Taylor expanded in x around 0 65.8%

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

   1. associate-*r/ 65.8%

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

   2. *-commutative 65.8%

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

   3. frac-add 61.0%

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

   4. *-un-lft-identity 61.0%

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

10. Applied egg-rr 61.0%

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

11. Taylor expanded in z around 0 68.8%

    \[\leadsto y \cdot \color{blue}{\frac{1 + 0.5 \cdot {x}^{2}}{z \cdot x}} \]
12. Step-by-step derivation

    1. unpow2 68.8%

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

    2. *-commutative 68.8%

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

13. Simplified 68.8%

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

14. Final simplification 68.8%

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

Alternative 9: 65.0% accurate, 9.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 77.7%

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

   2. Taylor expanded in x around 0 38.8%

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

   3. Taylor expanded in x around inf 38.8%

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

      1. associate-/l* 38.0%

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

   5. Simplified 38.0%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/r* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around 0 93.6%

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

4. Final simplification 65.4%

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

Alternative 10: 65.1% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.42)
   (* (* x y) (/ 0.5 z))
   (if (<= x 1.4) (/ y (* x z)) (* 0.5 (/ y (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = (x * y) * (0.5 / z);
	} else if (x <= 1.4) {
		tmp = y / (x * z);
	} else {
		tmp = 0.5 * (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 <= (-1.42d0)) then
        tmp = (x * y) * (0.5d0 / z)
    else if (x <= 1.4d0) then
        tmp = y / (x * z)
    else
        tmp = 0.5d0 * (y / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = (x * y) * (0.5 / z);
	} else if (x <= 1.4) {
		tmp = y / (x * z);
	} else {
		tmp = 0.5 * (y / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.42:
		tmp = (x * y) * (0.5 / z)
	elif x <= 1.4:
		tmp = y / (x * z)
	else:
		tmp = 0.5 * (y / (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.42)
		tmp = Float64(Float64(x * y) * Float64(0.5 / z));
	elseif (x <= 1.4)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(0.5 * Float64(y / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.42)
		tmp = (x * y) * (0.5 / z);
	elseif (x <= 1.4)
		tmp = y / (x * z);
	else
		tmp = 0.5 * (y / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.42], N[(N[(x * y), $MachinePrecision] * N[(0.5 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4199999999999999

   1. Initial program 74.6%

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

      1. associate-*r/ 68.3%

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

      2. associate-/r* 69.8%

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

   3. Simplified 69.8%

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

      1. associate-/r* 68.3%

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

      2. associate-*r/ 74.6%

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

      3. add-log-exp 74.6%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      4. *-un-lft-identity 74.6%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      5. log-prod 74.6%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right)} \]

      6. metadata-eval 74.6%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x \cdot \frac{y}{x}}{z}}\right) \]

      7. add-log-exp 74.6%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

      8. associate-*r/ 100.0%

         \[\leadsto 0 + \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z} \]

      9. associate-/r* 79.4%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot y}{x \cdot z}} \]

      10. times-frac 90.5%

          \[\leadsto 0 + \color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}} \]

   5. Applied egg-rr 90.5%

      \[\leadsto \color{blue}{0 + \frac{\cosh x}{x} \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. +-lft-identity 90.5%

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

      2. times-frac 79.4%

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

      3. *-rgt-identity 79.4%

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

      4. associate-*r/ 79.4%

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

      5. *-commutative 79.4%

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

      6. associate-/l/ 84.1%

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

      7. associate-*r* 84.1%

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

      8. associate-/l/ 79.4%

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

      9. associate-*r/ 79.4%

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

      10. *-rgt-identity 79.4%

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

      11. *-commutative 79.4%

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

   7. Simplified 79.4%

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

   8. Taylor expanded in x around 0 30.0%

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

      1. associate-*r/ 30.0%

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

      2. *-commutative 30.0%

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

      3. frac-add 37.8%

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

      4. *-un-lft-identity 37.8%

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

   10. Applied egg-rr 37.8%

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

   11. Taylor expanded in x around inf 33.1%

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

       1. associate-*r/ 33.1%

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

       2. /-rgt-identity 33.1%

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

       3. associate-/r/ 33.1%

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

       4. associate-*l/ 33.1%

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

       5. *-commutative 33.1%

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

       6. associate-/r/ 33.1%

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

       7. /-rgt-identity 33.1%

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

       8. *-commutative 33.1%

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

   13. Simplified 33.1%

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

   if -1.4199999999999999 < x < 1.3999999999999999

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/r* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around 0 93.6%

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

   if 1.3999999999999999 < x

   1. Initial program 80.6%

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

   2. Taylor expanded in x around 0 44.2%

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

   3. Taylor expanded in x around inf 44.2%

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

      1. associate-/l* 46.9%

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

   5. Simplified 46.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 11: 56.2% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+26} \lor \neg \left(y \leq 2.6 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+26) (not (<= y 2.6e+71))) (/ (/ y z) x) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+26) || !(y <= 2.6e+71)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3d+26)) .or. (.not. (y <= 2.6d+71))) then
        tmp = (y / z) / x
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+26) || !(y <= 2.6e+71)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+26) or not (y <= 2.6e+71):
		tmp = (y / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+26) || !(y <= 2.6e+71))
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e+26) || ~((y <= 2.6e+71)))
		tmp = (y / z) / x;
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+26], N[Not[LessEqual[y, 2.6e+71]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999997e26 or 2.59999999999999991e71 < y

   1. Initial program 87.4%

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

      1. associate-*r/ 84.7%

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

      2. associate-/r* 88.3%

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

   3. Simplified 88.3%

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

      1. associate-*r/ 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-/r* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 62.5%

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

   if -2.99999999999999997e26 < y < 2.59999999999999991e71

   1. Initial program 79.7%

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

      1. associate-*r/ 71.4%

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

      2. associate-/r* 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around 0 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-/r* 49.4%

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

   6. Simplified 49.4%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+26} \lor \neg \left(y \leq 2.6 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 12: 49.2% 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 83.1%

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

   1. associate-*r/ 77.2%

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

   2. associate-/r* 79.5%

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

3. Simplified 79.5%

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

4. Taylor expanded in x around 0 49.0%

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

5. Final simplification 49.0%

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

Developer target: 96.6% 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 2023268 
(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))