Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 95.9% → 95.9%

Time: 6.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Final simplification 97.9%

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

Alternative 2: 78.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.5e-8) (/ x z) (* (sin y) (/ x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e-8) {
		tmp = x / z;
	} else {
		tmp = sin(y) * (x / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.5d-8) then
        tmp = x / z
    else
        tmp = sin(y) * (x / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.5e-8) {
		tmp = x / z;
	} else {
		tmp = Math.sin(y) * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.5e-8:
		tmp = x / z
	else:
		tmp = math.sin(y) * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.5e-8)
		tmp = Float64(x / z);
	else
		tmp = Float64(sin(y) * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.5e-8)
		tmp = x / z;
	else
		tmp = sin(y) * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.5e-8], N[(x / z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.49999999999999987e-8

   1. Initial program 99.7%

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

      1. associate-*l/ 98.4%

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

      2. times-frac 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*r/ 82.3%

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

      5. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.0%

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

   if 1.49999999999999987e-8 < y

   1. Initial program 92.9%

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

      1. associate-*l/ 92.5%

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

      2. times-frac 92.8%

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

      3. *-commutative 92.8%

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

      4. associate-*r/ 92.7%

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

      5. *-commutative 92.7%

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

   3. Simplified 92.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 3: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00035:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.00035)
   (/ (* x (+ 1.0 (* -0.16666666666666666 (* y y)))) z)
   (* (/ (sin y) z) (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00035) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = (sin(y) / 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 (y <= 0.00035d0) then
        tmp = (x * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))) / z
    else
        tmp = (sin(y) / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00035) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = (Math.sin(y) / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.00035:
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z
	else:
		tmp = (math.sin(y) / z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.00035)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))) / z);
	else
		tmp = Float64(Float64(sin(y) / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.00035)
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	else
		tmp = (sin(y) / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.00035], N[(N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.49999999999999996e-4

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 67.7%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}}{z} \]
   3. Step-by-step derivation

      1. unpow2 67.7%

         \[\leadsto \frac{x \cdot \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)}\right)}{z} \]

   4. Simplified 67.7%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}}{z} \]

   if 3.49999999999999996e-4 < y

   1. Initial program 92.8%

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

      1. associate-*r/ 92.8%

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

      2. associate-/l/ 92.7%

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

      3. *-commutative 92.7%

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

      4. times-frac 92.7%

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

   3. Simplified 92.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00035:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 59.9% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6200:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y \cdot z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6200.0)
   (/ (* x (+ 1.0 (* -0.16666666666666666 (* y y)))) z)
   (/ y (/ (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6200.0) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = y / ((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 (y <= 6200.0d0) then
        tmp = (x * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))) / z
    else
        tmp = y / ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 6200.0) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = y / ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6200.0:
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z
	else:
		tmp = y / ((y * z) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6200.0)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))) / z);
	else
		tmp = Float64(y / Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6200.0)
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	else
		tmp = y / ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6200.0], N[(N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6200

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 67.9%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}}{z} \]
   3. Step-by-step derivation

      1. unpow2 67.9%

         \[\leadsto \frac{x \cdot \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)}\right)}{z} \]

   4. Simplified 67.9%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}}{z} \]

   if 6200 < y

   1. Initial program 92.5%

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

      1. associate-*r/ 92.6%

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

      2. associate-/l/ 92.5%

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

      3. *-commutative 92.5%

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

      4. times-frac 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around 0 23.3%

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

      1. frac-times 27.5%

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

      2. associate-/l* 35.5%

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

      3. associate-*l/ 35.3%

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

      4. *-commutative 35.3%

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

   6. Applied egg-rr 35.3%

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

   7. Taylor expanded in y around 0 35.5%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6200:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y \cdot z}{x}}\\ \end{array} \]

Alternative 5: 60.0% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.15e+84) (/ x z) (* (/ x y) (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.15e+84) {
		tmp = x / z;
	} else {
		tmp = (x / y) * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.15d+84) then
        tmp = x / z
    else
        tmp = (x / y) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.15e+84) {
		tmp = x / z;
	} else {
		tmp = (x / y) * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.15e+84:
		tmp = x / z
	else:
		tmp = (x / y) * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.15e+84)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x / y) * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.15e+84)
		tmp = x / z;
	else
		tmp = (x / y) * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.15e+84], N[(x / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.1499999999999999e84

   1. Initial program 99.7%

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

      1. associate-*l/ 98.5%

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

      2. times-frac 80.1%

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

      3. *-commutative 80.1%

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

      4. associate-*r/ 83.9%

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

      5. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 68.2%

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

   if 1.1499999999999999e84 < y

   1. Initial program 89.2%

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

      1. associate-*r/ 89.3%

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

      2. associate-/l/ 91.1%

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

      3. *-commutative 91.1%

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

      4. times-frac 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around 0 25.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.15 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{y}{z}\\ \end{array} \]

Alternative 6: 60.8% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4e-11) (/ x z) (/ x (/ (* y z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4e-11) {
		tmp = x / z;
	} else {
		tmp = x / ((y * 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 (y <= 4d-11) then
        tmp = x / z
    else
        tmp = x / ((y * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4e-11) {
		tmp = x / z;
	} else {
		tmp = x / ((y * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4e-11:
		tmp = x / z
	else:
		tmp = x / ((y * z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(x / Float64(Float64(y * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4e-11)
		tmp = x / z;
	else
		tmp = x / ((y * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4e-11], N[(x / z), $MachinePrecision], N[(x / N[(N[(y * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.99999999999999976e-11

   1. Initial program 99.7%

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

      1. associate-*l/ 98.4%

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

      2. times-frac 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*r/ 82.3%

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

      5. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.0%

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

   if 3.99999999999999976e-11 < y

   1. Initial program 92.9%

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

      1. associate-/l* 92.5%

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

      2. associate-/r/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 21.5%

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

      1. *-commutative 21.5%

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

      2. associate-*r/ 31.8%

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

   6. Applied egg-rr 31.8%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y \cdot z}{y}}\\ \end{array} \]

Alternative 7: 62.6% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.4e-11) (/ x z) (/ y (* y (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-11) {
		tmp = x / z;
	} else {
		tmp = y / (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 (y <= 2.4d-11) then
        tmp = x / z
    else
        tmp = y / (y * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.4e-11) {
		tmp = x / z;
	} else {
		tmp = y / (y * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.4e-11:
		tmp = x / z
	else:
		tmp = y / (y * (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(y * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.4e-11)
		tmp = x / z;
	else
		tmp = y / (y * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.4e-11], N[(x / z), $MachinePrecision], N[(y / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4000000000000001e-11

   1. Initial program 99.7%

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

      1. associate-*l/ 98.4%

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

      2. times-frac 78.1%

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

      3. *-commutative 78.1%

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

      4. associate-*r/ 82.3%

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

      5. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 74.0%

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

   if 2.4000000000000001e-11 < y

   1. Initial program 92.9%

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

      1. associate-*r/ 92.9%

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

      2. associate-/l/ 92.8%

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

      3. *-commutative 92.8%

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

      4. times-frac 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around 0 24.3%

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

      1. frac-times 28.5%

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

      2. associate-/l* 36.1%

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

      3. associate-*l/ 35.9%

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

      4. *-commutative 35.9%

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

   6. Applied egg-rr 35.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 8: 62.7% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00082:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.00082) (/ x z) (/ y (* z (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00082) {
		tmp = x / z;
	} else {
		tmp = y / (z * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 0.00082d0) then
        tmp = x / z
    else
        tmp = y / (z * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00082) {
		tmp = x / z;
	} else {
		tmp = y / (z * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.00082:
		tmp = x / z
	else:
		tmp = y / (z * (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.00082)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(z * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.00082)
		tmp = x / z;
	else
		tmp = y / (z * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.00082], N[(x / z), $MachinePrecision], N[(y / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.1999999999999998e-4

   1. Initial program 99.7%

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

      1. associate-*l/ 98.4%

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

      2. times-frac 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-*r/ 82.4%

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

      5. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around 0 74.1%

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

   if 8.1999999999999998e-4 < y

   1. Initial program 92.8%

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

      1. associate-*r/ 92.8%

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

      2. associate-/l/ 92.7%

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

      3. *-commutative 92.7%

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

      4. times-frac 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 23.2%

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

      1. *-commutative 23.2%

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

      2. clear-num 23.2%

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

      3. frac-times 35.1%

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

      4. *-un-lft-identity 35.1%

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

   6. Applied egg-rr 35.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00082:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 9: 62.7% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00011:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y \cdot z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.00011) (/ x z) (/ y (/ (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00011) {
		tmp = x / z;
	} else {
		tmp = y / ((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 (y <= 0.00011d0) then
        tmp = x / z
    else
        tmp = y / ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.00011) {
		tmp = x / z;
	} else {
		tmp = y / ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.00011:
		tmp = x / z
	else:
		tmp = y / ((y * z) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.00011)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.00011)
		tmp = x / z;
	else
		tmp = y / ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.00011], N[(x / z), $MachinePrecision], N[(y / N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.10000000000000004e-4

   1. Initial program 99.7%

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

      1. associate-*l/ 98.4%

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

      2. times-frac 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-*r/ 82.4%

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

      5. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around 0 74.1%

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

   if 1.10000000000000004e-4 < y

   1. Initial program 92.8%

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

      1. associate-*r/ 92.8%

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

      2. associate-/l/ 92.7%

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

      3. *-commutative 92.7%

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

      4. times-frac 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 23.2%

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

      1. frac-times 27.4%

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

      2. associate-/l* 35.1%

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

      3. associate-*l/ 34.9%

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

      4. *-commutative 34.9%

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

   6. Applied egg-rr 34.9%

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

   7. Taylor expanded in y around 0 35.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.00011:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y \cdot z}{x}}\\ \end{array} \]

Alternative 10: 58.8% accurate, 35.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

   1. associate-*l/ 96.8%

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

   2. times-frac 81.9%

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

   3. *-commutative 81.9%

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

   4. associate-*r/ 85.1%

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

   5. *-commutative 85.1%

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

3. Simplified 85.1%

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

4. Taylor expanded in y around 0 60.3%

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

5. Final simplification 60.3%

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

Developer target: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\sin y}\\ t_1 := \frac{x \cdot \frac{1}{t_0}}{z}\\ \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (sin y))) (t_1 (/ (* x (/ 1.0 t_0)) z)))
   (if (< z -4.2173720203427147e-29)
     t_1
     (if (< z 4.446702369113811e+64) (/ x (* z t_0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y / sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y / sin(y)
    t_1 = (x * (1.0d0 / t_0)) / z
    if (z < (-4.2173720203427147d-29)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x / (z * t_0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / Math.sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / math.sin(y)
	t_1 = (x * (1.0 / t_0)) / z
	tmp = 0
	if z < -4.2173720203427147e-29:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x / (z * t_0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / sin(y))
	t_1 = Float64(Float64(x * Float64(1.0 / t_0)) / z)
	tmp = 0.0
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x / Float64(z * t_0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / sin(y);
	t_1 = (x * (1.0 / t_0)) / z;
	tmp = 0.0;
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x / (z * t_0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[Less[z, -4.2173720203427147e-29], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x / N[(z * t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023258 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))