Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.5% → 96.6%

Time: 9.3s

Alternatives: 13

Speedup: 1.0×

• 63.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. associate-*r/ 81.0%

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

3. Simplified 81.0%

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

   1. associate-*r/ 85.3%

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

   2. associate-*l/ 85.3%

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

   3. *-commutative 85.3%

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

   4. associate-*l/ 97.5%

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

5. Applied egg-rr 97.5%

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

6. Final simplification 97.5%

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

Alternative 2: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{if}\;x \leq -1 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+229}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x \cdot -0.5 + \frac{-1}{x}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cosh x) (/ (/ y x) z))))
   (if (<= x -1e-11)
     t_0
     (if (<= x 1.6e-302)
       (/ (/ y z) x)
       (if (<= x 3.2e+229) t_0 (/ (- y) (/ z (+ (* x -0.5) (/ -1.0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) * ((y / x) / z);
	double tmp;
	if (x <= -1e-11) {
		tmp = t_0;
	} else if (x <= 1.6e-302) {
		tmp = (y / z) / x;
	} else if (x <= 3.2e+229) {
		tmp = t_0;
	} else {
		tmp = -y / (z / ((x * -0.5) + (-1.0 / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cosh(x) * ((y / x) / z)
    if (x <= (-1d-11)) then
        tmp = t_0
    else if (x <= 1.6d-302) then
        tmp = (y / z) / x
    else if (x <= 3.2d+229) then
        tmp = t_0
    else
        tmp = -y / (z / ((x * (-0.5d0)) + ((-1.0d0) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(x) * ((y / x) / z);
	double tmp;
	if (x <= -1e-11) {
		tmp = t_0;
	} else if (x <= 1.6e-302) {
		tmp = (y / z) / x;
	} else if (x <= 3.2e+229) {
		tmp = t_0;
	} else {
		tmp = -y / (z / ((x * -0.5) + (-1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) * ((y / x) / z)
	tmp = 0
	if x <= -1e-11:
		tmp = t_0
	elif x <= 1.6e-302:
		tmp = (y / z) / x
	elif x <= 3.2e+229:
		tmp = t_0
	else:
		tmp = -y / (z / ((x * -0.5) + (-1.0 / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) * Float64(Float64(y / x) / z))
	tmp = 0.0
	if (x <= -1e-11)
		tmp = t_0;
	elseif (x <= 1.6e-302)
		tmp = Float64(Float64(y / z) / x);
	elseif (x <= 3.2e+229)
		tmp = t_0;
	else
		tmp = Float64(Float64(-y) / Float64(z / Float64(Float64(x * -0.5) + Float64(-1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) * ((y / x) / z);
	tmp = 0.0;
	if (x <= -1e-11)
		tmp = t_0;
	elseif (x <= 1.6e-302)
		tmp = (y / z) / x;
	elseif (x <= 3.2e+229)
		tmp = t_0;
	else
		tmp = -y / (z / ((x * -0.5) + (-1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-11], t$95$0, If[LessEqual[x, 1.6e-302], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 3.2e+229], t$95$0, N[((-y) / N[(z / N[(N[(x * -0.5), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999939e-12 or 1.59999999999999989e-302 < x < 3.1999999999999998e229

   1. Initial program 89.3%

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

      1. associate-*r/ 83.4%

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

   3. Simplified 83.4%

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

   if -9.99999999999999939e-12 < x < 1.59999999999999989e-302

   1. Initial program 83.2%

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

      1. associate-*r/ 83.2%

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

   3. Simplified 83.2%

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

      1. associate-*r/ 83.2%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-*l/ 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in x around 0 95.7%

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

   if 3.1999999999999998e229 < x

   1. Initial program 55.6%

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

      1. associate-*r/ 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around 0 57.2%

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

   5. Taylor expanded in y around 0 73.0%

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

   6. Taylor expanded in z around -inf 57.2%

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

      1. mul-1-neg 57.2%

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

      2. associate-/l* 73.0%

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

      3. *-commutative 73.0%

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

   8. Simplified 73.0%

      \[\leadsto \color{blue}{-\frac{y}{\frac{z}{x \cdot -0.5 - \frac{1}{x}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-11}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-302}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+229}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x \cdot -0.5 + \frac{-1}{x}}}\\ \end{array} \]

Alternative 3: 90.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. associate-/l* 80.6%

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

   2. associate-/r/ 86.3%

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

   3. associate-*l/ 79.9%

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

   4. *-commutative 79.9%

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

3. Simplified 79.9%

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

   1. associate-/l* 86.5%

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

   2. associate-/r/ 91.2%

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

5. Applied egg-rr 91.2%

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

6. Final simplification 91.2%

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

Alternative 4: 66.8% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-161}:\\ \;\;\;\;\frac{z \cdot \frac{y}{z} + x \cdot \left(0.5 \cdot \left(y \cdot x\right)\right)}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+76)
   (+ (* 0.5 (/ (* y x) z)) (/ y (* x z)))
   (if (<= z -4e-161)
     (/ (+ (* z (/ y z)) (* x (* 0.5 (* y x)))) (* x z))
     (* (/ y z) (+ (/ 1.0 x) (* x 0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+76) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else if (z <= -4e-161) {
		tmp = ((z * (y / z)) + (x * (0.5 * (y * x)))) / (x * z);
	} else {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	}
	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 <= (-1.1d+76)) then
        tmp = (0.5d0 * ((y * x) / z)) + (y / (x * z))
    else if (z <= (-4d-161)) then
        tmp = ((z * (y / z)) + (x * (0.5d0 * (y * x)))) / (x * z)
    else
        tmp = (y / z) * ((1.0d0 / x) + (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+76) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else if (z <= -4e-161) {
		tmp = ((z * (y / z)) + (x * (0.5 * (y * x)))) / (x * z);
	} else {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+76:
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z))
	elif z <= -4e-161:
		tmp = ((z * (y / z)) + (x * (0.5 * (y * x)))) / (x * z)
	else:
		tmp = (y / z) * ((1.0 / x) + (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+76)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(y / Float64(x * z)));
	elseif (z <= -4e-161)
		tmp = Float64(Float64(Float64(z * Float64(y / z)) + Float64(x * Float64(0.5 * Float64(y * x)))) / Float64(x * z));
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(1.0 / x) + Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+76)
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	elseif (z <= -4e-161)
		tmp = ((z * (y / z)) + (x * (0.5 * (y * x)))) / (x * z);
	else
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+76], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-161], N[(N[(N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x * N[(0.5 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(1.0 / x), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e76

   1. Initial program 69.9%

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

      1. associate-*r/ 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in x around 0 73.9%

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

   if -1.1e76 < z < -4.00000000000000011e-161

   1. Initial program 87.6%

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

      1. associate-*r/ 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around 0 67.1%

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

      1. +-commutative 67.1%

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

      2. associate-/r* 67.0%

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

      3. *-un-lft-identity 67.0%

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

      4. associate-*l/ 67.0%

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

      5. associate-*r/ 67.0%

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

      6. associate-*r/ 67.0%

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

      7. frac-add 82.2%

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

      8. associate-*l/ 82.3%

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

      9. *-un-lft-identity 82.3%

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

      10. *-commutative 82.3%

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

      11. *-commutative 82.3%

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

   6. Applied egg-rr 82.3%

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

   if -4.00000000000000011e-161 < z

   1. Initial program 88.9%

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

      1. associate-/l* 83.9%

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

      2. associate-/r/ 89.9%

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

      3. associate-*l/ 79.5%

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

      4. *-commutative 79.5%

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

   3. Simplified 79.5%

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

      1. associate-/l* 89.9%

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

      2. associate-/r/ 94.2%

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

   5. Applied egg-rr 94.2%

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

   6. Taylor expanded in x around 0 76.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+76}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-161}:\\ \;\;\;\;\frac{z \cdot \frac{y}{z} + x \cdot \left(0.5 \cdot \left(y \cdot x\right)\right)}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \end{array} \]

Alternative 5: 66.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 40000000000:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{0.5}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+101)
   (* 0.5 (* y (/ x z)))
   (if (<= x 40000000000.0)
     (* (/ y z) (+ (/ 1.0 x) (* x 0.5)))
     (* (* y x) (/ 0.5 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+101) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 40000000000.0) {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	} else {
		tmp = (y * x) * (0.5 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.1d+101)) then
        tmp = 0.5d0 * (y * (x / z))
    else if (x <= 40000000000.0d0) then
        tmp = (y / z) * ((1.0d0 / x) + (x * 0.5d0))
    else
        tmp = (y * x) * (0.5d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+101) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 40000000000.0) {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	} else {
		tmp = (y * x) * (0.5 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+101:
		tmp = 0.5 * (y * (x / z))
	elif x <= 40000000000.0:
		tmp = (y / z) * ((1.0 / x) + (x * 0.5))
	else:
		tmp = (y * x) * (0.5 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+101)
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	elseif (x <= 40000000000.0)
		tmp = Float64(Float64(y / z) * Float64(Float64(1.0 / x) + Float64(x * 0.5)));
	else
		tmp = Float64(Float64(y * x) * Float64(0.5 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+101)
		tmp = 0.5 * (y * (x / z));
	elseif (x <= 40000000000.0)
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	else
		tmp = (y * x) * (0.5 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+101], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 40000000000.0], N[(N[(y / z), $MachinePrecision] * N[(N[(1.0 / x), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e101

   1. Initial program 67.4%

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

      1. associate-*r/ 60.5%

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

   3. Simplified 60.5%

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

   4. Taylor expanded in x around 0 44.1%

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

   5. Taylor expanded in x around inf 44.1%

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

      1. associate-*l/ 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -2.1e101 < x < 4e10

   1. Initial program 91.3%

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

      1. associate-/l* 90.0%

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

      2. associate-/r/ 93.6%

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

      3. associate-*l/ 88.9%

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

      4. *-commutative 88.9%

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

   3. Simplified 88.9%

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

      1. associate-/l* 93.9%

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

      2. associate-/r/ 94.6%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in x around 0 85.5%

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

   if 4e10 < x

   1. Initial program 82.1%

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

      1. associate-*r/ 69.6%

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

   3. Simplified 69.6%

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

   4. Taylor expanded in x around 0 55.3%

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

   5. Taylor expanded in x around inf 55.3%

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

      1. associate-*r/ 55.3%

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

      2. *-commutative 55.3%

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

   7. Simplified 55.3%

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

      1. div-inv 55.3%

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

      2. associate-*r* 55.3%

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

      3. associate-*r* 53.6%

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

      4. div-inv 53.6%

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

      5. clear-num 53.6%

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

      6. un-div-inv 53.6%

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

      7. remove-double-neg 53.6%

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

      8. remove-double-neg 53.6%

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

      9. distribute-frac-neg 53.6%

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

      10. frac-2neg 53.6%

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

      11. associate-*r/ 53.6%

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

      12. div-inv 53.6%

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

      13. times-frac 55.3%

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

      14. add-sqr-sqrt 31.2%

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

      15. sqrt-unprod 27.7%

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

      16. sqr-neg 27.7%

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

      17. sqrt-unprod 0.2%

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

      18. add-sqr-sqrt 0.3%

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

      19. add-sqr-sqrt 0.2%

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

      20. sqrt-unprod 31.2%

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

      21. sqr-neg 31.2%

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

      22. sqrt-unprod 29.3%

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

      23. add-sqr-sqrt 55.3%

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

   9. Applied egg-rr 55.3%

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

   10. Taylor expanded in z around 0 55.3%

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

       1. associate-*r/ 55.3%

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

       2. *-commutative 55.3%

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

       3. associate-*l/ 55.3%

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

   12. Simplified 55.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 40000000000:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{0.5}{z}\\ \end{array} \]

Alternative 6: 65.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(y \cdot x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.1e+101)
   (* 0.5 (* y (/ x z)))
   (if (<= x 4.2e-302)
     (* (/ y z) (+ (/ 1.0 x) (* x 0.5)))
     (/ (+ (/ y x) (* 0.5 (* y x))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+101) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 4.2e-302) {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	} else {
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.1d+101)) then
        tmp = 0.5d0 * (y * (x / z))
    else if (x <= 4.2d-302) then
        tmp = (y / z) * ((1.0d0 / x) + (x * 0.5d0))
    else
        tmp = ((y / x) + (0.5d0 * (y * x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.1e+101) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 4.2e-302) {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	} else {
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.1e+101:
		tmp = 0.5 * (y * (x / z))
	elif x <= 4.2e-302:
		tmp = (y / z) * ((1.0 / x) + (x * 0.5))
	else:
		tmp = ((y / x) + (0.5 * (y * x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.1e+101)
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	elseif (x <= 4.2e-302)
		tmp = Float64(Float64(y / z) * Float64(Float64(1.0 / x) + Float64(x * 0.5)));
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(y * x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.1e+101)
		tmp = 0.5 * (y * (x / z));
	elseif (x <= 4.2e-302)
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	else
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.1e+101], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e-302], N[(N[(y / z), $MachinePrecision] * N[(N[(1.0 / x), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e101

   1. Initial program 67.4%

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

      1. associate-*r/ 60.5%

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

   3. Simplified 60.5%

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

   4. Taylor expanded in x around 0 44.1%

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

   5. Taylor expanded in x around inf 44.1%

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

      1. associate-*l/ 55.2%

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

      2. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -2.1e101 < x < 4.20000000000000026e-302

   1. Initial program 86.2%

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

      1. associate-/l* 83.8%

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

      2. associate-/r/ 93.3%

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

      3. associate-*l/ 86.5%

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

      4. *-commutative 86.5%

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

   3. Simplified 86.5%

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

      1. associate-/l* 93.2%

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

      2. associate-/r/ 94.4%

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

   5. Applied egg-rr 94.4%

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

   6. Taylor expanded in x around 0 81.7%

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

   if 4.20000000000000026e-302 < x

   1. Initial program 90.9%

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

      1. associate-*r/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around 0 73.2%

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

      1. frac-2neg 73.2%

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

      2. div-inv 73.2%

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

      3. *-commutative 73.2%

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

      4. distribute-rgt-neg-in 73.2%

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

   6. Applied egg-rr 73.2%

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

      1. associate-*r/ 73.2%

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

      2. *-rgt-identity 73.2%

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

      3. distribute-rgt-neg-out 73.2%

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

      4. distribute-neg-frac 73.2%

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

      5. associate-/l* 72.4%

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

      6. distribute-neg-frac 72.4%

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

   8. Simplified 72.4%

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

   9. Taylor expanded in z around 0 76.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+101}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(y \cdot x\right)}{z}\\ \end{array} \]

Alternative 7: 66.0% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{1}{x \cdot z}\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(y \cdot x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e-8)
   (* y (+ (* 0.5 (/ x z)) (/ 1.0 (* x z))))
   (if (<= x 1.85e-301) (/ (/ y z) x) (/ (+ (/ y x) (* 0.5 (* y x))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e-8) {
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)));
	} else if (x <= 1.85e-301) {
		tmp = (y / z) / x;
	} else {
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2d-8)) then
        tmp = y * ((0.5d0 * (x / z)) + (1.0d0 / (x * z)))
    else if (x <= 1.85d-301) then
        tmp = (y / z) / x
    else
        tmp = ((y / x) + (0.5d0 * (y * x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e-8) {
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)));
	} else if (x <= 1.85e-301) {
		tmp = (y / z) / x;
	} else {
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e-8:
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)))
	elif x <= 1.85e-301:
		tmp = (y / z) / x
	else:
		tmp = ((y / x) + (0.5 * (y * x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e-8)
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(1.0 / Float64(x * z))));
	elseif (x <= 1.85e-301)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(y * x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e-8)
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)));
	elseif (x <= 1.85e-301)
		tmp = (y / z) / x;
	else
		tmp = ((y / x) + (0.5 * (y * x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e-8], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-301], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e-8

   1. Initial program 76.9%

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

      1. associate-*r/ 70.8%

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

   3. Simplified 70.8%

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

   4. Taylor expanded in x around 0 43.8%

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

   5. Taylor expanded in y around 0 49.7%

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

   if -2e-8 < x < 1.8499999999999999e-301

   1. Initial program 83.2%

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

      1. associate-*r/ 83.2%

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

   3. Simplified 83.2%

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

      1. associate-*r/ 83.2%

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

      2. associate-*l/ 83.0%

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

      3. *-commutative 83.0%

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

      4. associate-*l/ 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in x around 0 95.7%

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

   if 1.8499999999999999e-301 < x

   1. Initial program 90.9%

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

      1. associate-*r/ 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in x around 0 73.2%

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

      1. frac-2neg 73.2%

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

      2. div-inv 73.2%

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

      3. *-commutative 73.2%

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

      4. distribute-rgt-neg-in 73.2%

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

   6. Applied egg-rr 73.2%

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

      1. associate-*r/ 73.2%

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

      2. *-rgt-identity 73.2%

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

      3. distribute-rgt-neg-out 73.2%

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

      4. distribute-neg-frac 73.2%

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

      5. associate-/l* 72.4%

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

      6. distribute-neg-frac 72.4%

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

   8. Simplified 72.4%

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

   9. Taylor expanded in z around 0 76.4%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{1}{x \cdot z}\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(y \cdot x\right)}{z}\\ \end{array} \]

Alternative 8: 66.3% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e-53)
   (+ (* 0.5 (/ (* y x) z)) (/ y (* x z)))
   (* (/ y z) (+ (/ 1.0 x) (* x 0.5)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-53) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	}
	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 <= (-7.5d-53)) then
        tmp = (0.5d0 * ((y * x) / z)) + (y / (x * z))
    else
        tmp = (y / z) * ((1.0d0 / x) + (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e-53) {
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	} else {
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e-53:
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z))
	else:
		tmp = (y / z) * ((1.0 / x) + (x * 0.5))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e-53)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / z)) + Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(y / z) * Float64(Float64(1.0 / x) + Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e-53)
		tmp = (0.5 * ((y * x) / z)) + (y / (x * z));
	else
		tmp = (y / z) * ((1.0 / x) + (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e-53], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * N[(N[(1.0 / x), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000001e-53

   1. Initial program 79.5%

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

      1. associate-*r/ 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in x around 0 70.1%

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

   if -7.5000000000000001e-53 < z

   1. Initial program 87.6%

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

      1. associate-/l* 83.2%

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

      2. associate-/r/ 90.6%

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

      3. associate-*l/ 81.5%

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

      4. *-commutative 81.5%

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

   3. Simplified 81.5%

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

      1. associate-/l* 90.6%

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

      2. associate-/r/ 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{\left(0.5 \cdot x + \frac{1}{x}\right)} \cdot \frac{y}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-53}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot \left(\frac{1}{x} + x \cdot 0.5\right)\\ \end{array} \]

Alternative 9: 65.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 3.9 \cdot 10^{-5}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.42) (not (<= x 3.9e-5)))
   (* 0.5 (* y (/ x z)))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42) || !(x <= 3.9e-5)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.42d0)) .or. (.not. (x <= 3.9d-5))) then
        tmp = 0.5d0 * (y * (x / z))
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42) || !(x <= 3.9e-5)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.42) or not (x <= 3.9e-5):
		tmp = 0.5 * (y * (x / z))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.42) || !(x <= 3.9e-5))
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.42) || ~((x <= 3.9e-5)))
		tmp = 0.5 * (y * (x / z));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.42], N[Not[LessEqual[x, 3.9e-5]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4199999999999999 or 3.8999999999999999e-5 < x

   1. Initial program 80.0%

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

      1. associate-*r/ 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in x around 0 48.5%

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

   5. Taylor expanded in x around inf 48.5%

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

      1. associate-*l/ 50.8%

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

      2. *-commutative 50.8%

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

   7. Simplified 50.8%

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

   if -1.4199999999999999 < x < 3.8999999999999999e-5

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

   3. Simplified 90.4%

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

      1. associate-*r/ 90.4%

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

      2. associate-*l/ 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*l/ 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in x around 0 95.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 3.9 \cdot 10^{-5}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 10: 66.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{0.5}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.42)
   (* 0.5 (* y (/ x z)))
   (if (<= x 3.9e-5) (/ (/ y z) x) (* (* y x) (/ 0.5 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 3.9e-5) {
		tmp = (y / z) / x;
	} else {
		tmp = (y * x) * (0.5 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.42d0)) then
        tmp = 0.5d0 * (y * (x / z))
    else if (x <= 3.9d-5) then
        tmp = (y / z) / x
    else
        tmp = (y * x) * (0.5d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 3.9e-5) {
		tmp = (y / z) / x;
	} else {
		tmp = (y * x) * (0.5 / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.42:
		tmp = 0.5 * (y * (x / z))
	elif x <= 3.9e-5:
		tmp = (y / z) / x
	else:
		tmp = (y * x) * (0.5 / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.42)
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	elseif (x <= 3.9e-5)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(Float64(y * x) * Float64(0.5 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.42)
		tmp = 0.5 * (y * (x / z));
	elseif (x <= 3.9e-5)
		tmp = (y / z) / x;
	else
		tmp = (y * x) * (0.5 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.42], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e-5], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4199999999999999

   1. Initial program 76.6%

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

      1. associate-*r/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in x around 0 43.0%

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

   5. Taylor expanded in x around inf 43.0%

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

      1. associate-*l/ 48.9%

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

      2. *-commutative 48.9%

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

   7. Simplified 48.9%

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

   if -1.4199999999999999 < x < 3.8999999999999999e-5

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

   3. Simplified 90.4%

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

      1. associate-*r/ 90.4%

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

      2. associate-*l/ 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-*l/ 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in x around 0 95.0%

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

   if 3.8999999999999999e-5 < x

   1. Initial program 83.6%

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

      1. associate-*r/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in x around 0 54.4%

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

   5. Taylor expanded in x around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. *-commutative 54.4%

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

   7. Simplified 54.4%

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

      1. div-inv 54.4%

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

      2. associate-*r* 54.4%

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

      3. associate-*r* 52.8%

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

      4. div-inv 52.8%

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

      5. clear-num 52.8%

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

      6. un-div-inv 52.8%

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

      7. remove-double-neg 52.8%

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

      8. remove-double-neg 52.8%

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

      9. distribute-frac-neg 52.8%

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

      10. frac-2neg 52.8%

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

      11. associate-*r/ 52.8%

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

      12. div-inv 52.8%

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

      13. times-frac 54.4%

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

      14. add-sqr-sqrt 32.2%

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

      15. sqrt-unprod 30.4%

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

      16. sqr-neg 30.4%

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

      17. sqrt-unprod 0.2%

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

      18. add-sqr-sqrt 2.0%

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

      19. add-sqr-sqrt 0.2%

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

      20. sqrt-unprod 30.4%

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

      21. sqr-neg 30.4%

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

      22. sqrt-unprod 28.6%

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

      23. add-sqr-sqrt 54.4%

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

   9. Applied egg-rr 54.4%

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

   10. Taylor expanded in z around 0 54.4%

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

       1. associate-*r/ 54.4%

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

       2. *-commutative 54.4%

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

       3. associate-*l/ 54.4%

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

   12. Simplified 54.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{0.5}{z}\\ \end{array} \]

Alternative 11: 52.6% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-130} \lor \neg \left(z \leq 3.8\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-130) (not (<= z 3.8))) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-130) || !(z <= 3.8)) {
		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 ((z <= (-5d-130)) .or. (.not. (z <= 3.8d0))) 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 ((z <= -5e-130) || !(z <= 3.8)) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-130) or not (z <= 3.8):
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-130) || !(z <= 3.8))
		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 ((z <= -5e-130) || ~((z <= 3.8)))
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-130], N[Not[LessEqual[z, 3.8]], $MachinePrecision]], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999996e-130 or 3.7999999999999998 < z

   1. Initial program 80.1%

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

      1. associate-*r/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in x around 0 52.7%

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

   if -4.9999999999999996e-130 < z < 3.7999999999999998

   1. Initial program 91.9%

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

      1. associate-*l/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around 0 57.3%

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

      1. associate-*l/ 57.4%

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

      2. *-un-lft-identity 57.4%

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

   6. Applied egg-rr 57.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-130} \lor \neg \left(z \leq 3.8\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 12: 55.5% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -40000000:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -40000000.0) (/ y (* x z)) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -40000000.0) {
		tmp = y / (x * z);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-40000000.0d0)) then
        tmp = y / (x * z)
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -40000000.0) {
		tmp = y / (x * z);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -40000000.0:
		tmp = y / (x * z)
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -40000000.0)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -40000000.0)
		tmp = y / (x * z);
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -40000000.0], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e7

   1. Initial program 77.4%

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

      1. associate-*r/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in x around 0 55.6%

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

   if -4e7 < z

   1. Initial program 87.7%

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

      1. associate-*r/ 83.7%

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

   3. Simplified 83.7%

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

      1. associate-*r/ 87.7%

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

      2. associate-*l/ 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-*l/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 63.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -40000000:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 13: 49.5% 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 85.3%

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

   1. associate-*r/ 81.0%

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

3. Simplified 81.0%

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

4. Taylor expanded in x around 0 49.3%

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

5. Final simplification 49.3%

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

Developer target: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{if}\;y < -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ (/ y z) x) (cosh x))))
   (if (< y -4.618902267687042e-52)
     t_0
     (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / z) / x) * cosh(x)
    if (y < (-4.618902267687042d-52)) then
        tmp = t_0
    else if (y < 1.038530535935153d-39) then
        tmp = ((cosh(x) * y) / x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / z) / x) * Math.cosh(x);
	double tmp;
	if (y < -4.618902267687042e-52) {
		tmp = t_0;
	} else if (y < 1.038530535935153e-39) {
		tmp = ((Math.cosh(x) * y) / x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / z) / x) * math.cosh(x)
	tmp = 0
	if y < -4.618902267687042e-52:
		tmp = t_0
	elif y < 1.038530535935153e-39:
		tmp = ((math.cosh(x) * y) / x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / z) / x) * cosh(x))
	tmp = 0.0
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = Float64(Float64(Float64(cosh(x) * y) / x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / z) / x) * cosh(x);
	tmp = 0.0;
	if (y < -4.618902267687042e-52)
		tmp = t_0;
	elseif (y < 1.038530535935153e-39)
		tmp = ((cosh(x) * y) / x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] * N[Cosh[x], $MachinePrecision]), $MachinePrecision]}, If[Less[y, -4.618902267687042e-52], t$95$0, If[Less[y, 1.038530535935153e-39], N[(N[(N[(N[Cosh[x], $MachinePrecision] * y), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023306 
(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))