Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 85.0% → 97.8%

Time: 9.3s

Alternatives: 15

Speedup: 1.0×

• 64.1% 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: 85.0% 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: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x}{\frac{\cosh x}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* (cosh x) (/ y x)) z)))
   (if (<= t_0 2e+297) t_0 (/ y (/ x (/ (cosh x) z))))))

C

double code(double x, double y, double z) {
	double t_0 = (cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= 2e+297) {
		tmp = t_0;
	} else {
		tmp = y / (x / (cosh(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 = (cosh(x) * (y / x)) / z
    if (t_0 <= 2d+297) then
        tmp = t_0
    else
        tmp = y / (x / (cosh(x) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= 2e+297) {
		tmp = t_0;
	} else {
		tmp = y / (x / (Math.cosh(x) / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cosh(x) * (y / x)) / z
	tmp = 0
	if t_0 <= 2e+297:
		tmp = t_0
	else:
		tmp = y / (x / (math.cosh(x) / z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cosh(x) * Float64(y / x)) / z)
	tmp = 0.0
	if (t_0 <= 2e+297)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(x / Float64(cosh(x) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (cosh(x) * (y / x)) / z;
	tmp = 0.0;
	if (t_0 <= 2e+297)
		tmp = t_0;
	else
		tmp = y / (x / (cosh(x) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, 2e+297], t$95$0, N[(y / N[(x / N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 2e297

   1. Initial program 99.3%

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

   if 2e297 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 59.1%

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

      1. associate-*r/ 95.8%

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

      2. associate-/l/ 78.9%

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

      3. associate-*l/ 78.9%

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

      4. *-commutative 78.9%

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

      5. *-commutative 78.9%

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

   3. Simplified 78.9%

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

      1. clear-num 78.9%

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

      2. un-div-inv 78.9%

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

      3. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x}{\frac{\cosh x}{z}}}\\ \end{array} \]

Alternative 2: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-53} \lor \neg \left(x \leq 9.2 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e-53) (not (<= x 9.2e-26)))
   (* y (/ (cosh x) (* x z)))
   (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-53) || !(x <= 9.2e-26)) {
		tmp = y * (cosh(x) / (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 ((x <= (-4d-53)) .or. (.not. (x <= 9.2d-26))) then
        tmp = y * (cosh(x) / (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 ((x <= -4e-53) || !(x <= 9.2e-26)) {
		tmp = y * (Math.cosh(x) / (x * z));
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e-53) or not (x <= 9.2e-26):
		tmp = y * (math.cosh(x) / (x * z))
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e-53) || !(x <= 9.2e-26))
		tmp = Float64(y * Float64(cosh(x) / 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 ((x <= -4e-53) || ~((x <= 9.2e-26)))
		tmp = y * (cosh(x) / (x * z));
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e-53], N[Not[LessEqual[x, 9.2e-26]], $MachinePrecision]], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000012e-53 or 9.20000000000000035e-26 < x

   1. Initial program 75.9%

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

      1. associate-*r/ 99.3%

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

      2. associate-/l/ 75.8%

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

      3. associate-*l/ 75.9%

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

      4. *-commutative 75.9%

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

      5. *-commutative 75.9%

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

   3. Simplified 75.9%

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

   if -4.00000000000000012e-53 < x < 9.20000000000000035e-26

   1. Initial program 96.6%

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

      1. associate-*r/ 96.6%

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

      2. associate-/l/ 88.6%

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

      3. associate-*l/ 86.6%

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

      4. *-commutative 86.6%

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

      5. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in x around 0 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-/r* 96.6%

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

   6. Simplified 96.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-53} \lor \neg \left(x \leq 9.2 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 3: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-66} \lor \neg \left(y \leq 9.5 \cdot 10^{-306}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e-66) (not (<= y 9.5e-306)))
   (* (cosh x) (/ (/ y z) x))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e-66) || !(y <= 9.5e-306)) {
		tmp = cosh(x) * ((y / z) / x);
	} 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 <= (-1.25d-66)) .or. (.not. (y <= 9.5d-306))) then
        tmp = cosh(x) * ((y / z) / x)
    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 <= -1.25e-66) || !(y <= 9.5e-306)) {
		tmp = Math.cosh(x) * ((y / z) / x);
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e-66) or not (y <= 9.5e-306):
		tmp = math.cosh(x) * ((y / z) / x)
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e-66) || !(y <= 9.5e-306))
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	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 ((y <= -1.25e-66) || ~((y <= 9.5e-306)))
		tmp = cosh(x) * ((y / z) / x);
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e-66], N[Not[LessEqual[y, 9.5e-306]], $MachinePrecision]], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e-66 or 9.5e-306 < y

   1. Initial program 90.3%

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

      1. associate-*r/ 86.0%

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

      2. associate-/l/ 80.7%

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

      3. associate-/r* 89.8%

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

   3. Simplified 89.8%

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

   if -1.2499999999999999e-66 < y < 9.5e-306

   1. Initial program 63.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-/l/ 78.9%

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

      3. associate-*l/ 78.3%

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

      4. *-commutative 78.3%

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

      5. *-commutative 78.3%

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

   3. Simplified 78.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-66} \lor \neg \left(y \leq 9.5 \cdot 10^{-306}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 4: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-94} \lor \neg \left(z \leq 3.1 \cdot 10^{-136}\right):\\ \;\;\;\;\frac{y}{\frac{x}{\frac{\cosh x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4e-94) (not (<= z 3.1e-136)))
   (/ y (/ x (/ (cosh x) z)))
   (* (cosh x) (/ (/ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4e-94) || !(z <= 3.1e-136)) {
		tmp = y / (x / (cosh(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-94)) .or. (.not. (z <= 3.1d-136))) then
        tmp = y / (x / (cosh(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-94) || !(z <= 3.1e-136)) {
		tmp = y / (x / (Math.cosh(x) / z));
	} else {
		tmp = Math.cosh(x) * ((y / z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4e-94) or not (z <= 3.1e-136):
		tmp = y / (x / (math.cosh(x) / z))
	else:
		tmp = math.cosh(x) * ((y / z) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4e-94) || !(z <= 3.1e-136))
		tmp = Float64(y / Float64(x / Float64(cosh(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-94) || ~((z <= 3.1e-136)))
		tmp = y / (x / (cosh(x) / z));
	else
		tmp = cosh(x) * ((y / z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4e-94], N[Not[LessEqual[z, 3.1e-136]], $MachinePrecision]], N[(y / N[(x / N[(N[Cosh[x], $MachinePrecision] / 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 < -3.9999999999999998e-94 or 3.1e-136 < z

   1. Initial program 85.9%

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

      1. associate-*r/ 97.2%

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

      2. associate-/l/ 80.1%

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

      3. associate-*l/ 80.0%

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

      4. *-commutative 80.0%

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

      5. *-commutative 80.0%

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

   3. Simplified 80.0%

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

      1. clear-num 80.0%

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

      2. un-div-inv 80.1%

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

      3. associate-/l* 99.3%

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

   5. Applied egg-rr 99.3%

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

   if -3.9999999999999998e-94 < z < 3.1e-136

   1. Initial program 83.6%

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

      1. associate-*r/ 83.6%

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

      2. associate-/l/ 84.8%

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

      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 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-94} \lor \neg \left(z \leq 3.1 \cdot 10^{-136}\right):\\ \;\;\;\;\frac{y}{\frac{x}{\frac{\cosh x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 5: 69.3% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{z}{x \cdot y}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+155}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\frac{x}{\frac{x}{z \cdot z}}}\\ \mathbf{elif}\;x \leq -900:\\ \;\;\;\;\frac{z \cdot 0.5 + \frac{y}{x} \cdot t_0}{z \cdot t_0}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot \left(x \cdot z\right)\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ z (* x y))))
   (if (<= x -1.55e+155)
     (/ (* y (+ (* x (* z 0.5)) (/ z x))) (/ x (/ x (* z z))))
     (if (<= x -900.0)
       (/ (+ (* z 0.5) (* (/ y x) t_0)) (* z t_0))
       (if (<= x 1.32e+159)
         (+ (/ (/ y x) z) (* 0.5 (* y (/ x z))))
         (/ (* 0.5 (* y (* x z))) (* x (* z (/ z x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z / (x * y);
	double tmp;
	if (x <= -1.55e+155) {
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)));
	} else if (x <= -900.0) {
		tmp = ((z * 0.5) + ((y / x) * t_0)) / (z * t_0);
	} else if (x <= 1.32e+159) {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	} else {
		tmp = (0.5 * (y * (x * z))) / (x * (z * (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 = z / (x * y)
    if (x <= (-1.55d+155)) then
        tmp = (y * ((x * (z * 0.5d0)) + (z / x))) / (x / (x / (z * z)))
    else if (x <= (-900.0d0)) then
        tmp = ((z * 0.5d0) + ((y / x) * t_0)) / (z * t_0)
    else if (x <= 1.32d+159) then
        tmp = ((y / x) / z) + (0.5d0 * (y * (x / z)))
    else
        tmp = (0.5d0 * (y * (x * z))) / (x * (z * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z / (x * y);
	double tmp;
	if (x <= -1.55e+155) {
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)));
	} else if (x <= -900.0) {
		tmp = ((z * 0.5) + ((y / x) * t_0)) / (z * t_0);
	} else if (x <= 1.32e+159) {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	} else {
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z / (x * y)
	tmp = 0
	if x <= -1.55e+155:
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)))
	elif x <= -900.0:
		tmp = ((z * 0.5) + ((y / x) * t_0)) / (z * t_0)
	elif x <= 1.32e+159:
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)))
	else:
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z / Float64(x * y))
	tmp = 0.0
	if (x <= -1.55e+155)
		tmp = Float64(Float64(y * Float64(Float64(x * Float64(z * 0.5)) + Float64(z / x))) / Float64(x / Float64(x / Float64(z * z))));
	elseif (x <= -900.0)
		tmp = Float64(Float64(Float64(z * 0.5) + Float64(Float64(y / x) * t_0)) / Float64(z * t_0));
	elseif (x <= 1.32e+159)
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y * Float64(x / z))));
	else
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x * z))) / Float64(x * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z / (x * y);
	tmp = 0.0;
	if (x <= -1.55e+155)
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)));
	elseif (x <= -900.0)
		tmp = ((z * 0.5) + ((y / x) * t_0)) / (z * t_0);
	elseif (x <= 1.32e+159)
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	else
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+155], N[(N[(y * N[(N[(x * N[(z * 0.5), $MachinePrecision]), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -900.0], N[(N[(N[(z * 0.5), $MachinePrecision] + N[(N[(y / x), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(z * t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e+159], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.54999999999999995e155

   1. Initial program 64.3%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 50.0%

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

      3. associate-*l/ 50.0%

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

      4. *-commutative 50.0%

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

      5. *-commutative 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in x around 0 34.8%

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

      1. +-commutative 34.8%

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

      2. associate-/l* 34.7%

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

      3. *-commutative 34.7%

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

      4. associate-/r* 34.7%

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

   6. Simplified 34.7%

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

      1. associate-/l/ 34.7%

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

      2. +-commutative 34.7%

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

      3. associate-*r/ 34.7%

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

      4. frac-add 26.1%

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

      5. *-commutative 26.1%

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

      6. *-commutative 26.1%

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

   8. Applied egg-rr 26.1%

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

      1. +-commutative 26.1%

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

      2. associate-*r* 26.1%

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

      3. *-commutative 26.1%

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

      4. distribute-rgt-out 26.1%

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

      5. associate-*l* 26.1%

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

      6. associate-*l* 57.9%

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

   10. Simplified 57.9%

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

       1. expm1-log1p-u 57.9%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(z \cdot \frac{z}{x}\right)\right)\right)}} \]

       2. expm1-udef 64.8%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(z \cdot \frac{z}{x}\right)\right)} - 1}} \]

       3. associate-*r/ 64.8%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{z \cdot z}{x}}\right)} - 1} \]

   12. Applied egg-rr 64.8%

       \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \frac{z \cdot z}{x}\right)} - 1}} \]
   13. Step-by-step derivation

       1. expm1-def 57.9%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{z \cdot z}{x}\right)\right)}} \]

       2. expm1-log1p 57.9%

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

       3. unpow2 57.9%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{x \cdot \frac{\color{blue}{{z}^{2}}}{x}} \]

       4. associate-*r/ 25.8%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\frac{x \cdot {z}^{2}}{x}}} \]

       5. associate-/l* 61.4%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\frac{x}{\frac{x}{{z}^{2}}}}} \]

       6. unpow2 61.4%

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

   14. Simplified 61.4%

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

   if -1.54999999999999995e155 < x < -900

   1. Initial program 89.7%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 82.1%

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

      3. associate-*l/ 82.1%

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

      4. *-commutative 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in x around 0 31.1%

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

      1. +-commutative 31.1%

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

      2. associate-/l* 26.4%

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

      3. *-commutative 26.4%

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

      4. associate-/r* 26.4%

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

   6. Simplified 26.4%

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

   7. Taylor expanded in y around 0 31.1%

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

      1. associate-*r/ 26.4%

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

   9. Simplified 26.4%

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

       1. fma-def 26.4%

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

       2. associate-*r/ 31.1%

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

       3. *-commutative 31.1%

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

       4. clear-num 31.1%

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

       5. fma-def 31.1%

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

       6. +-commutative 31.1%

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

       7. un-div-inv 31.1%

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

       8. frac-add 45.2%

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

       9. *-commutative 45.2%

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

       10. *-commutative 45.2%

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

   11. Applied egg-rr 45.2%

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

   if -900 < x < 1.32000000000000007e159

   1. Initial program 92.3%

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

      1. associate-*r/ 96.8%

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

      2. associate-/l/ 87.7%

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

      3. associate-*l/ 86.2%

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

      4. *-commutative 86.2%

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

      5. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in x around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. associate-/l* 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-/r* 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around 0 81.4%

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

      1. associate-*r/ 83.3%

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

   9. Simplified 83.3%

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

   if 1.32000000000000007e159 < x

   1. Initial program 63.6%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 78.8%

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

      3. associate-*l/ 78.8%

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

      4. *-commutative 78.8%

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

      5. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in x around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. associate-/l* 47.7%

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

      3. *-commutative 47.7%

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

      4. associate-/r* 47.7%

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

   6. Simplified 47.7%

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

      1. associate-/l/ 47.7%

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

      2. +-commutative 47.7%

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

      3. associate-*r/ 47.7%

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

      4. frac-add 55.4%

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

      5. *-commutative 55.4%

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

      6. *-commutative 55.4%

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

   8. Applied egg-rr 55.4%

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

      1. +-commutative 55.4%

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

      2. associate-*r* 55.4%

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

      3. *-commutative 55.4%

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

      4. distribute-rgt-out 55.4%

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

      5. associate-*l* 55.4%

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

      6. associate-*l* 70.1%

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

   10. Simplified 70.1%

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

   11. Taylor expanded in x around inf 70.1%

       \[\leadsto \frac{\color{blue}{0.5 \cdot \left(y \cdot \left(z \cdot x\right)\right)}}{x \cdot \left(z \cdot \frac{z}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+155}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\frac{x}{\frac{x}{z \cdot z}}}\\ \mathbf{elif}\;x \leq -900:\\ \;\;\;\;\frac{z \cdot 0.5 + \frac{y}{x} \cdot \frac{z}{x \cdot y}}{z \cdot \frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot \left(x \cdot z\right)\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \]

Alternative 6: 69.1% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\frac{x}{\frac{x}{z \cdot z}}}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot \left(x \cdot z\right)\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.6e+18)
   (/ (* y (+ (* x (* z 0.5)) (/ z x))) (/ x (/ x (* z z))))
   (if (<= x 4.3e+157)
     (+ (/ (/ y x) z) (* 0.5 (* y (/ x z))))
     (/ (* 0.5 (* y (* x z))) (* x (* z (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.6e+18) {
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)));
	} else if (x <= 4.3e+157) {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	} else {
		tmp = (0.5 * (y * (x * z))) / (x * (z * (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 <= (-7.6d+18)) then
        tmp = (y * ((x * (z * 0.5d0)) + (z / x))) / (x / (x / (z * z)))
    else if (x <= 4.3d+157) then
        tmp = ((y / x) / z) + (0.5d0 * (y * (x / z)))
    else
        tmp = (0.5d0 * (y * (x * z))) / (x * (z * (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.6e+18) {
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)));
	} else if (x <= 4.3e+157) {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	} else {
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.6e+18:
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)))
	elif x <= 4.3e+157:
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)))
	else:
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.6e+18)
		tmp = Float64(Float64(y * Float64(Float64(x * Float64(z * 0.5)) + Float64(z / x))) / Float64(x / Float64(x / Float64(z * z))));
	elseif (x <= 4.3e+157)
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y * Float64(x / z))));
	else
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x * z))) / Float64(x * Float64(z * Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.6e+18)
		tmp = (y * ((x * (z * 0.5)) + (z / x))) / (x / (x / (z * z)));
	elseif (x <= 4.3e+157)
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	else
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.6e+18], N[(N[(y * N[(N[(x * N[(z * 0.5), $MachinePrecision]), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x / N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.3e+157], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6e18

   1. Initial program 77.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 65.6%

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

      3. associate-*l/ 65.6%

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

      4. *-commutative 65.6%

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

      5. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in x around 0 34.0%

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

      1. +-commutative 34.0%

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

      2. associate-/l* 30.9%

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

      3. *-commutative 30.9%

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

      4. associate-/r* 30.9%

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

   6. Simplified 30.9%

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

      1. associate-/l/ 30.9%

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

      2. +-commutative 30.9%

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

      3. associate-*r/ 30.9%

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

      4. frac-add 27.9%

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

      5. *-commutative 27.9%

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

      6. *-commutative 27.9%

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

   8. Applied egg-rr 27.9%

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

      1. +-commutative 27.9%

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

      2. associate-*r* 27.9%

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

      3. *-commutative 27.9%

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

      4. distribute-rgt-out 27.9%

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

      5. associate-*l* 27.9%

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

      6. associate-*l* 44.1%

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

   10. Simplified 44.1%

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

       1. expm1-log1p-u 44.1%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(z \cdot \frac{z}{x}\right)\right)\right)}} \]

       2. expm1-udef 54.7%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \left(z \cdot \frac{z}{x}\right)\right)} - 1}} \]

       3. associate-*r/ 54.7%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{z \cdot z}{x}}\right)} - 1} \]

   12. Applied egg-rr 54.7%

       \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \frac{z \cdot z}{x}\right)} - 1}} \]
   13. Step-by-step derivation

       1. expm1-def 44.1%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{z \cdot z}{x}\right)\right)}} \]

       2. expm1-log1p 44.1%

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

       3. unpow2 44.1%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{x \cdot \frac{\color{blue}{{z}^{2}}}{x}} \]

       4. associate-*r/ 26.1%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\frac{x \cdot {z}^{2}}{x}}} \]

       5. associate-/l* 47.2%

          \[\leadsto \frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\color{blue}{\frac{x}{\frac{x}{{z}^{2}}}}} \]

       6. unpow2 47.2%

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

   14. Simplified 47.2%

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

   if -7.6e18 < x < 4.3e157

   1. Initial program 92.6%

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

      1. associate-*r/ 96.9%

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

      2. associate-/l/ 88.1%

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

      3. associate-*l/ 86.7%

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

      4. *-commutative 86.7%

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

      5. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. associate-/l* 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-/r* 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in y around 0 79.1%

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

      1. associate-*r/ 80.9%

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

   9. Simplified 80.9%

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

   if 4.3e157 < x

   1. Initial program 63.6%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 78.8%

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

      3. associate-*l/ 78.8%

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

      4. *-commutative 78.8%

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

      5. *-commutative 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in x around 0 47.9%

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

      1. +-commutative 47.9%

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

      2. associate-/l* 47.7%

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

      3. *-commutative 47.7%

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

      4. associate-/r* 47.7%

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

   6. Simplified 47.7%

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

      1. associate-/l/ 47.7%

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

      2. +-commutative 47.7%

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

      3. associate-*r/ 47.7%

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

      4. frac-add 55.4%

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

      5. *-commutative 55.4%

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

      6. *-commutative 55.4%

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

   8. Applied egg-rr 55.4%

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

      1. +-commutative 55.4%

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

      2. associate-*r* 55.4%

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

      3. *-commutative 55.4%

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

      4. distribute-rgt-out 55.4%

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

      5. associate-*l* 55.4%

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

      6. associate-*l* 70.1%

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

   10. Simplified 70.1%

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

   11. Taylor expanded in x around inf 70.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot \left(z \cdot 0.5\right) + \frac{z}{x}\right)}{\frac{x}{\frac{x}{z \cdot z}}}\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot \left(x \cdot z\right)\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \end{array} \]

Alternative 7: 68.9% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+18} \lor \neg \left(x \leq 9.4 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot \left(x \cdot z\right)\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.1e+18) (not (<= x 9.4e+156)))
   (/ (* 0.5 (* y (* x z))) (* x (* z (/ z x))))
   (+ (/ (/ y x) z) (* 0.5 (* y (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.1e+18) || !(x <= 9.4e+156)) {
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	} else {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.1d+18)) .or. (.not. (x <= 9.4d+156))) then
        tmp = (0.5d0 * (y * (x * z))) / (x * (z * (z / x)))
    else
        tmp = ((y / x) / z) + (0.5d0 * (y * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.1e+18) || !(x <= 9.4e+156)) {
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	} else {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.1e+18) or not (x <= 9.4e+156):
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)))
	else:
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.1e+18) || !(x <= 9.4e+156))
		tmp = Float64(Float64(0.5 * Float64(y * Float64(x * z))) / Float64(x * Float64(z * Float64(z / x))));
	else
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.1e+18) || ~((x <= 9.4e+156)))
		tmp = (0.5 * (y * (x * z))) / (x * (z * (z / x)));
	else
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.1e+18], N[Not[LessEqual[x, 9.4e+156]], $MachinePrecision]], N[(N[(0.5 * N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e18 or 9.4e156 < x

   1. Initial program 72.3%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 70.2%

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

      3. associate-*l/ 70.2%

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

      4. *-commutative 70.2%

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

      5. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in x around 0 38.8%

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

      1. +-commutative 38.8%

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

      2. associate-/l* 36.8%

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

      3. *-commutative 36.8%

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

      4. associate-/r* 36.8%

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

   6. Simplified 36.8%

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

      1. associate-/l/ 36.8%

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

      2. +-commutative 36.8%

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

      3. associate-*r/ 36.8%

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

      4. frac-add 37.6%

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

      5. *-commutative 37.6%

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

      6. *-commutative 37.6%

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

   8. Applied egg-rr 37.6%

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

      1. +-commutative 37.6%

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

      2. associate-*r* 37.6%

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

      3. *-commutative 37.6%

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

      4. distribute-rgt-out 37.6%

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

      5. associate-*l* 37.6%

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

      6. associate-*l* 53.2%

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

   10. Simplified 53.2%

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

   11. Taylor expanded in x around inf 53.2%

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

   if -1.1e18 < x < 9.4e156

   1. Initial program 92.6%

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

      1. associate-*r/ 96.9%

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

      2. associate-/l/ 88.1%

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

      3. associate-*l/ 86.7%

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

      4. *-commutative 86.7%

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

      5. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around 0 74.0%

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

      1. +-commutative 74.0%

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

      2. associate-/l* 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-/r* 80.9%

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

   6. Simplified 80.9%

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

   7. Taylor expanded in y around 0 79.1%

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

      1. associate-*r/ 80.9%

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

   9. Simplified 80.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+18} \lor \neg \left(x \leq 9.4 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot \left(x \cdot z\right)\right)}{x \cdot \left(z \cdot \frac{z}{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 8: 67.3% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+85)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (+ (/ (/ y x) z) (* 0.5 (* y (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+85) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4d+85)) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = ((y / x) / z) + (0.5d0 * (y * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+85) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+85:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+85)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e+85)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = ((y / x) / z) + (0.5 * (y * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+85], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000001e85

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 82.9%

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

   if -4.0000000000000001e85 < y

   1. Initial program 83.4%

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

      1. associate-*r/ 99.0%

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

      2. associate-/l/ 80.6%

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

      3. associate-*l/ 79.5%

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

      4. *-commutative 79.5%

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

      5. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around 0 55.3%

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

      1. +-commutative 55.3%

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

      2. associate-/l* 60.2%

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

      3. *-commutative 60.2%

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

      4. associate-/r* 65.4%

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

   6. Simplified 65.4%

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

   7. Taylor expanded in y around 0 60.5%

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

      1. associate-*r/ 65.8%

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

   9. Simplified 65.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 9: 65.7% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5000000000000:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 5000000000000.0)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (* 0.5 (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5000000000000.0) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = 0.5 * (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 5000000000000.0d0) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = 0.5d0 * (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 5000000000000.0) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = 0.5 * (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5000000000000.0:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = 0.5 * (y * (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5000000000000.0)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 5000000000000.0)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = 0.5 * (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5000000000000.0], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5e12

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 73.0%

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

   if 5e12 < x

   1. Initial program 68.3%

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

   2. Taylor expanded in x around 0 36.1%

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

   3. Taylor expanded in x around inf 36.1%

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

      1. associate-*r/ 43.9%

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

   5. Simplified 43.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5000000000000:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 10: 61.5% accurate, 9.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.4)) {
		tmp = 0.5 * (x * (y / 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 ((x <= (-1.4d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = 0.5d0 * (x * (y / 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 ((x <= -1.4) || !(x <= 1.4)) {
		tmp = 0.5 * (x * (y / z));
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 74.8%

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

   2. Taylor expanded in x around 0 34.1%

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

   3. Taylor expanded in x around inf 34.1%

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

      1. associate-*l/ 26.2%

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

      2. *-commutative 26.2%

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

   5. Simplified 26.2%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 96.0%

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

      1. associate-*r/ 96.0%

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

      2. associate-/l/ 89.4%

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

      3. associate-*l/ 87.6%

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

      4. *-commutative 87.6%

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

      5. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/r* 96.0%

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

   6. Simplified 96.0%

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

4. Final simplification 60.3%

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

Alternative 11: 65.1% accurate, 9.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.4)) {
		tmp = 0.5 * (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 ((x <= (-1.4d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = 0.5d0 * (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 ((x <= -1.4) || !(x <= 1.4)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.4))
		tmp = Float64(0.5 * 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 ((x <= -1.4) || ~((x <= 1.4)))
		tmp = 0.5 * (y * (x / z));
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 74.8%

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

   2. Taylor expanded in x around 0 34.1%

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

   3. Taylor expanded in x around inf 34.1%

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

      1. associate-*r/ 35.6%

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

   5. Simplified 35.6%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 96.0%

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

      1. associate-*r/ 96.0%

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

      2. associate-/l/ 89.4%

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

      3. associate-*l/ 87.6%

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

      4. *-commutative 87.6%

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

      5. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/r* 96.0%

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

   6. Simplified 96.0%

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

4. Final simplification 65.1%

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

Alternative 12: 65.5% accurate, 9.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4)
   (/ (* 0.5 (* x y)) z)
   (if (<= x 1.4) (/ (/ y x) z) (* 0.5 (* y (/ x z))))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.4d0)) then
        tmp = (0.5d0 * (x * y)) / z
    else if (x <= 1.4d0) then
        tmp = (y / x) / z
    else
        tmp = 0.5d0 * (y * (x / z))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4:
		tmp = (0.5 * (x * y)) / z
	elif x <= 1.4:
		tmp = (y / x) / z
	else:
		tmp = 0.5 * (y * (x / z))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4], N[(N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 1.4], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 32.7%

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

   3. Taylor expanded in x around inf 32.7%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 96.0%

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

      1. associate-*r/ 96.0%

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

      2. associate-/l/ 89.4%

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

      3. associate-*l/ 87.6%

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

      4. *-commutative 87.6%

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

      5. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/r* 96.0%

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

   6. Simplified 96.0%

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

   if 1.3999999999999999 < x

   1. Initial program 70.3%

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

   2. Taylor expanded in x around 0 35.6%

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

   3. Taylor expanded in x around inf 35.6%

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

      1. associate-*r/ 41.5%

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

   5. Simplified 41.5%

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

4. Final simplification 65.8%

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

Alternative 13: 54.1% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+66) (/ y (* x z)) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+66) {
		tmp = y / (x * z);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5d+66)) then
        tmp = y / (x * z)
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+66) {
		tmp = y / (x * z);
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+66:
		tmp = y / (x * z)
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+66)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+66)
		tmp = y / (x * z);
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+66], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.99999999999999991e66

   1. Initial program 79.8%

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

      1. associate-*r/ 95.7%

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

      2. associate-/l/ 72.6%

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

      3. associate-*l/ 72.3%

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

      4. *-commutative 72.3%

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

      5. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in x around 0 59.7%

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

   if -4.99999999999999991e66 < z

   1. Initial program 86.3%

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

      1. associate-*r/ 98.6%

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

      2. associate-/l/ 83.4%

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

      3. associate-*l/ 82.4%

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

      4. *-commutative 82.4%

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

      5. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in x around 0 43.2%

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

      1. div-inv 44.3%

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

      2. associate-/r* 51.7%

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

   6. Applied egg-rr 51.7%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 14: 48.9% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

   1. associate-*r/ 98.1%

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

   2. associate-/l/ 81.6%

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

   3. associate-*l/ 80.7%

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

   4. *-commutative 80.7%

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

   5. *-commutative 80.7%

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

3. Simplified 80.7%

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

4. Taylor expanded in x around 0 46.9%

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

5. Final simplification 46.9%

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

Alternative 15: 48.3% accurate, 21.4× speedup

Math

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

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(Float64(y / x) / z)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

   1. associate-*r/ 98.1%

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

   2. associate-/l/ 81.6%

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

   3. associate-*l/ 80.7%

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

   4. *-commutative 80.7%

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

   5. *-commutative 80.7%

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

3. Simplified 80.7%

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

4. Taylor expanded in x around 0 46.9%

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

   1. *-commutative 46.9%

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

   2. associate-/r* 50.1%

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

6. Simplified 50.1%

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

7. Final simplification 50.1%

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

Developer target: 96.4% 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 2023196 
(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))