Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 85.6% → 98.6%

Time: 11.9s

Alternatives: 16

Speedup: 1.0×

• 64.8% 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: 85.6% 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: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-94} \lor \neg \left(z \leq 1.9 \cdot 10^{-82}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e-94) (not (<= z 1.9e-82)))
   (* y (/ (/ (cosh x) z) x))
   (/ (cosh x) (* x (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-94) || !(z <= 1.9e-82)) {
		tmp = y * ((cosh(x) / z) / x);
	} else {
		tmp = cosh(x) / (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1d-94)) .or. (.not. (z <= 1.9d-82))) then
        tmp = y * ((cosh(x) / z) / x)
    else
        tmp = cosh(x) / (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-94) || !(z <= 1.9e-82)) {
		tmp = y * ((Math.cosh(x) / z) / x);
	} else {
		tmp = Math.cosh(x) / (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e-94) or not (z <= 1.9e-82):
		tmp = y * ((math.cosh(x) / z) / x)
	else:
		tmp = math.cosh(x) / (x * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e-94) || !(z <= 1.9e-82))
		tmp = Float64(y * Float64(Float64(cosh(x) / z) / x));
	else
		tmp = Float64(cosh(x) / Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e-94) || ~((z <= 1.9e-82)))
		tmp = y * ((cosh(x) / z) / x);
	else
		tmp = cosh(x) / (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e-94], N[Not[LessEqual[z, 1.9e-82]], $MachinePrecision]], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999996e-95 or 1.9000000000000001e-82 < z

   1. Initial program 81.8%

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

      1. associate-/l* 67.6%

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

      2. associate-/r/ 70.4%

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

      3. *-commutative 70.4%

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

   3. Simplified 70.4%

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

      1. associate-/l/ 88.9%

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

      2. associate-/r/ 96.3%

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

      3. associate-/l* 80.9%

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

      4. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -9.9999999999999996e-95 < z < 1.9000000000000001e-82

   1. Initial program 90.3%

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

      1. associate-/l* 90.2%

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

      2. associate-/r/ 98.8%

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

      3. *-commutative 98.8%

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

   3. Simplified 98.8%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-94} \lor \neg \left(z \leq 1.9 \cdot 10^{-82}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 2: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cosh x \cdot \frac{y}{x}\\ \mathbf{if}\;t_0 \leq 10^{+172}:\\ \;\;\;\;\frac{t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cosh x) (/ y x))))
   (if (<= t_0 1e+172) (/ t_0 z) (* y (/ (/ (cosh x) z) x)))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) * (y / x);
	double tmp;
	if (t_0 <= 1e+172) {
		tmp = t_0 / z;
	} else {
		tmp = y * ((cosh(x) / 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) :: t_0
    real(8) :: tmp
    t_0 = cosh(x) * (y / x)
    if (t_0 <= 1d+172) then
        tmp = t_0 / z
    else
        tmp = y * ((cosh(x) / z) / 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);
	double tmp;
	if (t_0 <= 1e+172) {
		tmp = t_0 / z;
	} else {
		tmp = y * ((Math.cosh(x) / z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) * (y / x)
	tmp = 0
	if t_0 <= 1e+172:
		tmp = t_0 / z
	else:
		tmp = y * ((math.cosh(x) / z) / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) * Float64(y / x))
	tmp = 0.0
	if (t_0 <= 1e+172)
		tmp = Float64(t_0 / z);
	else
		tmp = Float64(y * Float64(Float64(cosh(x) / z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) * (y / x);
	tmp = 0.0;
	if (t_0 <= 1e+172)
		tmp = t_0 / z;
	else
		tmp = y * ((cosh(x) / z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+172], N[(t$95$0 / z), $MachinePrecision], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < 1.0000000000000001e172

   1. Initial program 97.0%

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

   if 1.0000000000000001e172 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 70.8%

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

      1. associate-/l* 59.7%

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

      2. associate-/r/ 72.0%

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

      3. *-commutative 72.0%

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

   3. Simplified 72.0%

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

      1. associate-/l/ 91.4%

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

      2. associate-/r/ 99.9%

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

      3. associate-/l* 69.9%

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

      4. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq 10^{+172}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \end{array} \]

Alternative 3: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0005 \lor \neg \left(x \leq 10^{-38}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.0005) (not (<= x 1e-38)))
   (* y (/ (/ (cosh x) z) x))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.0005) || !(x <= 1e-38)) {
		tmp = y * ((cosh(x) / z) / x);
	} 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 <= (-0.0005d0)) .or. (.not. (x <= 1d-38))) then
        tmp = y * ((cosh(x) / z) / x)
    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 <= -0.0005) || !(x <= 1e-38)) {
		tmp = y * ((Math.cosh(x) / z) / x);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.0005) or not (x <= 1e-38):
		tmp = y * ((math.cosh(x) / z) / x)
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.0005) || !(x <= 1e-38))
		tmp = Float64(y * Float64(Float64(cosh(x) / z) / x));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.0005) || ~((x <= 1e-38)))
		tmp = y * ((cosh(x) / z) / x);
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.0005], N[Not[LessEqual[x, 1e-38]], $MachinePrecision]], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000001e-4 or 9.9999999999999996e-39 < x

   1. Initial program 80.1%

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

      1. associate-/l* 63.8%

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

      2. associate-/r/ 69.5%

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

      3. *-commutative 69.5%

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

   3. Simplified 69.5%

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

      1. associate-/l/ 91.5%

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

      2. associate-/r/ 100.0%

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

      3. associate-/l* 78.0%

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

      4. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   if -5.0000000000000001e-4 < x < 9.9999999999999996e-39

   1. Initial program 90.7%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 90.7%

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

      1. associate-*r/ 94.7%

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

      2. associate-*l/ 94.9%

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

      3. *-un-lft-identity 94.9%

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

   6. Applied egg-rr 94.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0005 \lor \neg \left(x \leq 10^{-38}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 4: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. associate-*l/ 84.9%

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

3. Simplified 84.9%

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

4. Final simplification 84.9%

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

Alternative 5: 72.1% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{\left(x \cdot z\right) \cdot \left(x \cdot 0.5\right) + \frac{y \cdot z}{y}}{\frac{z}{y}}}{x \cdot z}\\ t_1 := 0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (/ (+ (* (* x z) (* x 0.5)) (/ (* y z) y)) (/ z y)) (* x z)))
        (t_1 (+ (* 0.5 (/ (* x y) z)) (/ y (* x z)))))
   (if (<= z -1.9e+90)
     t_1
     (if (<= z -9e-99)
       t_0
       (if (<= z 7.2e-74)
         (/ (+ (/ y x) (* 0.5 (* x y))) z)
         (if (<= z 3.7e+69) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = ((((x * z) * (x * 0.5)) + ((y * z) / y)) / (z / y)) / (x * z);
	double t_1 = (0.5 * ((x * y) / z)) + (y / (x * z));
	double tmp;
	if (z <= -1.9e+90) {
		tmp = t_1;
	} else if (z <= -9e-99) {
		tmp = t_0;
	} else if (z <= 7.2e-74) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (z <= 3.7e+69) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((((x * z) * (x * 0.5d0)) + ((y * z) / y)) / (z / y)) / (x * z)
    t_1 = (0.5d0 * ((x * y) / z)) + (y / (x * z))
    if (z <= (-1.9d+90)) then
        tmp = t_1
    else if (z <= (-9d-99)) then
        tmp = t_0
    else if (z <= 7.2d-74) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else if (z <= 3.7d+69) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((((x * z) * (x * 0.5)) + ((y * z) / y)) / (z / y)) / (x * z);
	double t_1 = (0.5 * ((x * y) / z)) + (y / (x * z));
	double tmp;
	if (z <= -1.9e+90) {
		tmp = t_1;
	} else if (z <= -9e-99) {
		tmp = t_0;
	} else if (z <= 7.2e-74) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (z <= 3.7e+69) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((((x * z) * (x * 0.5)) + ((y * z) / y)) / (z / y)) / (x * z)
	t_1 = (0.5 * ((x * y) / z)) + (y / (x * z))
	tmp = 0
	if z <= -1.9e+90:
		tmp = t_1
	elif z <= -9e-99:
		tmp = t_0
	elif z <= 7.2e-74:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	elif z <= 3.7e+69:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(Float64(Float64(x * z) * Float64(x * 0.5)) + Float64(Float64(y * z) / y)) / Float64(z / y)) / Float64(x * z))
	t_1 = Float64(Float64(0.5 * Float64(Float64(x * y) / z)) + Float64(y / Float64(x * z)))
	tmp = 0.0
	if (z <= -1.9e+90)
		tmp = t_1;
	elseif (z <= -9e-99)
		tmp = t_0;
	elseif (z <= 7.2e-74)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	elseif (z <= 3.7e+69)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((((x * z) * (x * 0.5)) + ((y * z) / y)) / (z / y)) / (x * z);
	t_1 = (0.5 * ((x * y) / z)) + (y / (x * z));
	tmp = 0.0;
	if (z <= -1.9e+90)
		tmp = t_1;
	elseif (z <= -9e-99)
		tmp = t_0;
	elseif (z <= 7.2e-74)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	elseif (z <= 3.7e+69)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(N[(N[(x * z), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+90], t$95$1, If[LessEqual[z, -9e-99], t$95$0, If[LessEqual[z, 7.2e-74], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.7e+69], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9000000000000001e90 or 3.6999999999999999e69 < z

   1. Initial program 79.5%

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

      1. associate-*l/ 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around 0 59.8%

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

   if -1.9000000000000001e90 < z < -9.0000000000000006e-99 or 7.2000000000000005e-74 < z < 3.6999999999999999e69

   1. Initial program 83.9%

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

      1. associate-*l/ 83.9%

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

   3. Simplified 83.9%

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

   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. Step-by-step derivation

      1. associate-/l* 57.2%

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

      2. *-un-lft-identity 57.2%

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

      3. div-inv 57.2%

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

      4. times-frac 57.2%

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

   6. Applied egg-rr 57.2%

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

      1. frac-times 57.2%

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

      2. *-un-lft-identity 57.2%

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

      3. div-inv 57.2%

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

      4. associate-*r/ 57.2%

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

      5. *-commutative 57.2%

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

      6. frac-add 60.4%

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

      7. associate-/r* 73.8%

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

      8. *-commutative 73.8%

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

      9. *-commutative 73.8%

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

      10. associate-*l/ 74.0%

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

      11. *-commutative 74.0%

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

   8. Applied egg-rr 74.0%

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

   if -9.0000000000000006e-99 < z < 7.2000000000000005e-74

   1. Initial program 90.5%

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

   2. Taylor expanded in x around 0 84.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-99}:\\ \;\;\;\;\frac{\frac{\left(x \cdot z\right) \cdot \left(x \cdot 0.5\right) + \frac{y \cdot z}{y}}{\frac{z}{y}}}{x \cdot z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+69}:\\ \;\;\;\;\frac{\frac{\left(x \cdot z\right) \cdot \left(x \cdot 0.5\right) + \frac{y \cdot z}{y}}{\frac{z}{y}}}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \end{array} \]

Alternative 6: 67.1% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{\left(x \cdot z\right) \cdot \left(x \cdot \left(y \cdot 0.5\right)\right)}{y}}{z \cdot \left(x \cdot \frac{z}{y}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.7e+105)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (/ (+ z (/ (* (* x z) (* x (* y 0.5))) y)) (* z (* x (/ z y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.7e+105) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = (z + (((x * z) * (x * (y * 0.5))) / y)) / (z * (x * (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.7d+105) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = (z + (((x * z) * (x * (y * 0.5d0))) / y)) / (z * (x * (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.7e+105) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = (z + (((x * z) * (x * (y * 0.5))) / y)) / (z * (x * (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.7e+105:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = (z + (((x * z) * (x * (y * 0.5))) / y)) / (z * (x * (z / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.7e+105)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(Float64(z + Float64(Float64(Float64(x * z) * Float64(x * Float64(y * 0.5))) / y)) / Float64(z * Float64(x * Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.7e+105)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = (z + (((x * z) * (x * (y * 0.5))) / y)) / (z * (x * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.7e+105], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(z + N[(N[(N[(x * z), $MachinePrecision] * N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(z * N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7e105

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 63.1%

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

   if 1.7e105 < y

   1. Initial program 84.8%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. +-commutative 84.6%

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

      2. clear-num 84.6%

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

      3. *-commutative 84.6%

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

      4. associate-*l/ 84.4%

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

      5. associate-*r/ 84.4%

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

      6. *-commutative 84.4%

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

      7. *-commutative 84.4%

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

      8. associate-*r* 84.4%

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

      9. frac-add 70.3%

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

      10. *-un-lft-identity 70.3%

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

      11. *-commutative 70.3%

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

      12. associate-*r* 70.3%

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

      13. *-commutative 70.3%

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

      14. associate-*l* 70.3%

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

      15. *-commutative 70.3%

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

   6. Applied egg-rr 70.3%

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

      1. associate-*r/ 79.6%

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

      2. associate-*l/ 88.5%

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

      3. *-commutative 88.5%

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

   8. Applied egg-rr 88.5%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{\left(x \cdot z\right) \cdot \left(x \cdot \left(y \cdot 0.5\right)\right)}{y}}{z \cdot \left(x \cdot \frac{z}{y}\right)}\\ \end{array} \]

Alternative 7: 66.7% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-255}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{1}{\frac{\frac{1}{y}}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e-255)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (+ (/ y (* x z)) (* 0.5 (/ 1.0 (/ (/ 1.0 y) (/ x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e-255) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = (y / (x * z)) + (0.5 * (1.0 / ((1.0 / 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 <= (-8.2d-255)) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = (y / (x * z)) + (0.5d0 * (1.0d0 / ((1.0d0 / y) / (x / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e-255) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = (y / (x * z)) + (0.5 * (1.0 / ((1.0 / y) / (x / z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.2e-255:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = (y / (x * z)) + (0.5 * (1.0 / ((1.0 / y) / (x / z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e-255)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(1.0 / Float64(Float64(1.0 / y) / Float64(x / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.2e-255)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = (y / (x * z)) + (0.5 * (1.0 / ((1.0 / y) / (x / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e-255], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(1.0 / N[(N[(1.0 / y), $MachinePrecision] / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e-255

   1. Initial program 91.6%

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

   2. Taylor expanded in x around 0 69.7%

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

   if -8.2e-255 < y

   1. Initial program 77.9%

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

      1. associate-*l/ 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in x around 0 62.0%

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

      1. associate-/l* 59.7%

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

      2. *-un-lft-identity 59.7%

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

      3. div-inv 59.7%

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

      4. times-frac 62.0%

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

   6. Applied egg-rr 62.0%

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

      1. associate-*r/ 63.6%

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

      2. clear-num 63.6%

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

      3. associate-*l/ 63.6%

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

      4. *-un-lft-identity 63.6%

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

   8. Applied egg-rr 63.6%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-255}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{1}{\frac{\frac{1}{y}}{\frac{x}{z}}}\\ \end{array} \]

Alternative 8: 66.5% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{1}{x \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.6e-255)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (* y (+ (* 0.5 (/ x z)) (/ 1.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e-255) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = y * ((0.5 * (x / z)) + (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 <= (-5.6d-255)) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = y * ((0.5d0 * (x / z)) + (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 <= -5.6e-255) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.6e-255:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.6e-255)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) + Float64(1.0 / Float64(x * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.6e-255)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = y * ((0.5 * (x / z)) + (1.0 / (x * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.6e-255], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.60000000000000023e-255

   1. Initial program 91.6%

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

   2. Taylor expanded in x around 0 69.7%

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

   if -5.60000000000000023e-255 < y

   1. Initial program 77.9%

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

      1. associate-/l* 71.4%

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

      2. associate-/r/ 78.4%

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

      3. *-commutative 78.4%

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

   3. Simplified 78.4%

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

      1. associate-/l/ 89.7%

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

      2. associate-/r/ 96.1%

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

      3. associate-/l* 77.6%

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

      4. associate-/r/ 98.3%

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

   5. Applied egg-rr 98.3%

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

   6. Taylor expanded in x around 0 63.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-255}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} + \frac{1}{x \cdot z}\right)\\ \end{array} \]

Alternative 9: 67.5% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.55e-227)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (+ (* 0.5 (/ (* x y) z)) (/ y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.55e-227) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = (0.5 * ((x * y) / z)) + (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 <= 1.55d-227) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = (0.5d0 * ((x * y) / z)) + (y / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.55e-227) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.55e-227:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.55e-227)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(Float64(0.5 * Float64(Float64(x * y) / z)) + Float64(y / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.55e-227)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.55e-227], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5499999999999999e-227

   1. Initial program 85.6%

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

   2. Taylor expanded in x around 0 66.2%

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

   if 1.5499999999999999e-227 < y

   1. Initial program 84.0%

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

      1. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in x around 0 67.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \end{array} \]

Alternative 10: 61.6% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;x \cdot \frac{y}{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.42) (not (<= x 1.45))) (* x (/ y (* z 2.0))) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42) || !(x <= 1.45)) {
		tmp = x * (y / (z * 2.0));
	} 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 <= 1.45d0))) then
        tmp = x * (y / (z * 2.0d0))
    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 <= 1.45)) {
		tmp = x * (y / (z * 2.0));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.42) or not (x <= 1.45):
		tmp = x * (y / (z * 2.0))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.42) || !(x <= 1.45))
		tmp = Float64(x * Float64(y / Float64(z * 2.0)));
	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 <= 1.45)))
		tmp = x * (y / (z * 2.0));
	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, 1.45]], $MachinePrecision]], N[(x * N[(y / N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4199999999999999 or 1.44999999999999996 < x

   1. Initial program 79.3%

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

      1. associate-*l/ 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around 0 40.8%

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

      1. associate-/l* 33.8%

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

      2. *-un-lft-identity 33.8%

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

      3. div-inv 33.8%

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

      4. times-frac 40.8%

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

   6. Applied egg-rr 40.8%

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

   7. Taylor expanded in x around inf 40.8%

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

      1. associate-*r/ 40.8%

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

      2. associate-*l/ 40.8%

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

      3. metadata-eval 40.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{2}}}{z} \cdot \left(x \cdot y\right) \]

      4. associate-/r* 40.8%

         \[\leadsto \color{blue}{\frac{1}{2 \cdot z}} \cdot \left(x \cdot y\right) \]

      5. *-commutative 40.8%

         \[\leadsto \frac{1}{\color{blue}{z \cdot 2}} \cdot \left(x \cdot y\right) \]

      6. associate-*l/ 40.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x \cdot y\right)}{z \cdot 2}} \]

      7. *-lft-identity 40.8%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{z \cdot 2} \]

      8. associate-*r/ 33.8%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z \cdot 2}} \]

   9. Simplified 33.8%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z \cdot 2}} \]

   if -1.4199999999999999 < x < 1.44999999999999996

   1. Initial program 91.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 89.6%

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

      1. associate-*r/ 93.4%

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

      2. associate-*l/ 93.5%

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

      3. *-un-lft-identity 93.5%

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

   6. Applied egg-rr 93.5%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;x \cdot \frac{y}{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 11: 65.5% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;y \cdot \frac{x}{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.42) (not (<= x 1.45))) (* y (/ x (* z 2.0))) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42) || !(x <= 1.45)) {
		tmp = y * (x / (z * 2.0));
	} 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 <= 1.45d0))) then
        tmp = y * (x / (z * 2.0d0))
    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 <= 1.45)) {
		tmp = y * (x / (z * 2.0));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.42) or not (x <= 1.45):
		tmp = y * (x / (z * 2.0))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.42) || !(x <= 1.45))
		tmp = Float64(y * Float64(x / Float64(z * 2.0)));
	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 <= 1.45)))
		tmp = y * (x / (z * 2.0));
	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, 1.45]], $MachinePrecision]], N[(y * N[(x / N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4199999999999999 or 1.44999999999999996 < x

   1. Initial program 79.3%

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

      1. associate-*l/ 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around 0 40.8%

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

   5. Taylor expanded in x around inf 40.8%

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

      1. associate-*r/ 40.8%

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

      2. associate-*l/ 40.8%

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

      3. associate-*r* 40.8%

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

      4. *-commutative 40.8%

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

      5. associate-*l/ 40.8%

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

      6. *-commutative 40.8%

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

      7. /-rgt-identity 40.8%

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

      8. associate-/l* 40.8%

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

      9. metadata-eval 40.8%

         \[\leadsto y \cdot \frac{\frac{x}{\color{blue}{2}}}{z} \]

      10. associate-/l/ 40.8%

          \[\leadsto y \cdot \color{blue}{\frac{x}{z \cdot 2}} \]

   7. Simplified 40.8%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z \cdot 2}} \]

   if -1.4199999999999999 < x < 1.44999999999999996

   1. Initial program 91.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 89.6%

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

      1. associate-*r/ 93.4%

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

      2. associate-*l/ 93.5%

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

      3. *-un-lft-identity 93.5%

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

   6. Applied egg-rr 93.5%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;y \cdot \frac{x}{z \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 12: 65.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{z}\\ \mathbf{elif}\;x \leq 1.45:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.42)
   (* (* x y) (/ 0.5 z))
   (if (<= x 1.45) (/ (/ y z) x) (* y (/ x (* z 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = (x * y) * (0.5 / z);
	} else if (x <= 1.45) {
		tmp = (y / z) / x;
	} else {
		tmp = y * (x / (z * 2.0));
	}
	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) :: tmp
    if (x <= (-1.42d0)) then
        tmp = (x * y) * (0.5d0 / z)
    else if (x <= 1.45d0) then
        tmp = (y / z) / x
    else
        tmp = y * (x / (z * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = (x * y) * (0.5 / z);
	} else if (x <= 1.45) {
		tmp = (y / z) / x;
	} else {
		tmp = y * (x / (z * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.42:
		tmp = (x * y) * (0.5 / z)
	elif x <= 1.45:
		tmp = (y / z) / x
	else:
		tmp = y * (x / (z * 2.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.42)
		tmp = Float64(Float64(x * y) * Float64(0.5 / z));
	elseif (x <= 1.45)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(y * Float64(x / Float64(z * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.42)
		tmp = (x * y) * (0.5 / z);
	elseif (x <= 1.45)
		tmp = (y / z) / x;
	else
		tmp = y * (x / (z * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.42], N[(N[(x * y), $MachinePrecision] * N[(0.5 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(y * N[(x / N[(z * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4199999999999999

   1. Initial program 78.2%

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

   2. Taylor expanded in x around 0 40.6%

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

   3. Taylor expanded in x around inf 40.6%

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

      1. associate-*r/ 40.6%

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

      2. associate-/l* 40.6%

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

      3. *-commutative 40.6%

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

   5. Simplified 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-/r/ 40.6%

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

   7. Applied egg-rr 40.6%

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

   if -1.4199999999999999 < x < 1.44999999999999996

   1. Initial program 91.2%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 89.6%

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

      1. associate-*r/ 93.4%

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

      2. associate-*l/ 93.5%

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

      3. *-un-lft-identity 93.5%

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

   6. Applied egg-rr 93.5%

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

   if 1.44999999999999996 < x

   1. Initial program 80.7%

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

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in x around 0 41.1%

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

   5. Taylor expanded in x around inf 41.1%

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

      1. associate-*r/ 41.1%

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

      2. associate-*l/ 41.1%

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

      3. associate-*r* 42.6%

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

      4. *-commutative 42.6%

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

      5. associate-*l/ 42.6%

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

      6. *-commutative 42.6%

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

      7. /-rgt-identity 42.6%

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

      8. associate-/l* 42.6%

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

      9. metadata-eval 42.6%

         \[\leadsto y \cdot \frac{\frac{x}{\color{blue}{2}}}{z} \]

      10. associate-/l/ 42.6%

          \[\leadsto y \cdot \color{blue}{\frac{x}{z \cdot 2}} \]

   7. Simplified 42.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{z}\\ \mathbf{elif}\;x \leq 1.45:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot 2}\\ \end{array} \]

Alternative 13: 66.5% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

2. Taylor expanded in x around 0 64.1%

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

3. Final simplification 64.1%

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

Alternative 14: 50.0% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-226}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.7e-226) (/ (/ y x) z) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.7e-226) {
		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 <= 1.7d-226) 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 <= 1.7e-226) {
		tmp = (y / x) / z;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.7e-226:
		tmp = (y / x) / z
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.7e-226)
		tmp = Float64(Float64(y / x) / z);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.7e-226)
		tmp = (y / x) / z;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.7e-226], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.70000000000000004e-226

   1. Initial program 85.6%

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

   2. Taylor expanded in x around 0 49.9%

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

   if 1.70000000000000004e-226 < y

   1. Initial program 84.0%

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

      1. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

   4. Taylor expanded in x around 0 46.0%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-226}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 15: 49.1% 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. associate-*l/ 84.9%

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

3. Simplified 84.9%

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

4. Taylor expanded in x around 0 45.5%

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

5. Final simplification 45.5%

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

Alternative 16: 52.7% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

   1. associate-*l/ 84.9%

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

3. Simplified 84.9%

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

4. Taylor expanded in x around 0 45.7%

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

   1. associate-*r/ 51.9%

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

   2. associate-*l/ 51.9%

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

   3. *-un-lft-identity 51.9%

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

6. Applied egg-rr 51.9%

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

7. Final simplification 51.9%

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

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 2023301 
(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))