Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 85.3% → 99.8%

Time: 8.7s

Alternatives: 14

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cosh x \cdot \frac{y}{x}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+285} \lor \neg \left(t_0 \leq 10^{+249}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cosh x) (/ y x))))
   (if (or (<= t_0 -5e+285) (not (<= t_0 1e+249)))
     (* y (/ (/ (cosh x) x) z))
     (/ t_0 z))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) * (y / x);
	double tmp;
	if ((t_0 <= -5e+285) || !(t_0 <= 1e+249)) {
		tmp = y * ((cosh(x) / x) / z);
	} else {
		tmp = t_0 / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cosh(x) * (y / x)
    if ((t_0 <= (-5d+285)) .or. (.not. (t_0 <= 1d+249))) then
        tmp = y * ((cosh(x) / x) / z)
    else
        tmp = t_0 / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(x) * (y / x);
	double tmp;
	if ((t_0 <= -5e+285) || !(t_0 <= 1e+249)) {
		tmp = y * ((Math.cosh(x) / x) / z);
	} else {
		tmp = t_0 / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) * (y / x)
	tmp = 0
	if (t_0 <= -5e+285) or not (t_0 <= 1e+249):
		tmp = y * ((math.cosh(x) / x) / z)
	else:
		tmp = t_0 / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) * Float64(y / x))
	tmp = 0.0
	if ((t_0 <= -5e+285) || !(t_0 <= 1e+249))
		tmp = Float64(y * Float64(Float64(cosh(x) / x) / z));
	else
		tmp = Float64(t_0 / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) * (y / x);
	tmp = 0.0;
	if ((t_0 <= -5e+285) || ~((t_0 <= 1e+249)))
		tmp = y * ((cosh(x) / x) / z);
	else
		tmp = t_0 / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -5e+285], N[Not[LessEqual[t$95$0, 1e+249]], $MachinePrecision]], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t$95$0 / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < -5.00000000000000016e285 or 9.9999999999999992e248 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 69.3%

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

      1. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

      1. associate-/r/ 62.3%

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

      2. associate-/l* 72.7%

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

      3. *-commutative 72.7%

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

      4. expm1-log1p-u 41.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

      5. expm1-udef 41.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

      6. associate-/l* 46.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

      7. times-frac 49.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

   5. Applied egg-rr 49.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 49.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 90.1%

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

      3. associate-*r/ 91.2%

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

      4. *-commutative 91.2%

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

      5. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   if -5.00000000000000016e285 < (*.f64 (cosh.f64 x) (/.f64 y x)) < 9.9999999999999992e248

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq -5 \cdot 10^{+285} \lor \neg \left(\cosh x \cdot \frac{y}{x} \leq 10^{+249}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array} \]

Alternative 2: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-99} \lor \neg \left(z \leq 3 \cdot 10^{-135}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.2e-99) (not (<= z 3e-135)))
   (* y (/ (/ (cosh x) x) z))
   (/ (cosh x) (* x (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e-99) || !(z <= 3e-135)) {
		tmp = y * ((cosh(x) / x) / z);
	} else {
		tmp = cosh(x) / (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.2d-99)) .or. (.not. (z <= 3d-135))) then
        tmp = y * ((cosh(x) / x) / z)
    else
        tmp = cosh(x) / (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e-99) || !(z <= 3e-135)) {
		tmp = y * ((Math.cosh(x) / x) / z);
	} else {
		tmp = Math.cosh(x) / (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.2e-99) or not (z <= 3e-135):
		tmp = y * ((math.cosh(x) / x) / z)
	else:
		tmp = math.cosh(x) / (x * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.2e-99) || !(z <= 3e-135))
		tmp = Float64(y * Float64(Float64(cosh(x) / x) / z));
	else
		tmp = Float64(cosh(x) / Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.2e-99) || ~((z <= 3e-135)))
		tmp = y * ((cosh(x) / x) / z);
	else
		tmp = cosh(x) / (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.2e-99], N[Not[LessEqual[z, 3e-135]], $MachinePrecision]], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e-99 or 3.00000000000000012e-135 < z

   1. Initial program 76.1%

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

      1. associate-*l/ 76.0%

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

   3. Simplified 76.0%

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

      1. associate-/r/ 68.8%

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

      2. associate-/l* 72.9%

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

      3. *-commutative 72.9%

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

      4. expm1-log1p-u 47.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

      5. expm1-udef 35.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

      6. associate-/l* 39.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

      7. times-frac 42.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

   5. Applied egg-rr 42.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 51.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 85.3%

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

      3. associate-*r/ 91.5%

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

      4. *-commutative 91.5%

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

      5. associate-*r/ 98.7%

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

   7. Simplified 98.7%

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

   if -1.2e-99 < z < 3.00000000000000012e-135

   1. Initial program 86.6%

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

      1. associate-/l* 86.6%

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

      2. associate-/r/ 98.6%

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

      3. associate-*l/ 87.5%

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

      4. *-commutative 87.5%

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

   3. Simplified 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-/l* 86.6%

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

      3. associate-/r/ 98.6%

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

   5. Applied egg-rr 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-99} \lor \neg \left(z \leq 3 \cdot 10^{-135}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 3: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x}{x}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+86} \lor \neg \left(y \leq 2000000000\right):\\ \;\;\;\;y \cdot \frac{t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t_0}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (cosh x) x)))
   (if (or (<= y -8.5e+86) (not (<= y 2000000000.0)))
     (* y (/ t_0 z))
     (/ (* y t_0) z))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) / x;
	double tmp;
	if ((y <= -8.5e+86) || !(y <= 2000000000.0)) {
		tmp = y * (t_0 / z);
	} else {
		tmp = (y * t_0) / 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) / x
    if ((y <= (-8.5d+86)) .or. (.not. (y <= 2000000000.0d0))) then
        tmp = y * (t_0 / z)
    else
        tmp = (y * t_0) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(x) / x;
	double tmp;
	if ((y <= -8.5e+86) || !(y <= 2000000000.0)) {
		tmp = y * (t_0 / z);
	} else {
		tmp = (y * t_0) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) / x
	tmp = 0
	if (y <= -8.5e+86) or not (y <= 2000000000.0):
		tmp = y * (t_0 / z)
	else:
		tmp = (y * t_0) / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) / x)
	tmp = 0.0
	if ((y <= -8.5e+86) || !(y <= 2000000000.0))
		tmp = Float64(y * Float64(t_0 / z));
	else
		tmp = Float64(Float64(y * t_0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) / x;
	tmp = 0.0;
	if ((y <= -8.5e+86) || ~((y <= 2000000000.0)))
		tmp = y * (t_0 / z);
	else
		tmp = (y * t_0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision]}, If[Or[LessEqual[y, -8.5e+86], N[Not[LessEqual[y, 2000000000.0]], $MachinePrecision]], N[(y * N[(t$95$0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * t$95$0), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000005e86 or 2e9 < y

   1. Initial program 85.8%

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

      1. associate-*l/ 85.8%

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

   3. Simplified 85.8%

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

      1. associate-/r/ 82.9%

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

      2. associate-/l* 91.4%

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

      3. *-commutative 91.4%

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

      4. expm1-log1p-u 57.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

      5. expm1-udef 56.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

      6. associate-/l* 56.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

      7. times-frac 61.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

   5. Applied egg-rr 61.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 62.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 99.8%

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

      3. associate-*r/ 85.8%

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

      4. *-commutative 85.8%

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

      5. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

   if -8.5000000000000005e86 < y < 2e9

   1. Initial program 74.4%

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

      1. expm1-log1p-u 44.7%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cosh x \cdot \frac{y}{x}\right)\right)}}{z} \]

      2. expm1-udef 30.7%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(\cosh x \cdot \frac{y}{x}\right)} - 1}}{z} \]

   3. Applied egg-rr 30.7%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(\cosh x \cdot \frac{y}{x}\right)} - 1}}{z} \]
   4. Step-by-step derivation

      1. expm1-def 44.7%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cosh x \cdot \frac{y}{x}\right)\right)}}{z} \]

      2. expm1-log1p 74.4%

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

      3. associate-*r/ 99.9%

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

      4. associate-*l/ 99.8%

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

      5. *-commutative 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+86} \lor \neg \left(y \leq 2000000000\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{x}}{z}\\ \end{array} \]

Alternative 4: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.2%

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

   1. associate-*l/ 79.1%

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

3. Simplified 79.1%

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

   1. associate-/r/ 74.0%

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

   2. associate-/l* 77.2%

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

   3. *-commutative 77.2%

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

   4. expm1-log1p-u 48.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

   5. expm1-udef 38.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

   6. associate-/l* 42.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

   7. times-frac 45.7%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

5. Applied egg-rr 45.7%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
6. Step-by-step derivation

   1. expm1-def 52.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

   2. expm1-log1p 89.6%

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

   3. associate-*r/ 93.9%

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

   4. *-commutative 93.9%

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

   5. associate-*r/ 95.4%

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

7. Simplified 95.4%

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

8. Final simplification 95.4%

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

Alternative 5: 66.6% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -195000 \lor \neg \left(x \leq 2.1 \cdot 10^{-38}\right):\\ \;\;\;\;y \cdot \frac{z + \left(x \cdot 0.5\right) \cdot \left(x \cdot z\right)}{z \cdot \left(x \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -195000.0) (not (<= x 2.1e-38)))
   (* y (/ (+ z (* (* x 0.5) (* x z))) (* z (* x z))))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -195000.0) || !(x <= 2.1e-38)) {
		tmp = y * ((z + ((x * 0.5) * (x * z))) / (z * (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 ((x <= (-195000.0d0)) .or. (.not. (x <= 2.1d-38))) then
        tmp = y * ((z + ((x * 0.5d0) * (x * z))) / (z * (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 ((x <= -195000.0) || !(x <= 2.1e-38)) {
		tmp = y * ((z + ((x * 0.5) * (x * z))) / (z * (x * z)));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -195000.0) or not (x <= 2.1e-38):
		tmp = y * ((z + ((x * 0.5) * (x * z))) / (z * (x * z)))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -195000.0) || !(x <= 2.1e-38))
		tmp = Float64(y * Float64(Float64(z + Float64(Float64(x * 0.5) * Float64(x * z))) / Float64(z * 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 ((x <= -195000.0) || ~((x <= 2.1e-38)))
		tmp = y * ((z + ((x * 0.5) * (x * z))) / (z * (x * z)));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -195000.0], N[Not[LessEqual[x, 2.1e-38]], $MachinePrecision]], N[(y * N[(N[(z + N[(N[(x * 0.5), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -195000 or 2.10000000000000013e-38 < x

   1. Initial program 67.6%

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

      1. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

      1. associate-/r/ 58.4%

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

      2. associate-/l* 61.7%

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

      3. *-commutative 61.7%

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

      4. expm1-log1p-u 34.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

      5. expm1-udef 31.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

      6. associate-/l* 37.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

      7. times-frac 41.8%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

   5. Applied egg-rr 41.8%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 45.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 86.7%

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

      3. associate-*r/ 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 43.8%

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

      1. associate-*r/ 43.8%

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

      2. frac-add 49.1%

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

      3. *-commutative 49.1%

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

      4. *-un-lft-identity 49.1%

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

   10. Applied egg-rr 49.1%

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

   if -195000 < x < 2.10000000000000013e-38

   1. Initial program 89.4%

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

      1. associate-*l/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 88.9%

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

      1. *-un-lft-identity 88.9%

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

      2. times-frac 90.0%

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

   6. Applied egg-rr 90.0%

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

      1. associate-*l/ 90.2%

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

      2. *-un-lft-identity 90.2%

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

   8. Applied egg-rr 90.2%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -195000 \lor \neg \left(x \leq 2.1 \cdot 10^{-38}\right):\\ \;\;\;\;y \cdot \frac{z + \left(x \cdot 0.5\right) \cdot \left(x \cdot z\right)}{z \cdot \left(x \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 6: 65.5% accurate, 8.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.2%

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

   1. associate-*l/ 79.1%

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

3. Simplified 79.1%

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

   1. associate-/r/ 74.0%

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

   2. associate-/l* 77.2%

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

   3. *-commutative 77.2%

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

   4. expm1-log1p-u 48.6%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

   5. expm1-udef 38.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

   6. associate-/l* 42.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

   7. times-frac 45.7%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

5. Applied egg-rr 45.7%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
6. Step-by-step derivation

   1. expm1-def 52.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

   2. expm1-log1p 89.6%

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

   3. associate-*r/ 93.9%

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

   4. *-commutative 93.9%

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

   5. associate-*r/ 95.4%

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

7. Simplified 95.4%

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

8. Taylor expanded in x around 0 67.2%

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

9. Final simplification 67.2%

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

Alternative 7: 62.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -350.0) (not (<= x 1.45))) (* 0.5 (/ x (/ z y))) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -350.0) || !(x <= 1.45)) {
		tmp = 0.5 * (x / (z / y));
	} 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 <= (-350.0d0)) .or. (.not. (x <= 1.45d0))) then
        tmp = 0.5d0 * (x / (z / y))
    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 <= -350.0) || !(x <= 1.45)) {
		tmp = 0.5 * (x / (z / y));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -350.0) or not (x <= 1.45):
		tmp = 0.5 * (x / (z / y))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -350.0) || !(x <= 1.45))
		tmp = Float64(0.5 * Float64(x / Float64(z / y)));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -350.0) || ~((x <= 1.45)))
		tmp = 0.5 * (x / (z / y));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -350.0], N[Not[LessEqual[x, 1.45]], $MachinePrecision]], N[(0.5 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -350 or 1.44999999999999996 < x

   1. Initial program 68.1%

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

   2. Taylor expanded in x around 0 36.2%

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

   3. Taylor expanded in x around inf 36.2%

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

      1. associate-/l* 29.8%

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

   5. Simplified 29.8%

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

   if -350 < x < 1.44999999999999996

   1. Initial program 88.8%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. *-un-lft-identity 91.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. associate-*l/ 93.0%

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

      2. *-un-lft-identity 93.0%

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

   8. Applied egg-rr 93.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 8: 62.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350 \lor \neg \left(x \leq 1.42\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -350.0) (not (<= x 1.42))) (* x (* y (/ 0.5 z))) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -350.0) || !(x <= 1.42)) {
		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 <= (-350.0d0)) .or. (.not. (x <= 1.42d0))) 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 <= -350.0) || !(x <= 1.42)) {
		tmp = x * (y * (0.5 / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -350.0) or not (x <= 1.42):
		tmp = x * (y * (0.5 / z))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -350.0) || !(x <= 1.42))
		tmp = Float64(x * Float64(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 <= -350.0) || ~((x <= 1.42)))
		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, -350.0], N[Not[LessEqual[x, 1.42]], $MachinePrecision]], N[(x * N[(y * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -350 or 1.4199999999999999 < x

   1. Initial program 68.1%

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

      1. associate-*l/ 68.1%

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

   3. Simplified 68.1%

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

      1. associate-/r/ 58.0%

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

      2. associate-/l* 60.5%

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

      3. *-commutative 60.5%

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

      4. expm1-log1p-u 31.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

      5. expm1-udef 31.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

      6. associate-/l* 38.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

      7. times-frac 42.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

   5. Applied egg-rr 42.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 42.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 85.7%

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

      3. associate-*r/ 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 40.1%

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

   9. Taylor expanded in x around inf 36.2%

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

       1. associate-*r/ 36.2%

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

       2. *-commutative 36.2%

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

       3. associate-*r/ 36.2%

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

       4. associate-*l* 29.8%

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

   11. Simplified 29.8%

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

   if -350 < x < 1.4199999999999999

   1. Initial program 88.8%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. *-un-lft-identity 91.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. associate-*l/ 93.0%

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

      2. *-un-lft-identity 93.0%

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

   8. Applied egg-rr 93.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350 \lor \neg \left(x \leq 1.42\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 9: 65.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350 \lor \neg \left(x \leq 1.42\right):\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -350.0) (not (<= x 1.42))) (* y (* x (/ 0.5 z))) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -350.0) || !(x <= 1.42)) {
		tmp = y * (x * (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 <= (-350.0d0)) .or. (.not. (x <= 1.42d0))) then
        tmp = y * (x * (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 <= -350.0) || !(x <= 1.42)) {
		tmp = y * (x * (0.5 / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -350.0) or not (x <= 1.42):
		tmp = y * (x * (0.5 / z))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -350.0) || !(x <= 1.42))
		tmp = Float64(y * Float64(x * 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 <= -350.0) || ~((x <= 1.42)))
		tmp = y * (x * (0.5 / z));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -350.0], N[Not[LessEqual[x, 1.42]], $MachinePrecision]], N[(y * N[(x * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -350 or 1.4199999999999999 < x

   1. Initial program 68.1%

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

   2. Taylor expanded in x around 0 36.2%

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

   3. Taylor expanded in x around inf 36.2%

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

      1. *-commutative 36.2%

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

      2. *-commutative 36.2%

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

      3. associate-*r* 36.2%

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

      4. *-commutative 36.2%

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

   5. Simplified 36.2%

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

      1. *-commutative 36.2%

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

      2. associate-*l/ 40.1%

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

      3. *-commutative 40.1%

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

      4. *-un-lft-identity 40.1%

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

      5. times-frac 40.1%

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

      6. /-rgt-identity 40.1%

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

   7. Applied egg-rr 40.1%

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

   if -350 < x < 1.4199999999999999

   1. Initial program 88.8%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. *-un-lft-identity 91.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. associate-*l/ 93.0%

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

      2. *-un-lft-identity 93.0%

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

   8. Applied egg-rr 93.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350 \lor \neg \left(x \leq 1.42\right):\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 10: 62.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 1.42:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -350.0)
   (* x (* 0.5 (/ y z)))
   (if (<= x 1.42) (/ (/ y z) x) (* x (* y (/ 0.5 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -350.0) {
		tmp = x * (0.5 * (y / z));
	} else if (x <= 1.42) {
		tmp = (y / z) / x;
	} else {
		tmp = x * (y * (0.5 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-350.0d0)) then
        tmp = x * (0.5d0 * (y / z))
    else if (x <= 1.42d0) then
        tmp = (y / z) / x
    else
        tmp = x * (y * (0.5d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -350.0) {
		tmp = x * (0.5 * (y / z));
	} else if (x <= 1.42) {
		tmp = (y / z) / x;
	} else {
		tmp = x * (y * (0.5 / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -350.0:
		tmp = x * (0.5 * (y / z))
	elif x <= 1.42:
		tmp = (y / z) / x
	else:
		tmp = x * (y * (0.5 / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -350.0)
		tmp = Float64(x * Float64(0.5 * Float64(y / z)));
	elseif (x <= 1.42)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -350.0)
		tmp = x * (0.5 * (y / z));
	elseif (x <= 1.42)
		tmp = (y / z) / x;
	else
		tmp = x * (y * (0.5 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -350.0], N[(x * N[(0.5 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.42], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(x * N[(y * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -350

   1. Initial program 64.8%

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

   2. Taylor expanded in x around 0 29.0%

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

   3. Taylor expanded in x around inf 29.0%

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

      1. associate-*r/ 29.0%

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

      2. *-commutative 29.0%

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

      3. associate-/l* 29.0%

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

   5. Simplified 29.0%

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

      1. associate-/r* 23.7%

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

      2. associate-/r/ 23.7%

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

      3. metadata-eval 23.7%

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

      4. associate-*l/ 23.7%

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

      5. clear-num 23.7%

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

      6. *-commutative 23.7%

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

   7. Applied egg-rr 23.7%

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

   if -350 < x < 1.4199999999999999

   1. Initial program 88.8%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. *-un-lft-identity 91.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. associate-*l/ 93.0%

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

      2. *-un-lft-identity 93.0%

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

   8. Applied egg-rr 93.0%

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

   if 1.4199999999999999 < x

   1. Initial program 70.8%

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

      1. associate-*l/ 70.8%

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

   3. Simplified 70.8%

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

      1. associate-/r/ 60.0%

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

      2. associate-/l* 63.1%

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

      3. *-commutative 63.1%

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

      4. expm1-log1p-u 35.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)\right)} \]

      5. expm1-udef 35.4%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{\frac{x \cdot z}{y}}\right)} - 1} \]

      6. associate-/l* 43.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x \cdot y}{x \cdot z}}\right)} - 1 \]

      7. times-frac 46.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\cosh x}{x} \cdot \frac{y}{z}}\right)} - 1 \]

   5. Applied egg-rr 46.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 46.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cosh x}{x} \cdot \frac{y}{z}\right)\right)} \]

      2. expm1-log1p 87.7%

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

      3. associate-*r/ 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 40.6%

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

   9. Taylor expanded in x around inf 42.1%

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

       1. associate-*r/ 42.1%

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

       2. *-commutative 42.1%

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

       3. associate-*r/ 42.1%

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

       4. associate-*l* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 1.42:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{z}\right)\\ \end{array} \]

Alternative 11: 65.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{z}\right)\\ \mathbf{elif}\;x \leq 1.42:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{z}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -350.0)
   (* y (* x (/ 0.5 z)))
   (if (<= x 1.42) (/ (/ y z) x) (/ 0.5 (/ z (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -350.0) {
		tmp = y * (x * (0.5 / z));
	} else if (x <= 1.42) {
		tmp = (y / z) / x;
	} else {
		tmp = 0.5 / (z / (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-350.0d0)) then
        tmp = y * (x * (0.5d0 / z))
    else if (x <= 1.42d0) then
        tmp = (y / z) / x
    else
        tmp = 0.5d0 / (z / (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -350.0) {
		tmp = y * (x * (0.5 / z));
	} else if (x <= 1.42) {
		tmp = (y / z) / x;
	} else {
		tmp = 0.5 / (z / (x * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -350.0:
		tmp = y * (x * (0.5 / z))
	elif x <= 1.42:
		tmp = (y / z) / x
	else:
		tmp = 0.5 / (z / (x * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -350.0)
		tmp = Float64(y * Float64(x * Float64(0.5 / z)));
	elseif (x <= 1.42)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(0.5 / Float64(z / Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -350.0)
		tmp = y * (x * (0.5 / z));
	elseif (x <= 1.42)
		tmp = (y / z) / x;
	else
		tmp = 0.5 / (z / (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -350.0], N[(y * N[(x * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.42], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(0.5 / N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -350

   1. Initial program 64.8%

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

   2. Taylor expanded in x around 0 29.0%

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

   3. Taylor expanded in x around inf 29.0%

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

      1. *-commutative 29.0%

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

      2. *-commutative 29.0%

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

      3. associate-*r* 29.0%

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

      4. *-commutative 29.0%

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

   5. Simplified 29.0%

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

      1. *-commutative 29.0%

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

      2. associate-*l/ 39.4%

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

      3. *-commutative 39.4%

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

      4. *-un-lft-identity 39.4%

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

      5. times-frac 39.4%

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

      6. /-rgt-identity 39.4%

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

   7. Applied egg-rr 39.4%

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

   if -350 < x < 1.4199999999999999

   1. Initial program 88.8%

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

      1. associate-*l/ 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. *-un-lft-identity 91.8%

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

      2. times-frac 92.9%

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

   6. Applied egg-rr 92.9%

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

      1. associate-*l/ 93.0%

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

      2. *-un-lft-identity 93.0%

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

   8. Applied egg-rr 93.0%

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

   if 1.4199999999999999 < x

   1. Initial program 70.8%

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

   2. Taylor expanded in x around 0 42.1%

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

   3. Taylor expanded in x around inf 42.1%

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

      1. associate-*r/ 42.1%

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

      2. *-commutative 42.1%

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

      3. associate-/l* 42.1%

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

   5. Simplified 42.1%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -350:\\ \;\;\;\;y \cdot \left(x \cdot \frac{0.5}{z}\right)\\ \mathbf{elif}\;x \leq 1.42:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{z}{x \cdot y}}\\ \end{array} \]

Alternative 12: 52.7% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+88} \lor \neg \left(y \leq 5 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+88) (not (<= y 5e+20))) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+88) || !(y <= 5e+20)) {
		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 <= (-1d+88)) .or. (.not. (y <= 5d+20))) 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 <= -1e+88) || !(y <= 5e+20)) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+88) or not (y <= 5e+20):
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+88) || !(y <= 5e+20))
		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 <= -1e+88) || ~((y <= 5e+20)))
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+88], N[Not[LessEqual[y, 5e+20]], $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 < -9.99999999999999959e87 or 5e20 < y

   1. Initial program 85.5%

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

      1. associate-*l/ 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around 0 65.0%

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

   if -9.99999999999999959e87 < y < 5e20

   1. Initial program 74.8%

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

   2. Taylor expanded in x around 0 50.0%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+88} \lor \neg \left(y \leq 5 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 13: 55.1% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-78}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1e-78) (/ (/ y z) x) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1e-78) {
		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 (z <= 1d-78) 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 (z <= 1e-78) {
		tmp = (y / z) / x;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1e-78:
		tmp = (y / z) / x
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1e-78)
		tmp = Float64(Float64(y / 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 (z <= 1e-78)
		tmp = (y / z) / x;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1e-78], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.99999999999999999e-79

   1. Initial program 81.4%

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

      1. associate-*l/ 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in x around 0 50.1%

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

      1. *-un-lft-identity 50.1%

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

      2. times-frac 59.4%

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

   6. Applied egg-rr 59.4%

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

      1. associate-*l/ 59.5%

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

      2. *-un-lft-identity 59.5%

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

   8. Applied egg-rr 59.5%

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

   if 9.99999999999999999e-79 < z

   1. Initial program 74.2%

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

      1. associate-*l/ 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around 0 57.0%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-78}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 14: 49.4% 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 79.2%

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

   1. associate-*l/ 79.1%

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

3. Simplified 79.1%

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

4. Taylor expanded in x around 0 52.3%

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

5. Final simplification 52.3%

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

Developer target: 97.1% 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 2023318 
(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))