Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.8% → 97.4%

Time: 9.4s

Alternatives: 15

Speedup: 1.0×

• 65.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+75) (/ (cosh x) (* x (/ z y))) (/ (* y (/ (cosh x) x)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+75) {
		tmp = cosh(x) / (x * (z / y));
	} else {
		tmp = (y * (cosh(x) / x)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.5d+75)) then
        tmp = cosh(x) / (x * (z / y))
    else
        tmp = (y * (cosh(x) / x)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+75) {
		tmp = Math.cosh(x) / (x * (z / y));
	} else {
		tmp = (y * (Math.cosh(x) / x)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+75:
		tmp = math.cosh(x) / (x * (z / y))
	else:
		tmp = (y * (math.cosh(x) / x)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+75)
		tmp = Float64(cosh(x) / Float64(x * Float64(z / y)));
	else
		tmp = Float64(Float64(y * Float64(cosh(x) / x)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+75)
		tmp = cosh(x) / (x * (z / y));
	else
		tmp = (y * (cosh(x) / x)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+75], N[(N[Cosh[x], $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000004e75

   1. Initial program 85.7%

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

      1. associate-/l* 85.7%

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

      2. associate-/r/ 99.8%

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

   3. Simplified 99.8%

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

   if -4.5000000000000004e75 < y

   1. Initial program 84.7%

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

      1. *-commutative 84.7%

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

      2. associate-*r/ 84.7%

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

   3. Simplified 84.7%

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

      1. frac-times 81.8%

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

      2. associate-*r/ 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-/r* 93.8%

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

      5. associate-*l/ 98.0%

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

   5. Applied egg-rr 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{x}}{z}\\ \end{array} \]

Alternative 2: 92.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((Math.cosh(x) * (y / x)) <= Double.POSITIVE_INFINITY) {
		tmp = (y / x) * (Math.cosh(x) / z);
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (math.cosh(x) * (y / x)) <= math.inf:
		tmp = (y / x) * (math.cosh(x) / z)
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < +inf.0

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   if +inf.0 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 0.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 70.4%

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

      3. associate-*l/ 70.4%

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

      4. *-commutative 70.4%

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

      5. *-commutative 70.4%

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

   3. Simplified 70.4%

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

4. Final simplification 92.3%

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

Alternative 3: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-35} \lor \neg \left(z \leq 2.8 \cdot 10^{-87}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-35) (not (<= z 2.8e-87)))
   (* y (/ (cosh x) (* x z)))
   (* (cosh x) (/ (/ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-35) || !(z <= 2.8e-87)) {
		tmp = y * (cosh(x) / (x * z));
	} else {
		tmp = cosh(x) * ((y / z) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4d-35)) .or. (.not. (z <= 2.8d-87))) then
        tmp = y * (cosh(x) / (x * z))
    else
        tmp = cosh(x) * ((y / z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-35) || !(z <= 2.8e-87)) {
		tmp = y * (Math.cosh(x) / (x * z));
	} else {
		tmp = Math.cosh(x) * ((y / z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-35) or not (z <= 2.8e-87):
		tmp = y * (math.cosh(x) / (x * z))
	else:
		tmp = math.cosh(x) * ((y / z) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-35) || !(z <= 2.8e-87))
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	else
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4e-35) || ~((z <= 2.8e-87)))
		tmp = y * (cosh(x) / (x * z));
	else
		tmp = cosh(x) * ((y / z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-35], N[Not[LessEqual[z, 2.8e-87]], $MachinePrecision]], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000003e-35 or 2.8000000000000001e-87 < z

   1. Initial program 80.1%

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

      1. associate-*r/ 92.0%

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

      2. associate-/l/ 81.6%

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

      3. associate-*l/ 81.6%

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

      4. *-commutative 81.6%

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

      5. *-commutative 81.6%

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

   3. Simplified 81.6%

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

   if -4.00000000000000003e-35 < z < 2.8000000000000001e-87

   1. Initial program 91.0%

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

      1. associate-*r/ 91.0%

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

      2. associate-/l/ 89.7%

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

      3. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-35} \lor \neg \left(z \leq 2.8 \cdot 10^{-87}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 4: 83.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. associate-*r/ 95.5%

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

   2. associate-/l/ 85.2%

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

   3. associate-*l/ 84.9%

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

   4. *-commutative 84.9%

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

   5. *-commutative 84.9%

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

3. Simplified 84.9%

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

4. Final simplification 84.9%

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

Alternative 5: 67.9% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x \cdot z}\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{-76}:\\ \;\;\;\;t_0 + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \frac{z}{x} + z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (* x z))))
   (if (<= z -8.4e-76)
     (+ t_0 (* 0.5 (/ (* y x) z)))
     (if (<= z -5.1e-174)
       (/ (+ (* (/ y x) (/ z x)) (* z (* y 0.5))) (* z (/ z x)))
       (+ t_0 (* 0.5 (* y (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (z <= -8.4e-76) {
		tmp = t_0 + (0.5 * ((y * x) / z));
	} else if (z <= -5.1e-174) {
		tmp = (((y / x) * (z / x)) + (z * (y * 0.5))) / (z * (z / x));
	} else {
		tmp = t_0 + (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) :: t_0
    real(8) :: tmp
    t_0 = y / (x * z)
    if (z <= (-8.4d-76)) then
        tmp = t_0 + (0.5d0 * ((y * x) / z))
    else if (z <= (-5.1d-174)) then
        tmp = (((y / x) * (z / x)) + (z * (y * 0.5d0))) / (z * (z / x))
    else
        tmp = t_0 + (0.5d0 * (y * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (z <= -8.4e-76) {
		tmp = t_0 + (0.5 * ((y * x) / z));
	} else if (z <= -5.1e-174) {
		tmp = (((y / x) * (z / x)) + (z * (y * 0.5))) / (z * (z / x));
	} else {
		tmp = t_0 + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (x * z)
	tmp = 0
	if z <= -8.4e-76:
		tmp = t_0 + (0.5 * ((y * x) / z))
	elif z <= -5.1e-174:
		tmp = (((y / x) * (z / x)) + (z * (y * 0.5))) / (z * (z / x))
	else:
		tmp = t_0 + (0.5 * (y * (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(x * z))
	tmp = 0.0
	if (z <= -8.4e-76)
		tmp = Float64(t_0 + Float64(0.5 * Float64(Float64(y * x) / z)));
	elseif (z <= -5.1e-174)
		tmp = Float64(Float64(Float64(Float64(y / x) * Float64(z / x)) + Float64(z * Float64(y * 0.5))) / Float64(z * Float64(z / x)));
	else
		tmp = Float64(t_0 + Float64(0.5 * Float64(y * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (x * z);
	tmp = 0.0;
	if (z <= -8.4e-76)
		tmp = t_0 + (0.5 * ((y * x) / z));
	elseif (z <= -5.1e-174)
		tmp = (((y / x) * (z / x)) + (z * (y * 0.5))) / (z * (z / x));
	else
		tmp = t_0 + (0.5 * (y * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.4e-76], N[(t$95$0 + N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.1e-174], N[(N[(N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.39999999999999969e-76

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*r/ 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in x around 0 54.1%

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

   if -8.39999999999999969e-76 < z < -5.10000000000000032e-174

   1. Initial program 95.1%

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

      1. *-commutative 95.1%

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

      2. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around 0 59.4%

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

      1. +-commutative 59.4%

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

      2. associate-/l* 63.7%

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

      3. *-commutative 63.7%

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

   6. Simplified 63.7%

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

      1. +-commutative 63.7%

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

      2. associate-/r* 77.4%

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

      3. associate-*r/ 77.4%

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

      4. frac-add 90.6%

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

   8. Applied egg-rr 90.6%

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

   if -5.10000000000000032e-174 < z

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*r/ 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around 0 70.6%

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

      1. +-commutative 70.6%

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

      2. associate-/l* 74.1%

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

      3. *-commutative 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 74.7%

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

   9. Simplified 74.7%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \frac{z}{x} + z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 6: 65.5% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-258} \lor \neg \left(y \leq 1.5 \cdot 10^{-292}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e-258) (not (<= y 1.5e-292)))
   (+ (/ y (* x z)) (* 0.5 (* y (/ x z))))
   (/ (* y (+ (* x 0.5) (/ 1.0 x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e-258) || !(y <= 1.5e-292)) {
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)));
	} else {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.2d-258)) .or. (.not. (y <= 1.5d-292))) then
        tmp = (y / (x * z)) + (0.5d0 * (y * (x / z)))
    else
        tmp = (y * ((x * 0.5d0) + (1.0d0 / x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e-258) || !(y <= 1.5e-292)) {
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)));
	} else {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e-258) or not (y <= 1.5e-292):
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)))
	else:
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e-258) || !(y <= 1.5e-292))
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(y * Float64(x / z))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * 0.5) + Float64(1.0 / x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e-258) || ~((y <= 1.5e-292)))
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)));
	else
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e-258], N[Not[LessEqual[y, 1.5e-292]], $MachinePrecision]], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * 0.5), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999998e-258 or 1.50000000000000008e-292 < y

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around 0 68.4%

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

      1. +-commutative 68.4%

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

      2. associate-/l* 70.0%

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

      3. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in y around 0 68.4%

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

      1. associate-*r/ 70.4%

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

   9. Simplified 70.4%

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

   if -4.1999999999999998e-258 < y < 1.50000000000000008e-292

   1. Initial program 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*r/ 61.1%

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

   3. Simplified 61.1%

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

      1. frac-times 50.5%

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

      2. associate-*r/ 46.5%

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

      3. *-commutative 46.5%

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

      4. associate-/r* 57.6%

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

      5. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 56.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-258} \lor \neg \left(y \leq 1.5 \cdot 10^{-292}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \end{array} \]

Alternative 7: 67.0% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x \cdot z}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+102}:\\ \;\;\;\;t_0 + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0 + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (* x z))))
   (if (<= y -2.5e+102)
     (+ t_0 (* 0.5 (/ (* y x) z)))
     (if (<= y 8e-295)
       (/ (* y (+ (* x 0.5) (/ 1.0 x))) z)
       (+ t_0 (* 0.5 (* y (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (y <= -2.5e+102) {
		tmp = t_0 + (0.5 * ((y * x) / z));
	} else if (y <= 8e-295) {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	} else {
		tmp = t_0 + (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) :: t_0
    real(8) :: tmp
    t_0 = y / (x * z)
    if (y <= (-2.5d+102)) then
        tmp = t_0 + (0.5d0 * ((y * x) / z))
    else if (y <= 8d-295) then
        tmp = (y * ((x * 0.5d0) + (1.0d0 / x))) / z
    else
        tmp = t_0 + (0.5d0 * (y * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (y <= -2.5e+102) {
		tmp = t_0 + (0.5 * ((y * x) / z));
	} else if (y <= 8e-295) {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	} else {
		tmp = t_0 + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (x * z)
	tmp = 0
	if y <= -2.5e+102:
		tmp = t_0 + (0.5 * ((y * x) / z))
	elif y <= 8e-295:
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z
	else:
		tmp = t_0 + (0.5 * (y * (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(x * z))
	tmp = 0.0
	if (y <= -2.5e+102)
		tmp = Float64(t_0 + Float64(0.5 * Float64(Float64(y * x) / z)));
	elseif (y <= 8e-295)
		tmp = Float64(Float64(y * Float64(Float64(x * 0.5) + Float64(1.0 / x))) / z);
	else
		tmp = Float64(t_0 + Float64(0.5 * Float64(y * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (x * z);
	tmp = 0.0;
	if (y <= -2.5e+102)
		tmp = t_0 + (0.5 * ((y * x) / z));
	elseif (y <= 8e-295)
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	else
		tmp = t_0 + (0.5 * (y * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+102], N[(t$95$0 + N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-295], N[(N[(y * N[(N[(x * 0.5), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(t$95$0 + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5e102

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r/ 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around 0 87.9%

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

   if -2.5e102 < y < 8.00000000000000048e-295

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-*r/ 83.0%

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

   3. Simplified 83.0%

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

      1. frac-times 77.1%

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

      2. associate-*r/ 76.2%

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

      3. *-commutative 76.2%

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

      4. associate-/r* 89.6%

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

      5. associate-*l/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 55.6%

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

   if 8.00000000000000048e-295 < y

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. associate-*r/ 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around 0 68.5%

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

      1. +-commutative 68.5%

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

      2. associate-/l* 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   7. Taylor expanded in y around 0 68.5%

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

      1. associate-*r/ 72.3%

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

   9. Simplified 72.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 8: 65.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{1}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.1e+97) (/ (* y (+ (* x 0.5) (/ 1.0 x))) z) (* y (/ (/ 1.0 x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.1e+97) {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	} else {
		tmp = y * ((1.0 / 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 <= 2.1d+97) then
        tmp = (y * ((x * 0.5d0) + (1.0d0 / x))) / z
    else
        tmp = y * ((1.0d0 / x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.1e+97) {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	} else {
		tmp = y * ((1.0 / x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.1e+97:
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z
	else:
		tmp = y * ((1.0 / x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.1e+97)
		tmp = Float64(Float64(y * Float64(Float64(x * 0.5) + Float64(1.0 / x))) / z);
	else
		tmp = Float64(y * Float64(Float64(1.0 / x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.1e+97)
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	else
		tmp = y * ((1.0 / x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.1e+97], N[(N[(y * N[(N[(x * 0.5), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * N[(N[(1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.10000000000000012e97

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*r/ 86.9%

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

   3. Simplified 86.9%

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

      1. frac-times 87.8%

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

      2. associate-*r/ 87.5%

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

      3. *-commutative 87.5%

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

      4. associate-/r* 94.2%

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

      5. associate-*l/ 96.9%

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

   5. Applied egg-rr 96.9%

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

   6. Taylor expanded in x around 0 68.6%

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

   if 2.10000000000000012e97 < z

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

      2. associate-*r/ 72.8%

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

   3. Simplified 72.8%

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

   4. Taylor expanded in x around 0 55.9%

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

      1. *-commutative 55.9%

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

      2. associate-/r* 42.9%

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

      3. div-inv 42.9%

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

      4. *-un-lft-identity 42.9%

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

      5. times-frac 56.0%

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

   6. Applied egg-rr 56.0%

      \[\leadsto \color{blue}{\frac{y}{1} \cdot \frac{\frac{1}{x}}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.1 \cdot 10^{+97}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{1}{x}}{z}\\ \end{array} \]

Alternative 9: 65.1% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e+102)
   (/ (- (/ 1.0 x) (* x -0.5)) (/ z y))
   (/ (* y (+ (* x 0.5) (/ 1.0 x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+102) {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	} else {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.5d+102)) then
        tmp = ((1.0d0 / x) - (x * (-0.5d0))) / (z / y)
    else
        tmp = (y * ((x * 0.5d0) + (1.0d0 / x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e+102) {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	} else {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e+102:
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y)
	else:
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e+102)
		tmp = Float64(Float64(Float64(1.0 / x) - Float64(x * -0.5)) / Float64(z / y));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * 0.5) + Float64(1.0 / x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e+102)
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	else
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e+102], N[(N[(N[(1.0 / x), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * 0.5), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e102

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r/ 84.3%

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

   3. Simplified 84.3%

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

      1. frac-times 97.7%

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

      2. associate-*r/ 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-/r* 99.8%

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

      5. associate-*l/ 84.3%

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

   5. Applied egg-rr 84.3%

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

   6. Taylor expanded in x around 0 72.3%

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

      1. associate-*r* 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r* 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in y around -inf 72.4%

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

       1. mul-1-neg 72.4%

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

       2. associate-/l* 85.9%

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

       3. *-commutative 85.9%

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

   11. Simplified 85.9%

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

   if -8.4999999999999996e102 < y

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*r/ 85.1%

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

   3. Simplified 85.1%

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

      1. frac-times 82.3%

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

      2. associate-*r/ 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-/r* 93.9%

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

      5. associate-*l/ 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in x around 0 63.4%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \end{array} \]

Alternative 10: 65.2% accurate, 8.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * ((0.5d0 * (x / z)) - ((-1.0d0) / (x * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. associate-*r/ 95.5%

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

   2. associate-/l/ 85.2%

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

   3. associate-*l/ 84.9%

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

   4. *-commutative 84.9%

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

   5. *-commutative 84.9%

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

3. Simplified 84.9%

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

4. Taylor expanded in x around 0 66.4%

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

5. Final simplification 66.4%

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

Alternative 11: 61.4% accurate, 9.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*r/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in x around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. associate-/l* 43.4%

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

      3. *-commutative 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in x around inf 40.5%

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

      1. associate-*r/ 40.5%

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

      2. associate-*r* 40.5%

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

      3. *-commutative 40.5%

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

      4. associate-*r* 40.5%

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

   9. Simplified 40.5%

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

       1. associate-*l* 40.5%

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

       2. *-un-lft-identity 40.5%

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

       3. times-frac 38.4%

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

       4. /-rgt-identity 38.4%

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

   11. Applied egg-rr 38.4%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-*r/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 90.5%

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

      1. associate-*l/ 92.4%

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

      2. div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

4. Final simplification 64.8%

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

Alternative 12: 65.5% accurate, 9.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*r/ 79.4%

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

   3. Simplified 79.4%

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

   4. Taylor expanded in x around 0 40.5%

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

      1. +-commutative 40.5%

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

      2. associate-/l* 43.4%

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

      3. *-commutative 43.4%

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

   6. Simplified 43.4%

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

   7. Taylor expanded in x around inf 40.5%

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

      1. associate-*r/ 40.5%

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

      2. associate-*r* 40.5%

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

      3. *-commutative 40.5%

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

      4. associate-*r* 40.5%

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

   9. Simplified 40.5%

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

       1. *-commutative 40.5%

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

       2. *-un-lft-identity 40.5%

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

       3. times-frac 44.1%

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

       4. /-rgt-identity 44.1%

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

   11. Applied egg-rr 44.1%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-*r/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 90.5%

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

      1. associate-*l/ 92.4%

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

      2. div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

4. Final simplification 67.7%

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

Alternative 13: 55.4% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-68} \lor \neg \left(y \leq 6.8 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.6e-68) (not (<= y 6.8e-146))) (/ (/ y z) x) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.6e-68) || !(y <= 6.8e-146)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9.6d-68)) .or. (.not. (y <= 6.8d-146))) then
        tmp = (y / z) / x
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.6e-68) || !(y <= 6.8e-146)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.6e-68) or not (y <= 6.8e-146):
		tmp = (y / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.6e-68) || !(y <= 6.8e-146))
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.6e-68) || ~((y <= 6.8e-146)))
		tmp = (y / z) / x;
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.6e-68], N[Not[LessEqual[y, 6.8e-146]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.59999999999999965e-68 or 6.8000000000000001e-146 < y

   1. Initial program 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*r/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 47.7%

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

      1. associate-*l/ 61.1%

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

      2. div-inv 61.1%

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

   6. Applied egg-rr 61.1%

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

   if -9.59999999999999965e-68 < y < 6.8000000000000001e-146

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*r/ 71.7%

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

   3. Simplified 71.7%

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

      1. frac-times 74.6%

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

      2. associate-*r/ 73.7%

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

      3. *-commutative 73.7%

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

      4. associate-/r* 87.2%

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

      5. associate-*l/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 37.8%

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

      1. associate-/l/ 49.6%

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

   8. Simplified 49.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-68} \lor \neg \left(y \leq 6.8 \cdot 10^{-146}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 14: 49.8% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e-125) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e-125) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.8d-125)) then
        tmp = y / (x * z)
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e-125) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.8e-125:
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e-125)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.8e-125)
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e-125], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999995e-125

   1. Initial program 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r/ 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 52.5%

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

   if -6.7999999999999995e-125 < y

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-*r/ 82.1%

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

   3. Simplified 82.1%

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

      1. frac-times 81.0%

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

      2. associate-*r/ 80.5%

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

      3. *-commutative 80.5%

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

      4. associate-/r* 92.2%

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

      5. associate-*l/ 97.6%

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

   5. Applied egg-rr 97.6%

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

   6. Taylor expanded in x around 0 45.6%

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

      1. associate-/l/ 50.4%

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

   8. Simplified 50.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 15: 48.4% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. *-commutative 84.9%

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

   2. associate-*r/ 84.9%

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

3. Simplified 84.9%

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

4. Taylor expanded in x around 0 48.1%

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

5. Final simplification 48.1%

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

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023174 
(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))