Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.4% → 99.8%

Time: 14.7s

Alternatives: 16

Speedup: 1.0×

• 64.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.4% 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: 99.8% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* (cosh x) (/ y x)) z)))
   (if (<= t_0 (- INFINITY))
     (* y (/ (/ (cosh x) z) x))
     (if (<= t_0 1e+302) t_0 (/ y (* z (/ x (cosh x))))))))

C

double code(double x, double y, double z) {
	double t_0 = (cosh(x) * (y / x)) / z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y * ((cosh(x) / z) / x);
	} else if (t_0 <= 1e+302) {
		tmp = t_0;
	} else {
		tmp = y / (z * (x / cosh(x)));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((Math.cosh(x) / z) / x);
	} else if (t_0 <= 1e+302) {
		tmp = t_0;
	} else {
		tmp = y / (z * (x / Math.cosh(x)));
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cosh(x) * Float64(y / x)) / z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(cosh(x) / z) / x));
	elseif (t_0 <= 1e+302)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(z * Float64(x / cosh(x))));
	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 <= -Inf)
		tmp = y * ((cosh(x) / z) / x);
	elseif (t_0 <= 1e+302)
		tmp = t_0;
	else
		tmp = y / (z * (x / cosh(x)));
	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, (-Infinity)], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+302], t$95$0, N[(y / N[(z * N[(x / N[Cosh[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 93.5%

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

      1. associate-*r/ 81.0%

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

      2. associate-/r* 81.9%

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

   3. Simplified 81.9%

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

      1. associate-*r/ 83.3%

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

      2. *-commutative 83.3%

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

      3. frac-times 93.5%

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

      4. expm1-log1p-u 0.0%

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

      5. expm1-udef 0.0%

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

      6. frac-times 0.0%

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

      7. *-commutative 0.0%

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

      8. associate-*r/ 0.0%

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

      9. associate-/r* 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. expm1-def 0.0%

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

      2. expm1-log1p 81.0%

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

      3. associate-*r/ 93.5%

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

      4. associate-*l/ 93.5%

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

      5. *-commutative 93.5%

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

      6. associate-*l/ 100.0%

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

      7. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

   if -inf.0 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 1.0000000000000001e302

   1. Initial program 99.6%

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

   if 1.0000000000000001e302 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 64.3%

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

      1. associate-*r/ 57.5%

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

      2. associate-/r* 71.5%

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

   3. Simplified 71.5%

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

      1. associate-*r/ 84.0%

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

      2. *-commutative 84.0%

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

      3. frac-times 64.3%

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

      4. expm1-log1p-u 64.3%

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

      5. expm1-udef 64.3%

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

      6. frac-times 72.9%

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

      7. *-commutative 72.9%

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

      8. associate-*r/ 66.0%

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

      9. associate-/r* 57.5%

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

   5. Applied egg-rr 57.5%

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

      1. expm1-def 57.5%

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

      2. expm1-log1p 57.5%

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

      3. associate-*r/ 64.3%

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

      4. associate-*l/ 64.3%

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

      5. *-commutative 64.3%

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

      6. associate-*l/ 99.9%

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

      7. associate-*r/ 99.9%

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

   7. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

      3. associate-/r/ 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

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

Alternative 2: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-121} \lor \neg \left(y \leq -3.2 \cdot 10^{-223}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e-121) (not (<= y -3.2e-223)))
   (* y (/ (/ (cosh x) z) x))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e-121) || !(y <= -3.2e-223)) {
		tmp = y * ((cosh(x) / z) / x);
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.2d-121)) .or. (.not. (y <= (-3.2d-223)))) then
        tmp = y * ((cosh(x) / z) / x)
    else
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e-121) || !(y <= -3.2e-223)) {
		tmp = y * ((Math.cosh(x) / z) / x);
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e-121) or not (y <= -3.2e-223):
		tmp = y * ((math.cosh(x) / z) / x)
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e-121) || !(y <= -3.2e-223))
		tmp = Float64(y * Float64(Float64(cosh(x) / z) / x));
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e-121) || ~((y <= -3.2e-223)))
		tmp = y * ((cosh(x) / z) / x);
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e-121], N[Not[LessEqual[y, -3.2e-223]], $MachinePrecision]], N[(y * N[(N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999967e-121 or -3.2000000000000001e-223 < y

   1. Initial program 84.5%

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

      1. associate-*r/ 78.1%

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

      2. associate-/r* 80.5%

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

   3. Simplified 80.5%

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

      1. associate-*r/ 85.6%

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

      2. *-commutative 85.6%

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

      3. frac-times 84.4%

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

      4. expm1-log1p-u 48.2%

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

      5. expm1-udef 34.5%

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

      6. frac-times 36.0%

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

      7. *-commutative 36.0%

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

      8. associate-*r/ 33.4%

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

      9. associate-/r* 32.0%

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

   5. Applied egg-rr 32.0%

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

      1. expm1-def 45.7%

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

      2. expm1-log1p 78.1%

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

      3. associate-*r/ 84.5%

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

      4. associate-*l/ 84.4%

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

      5. *-commutative 84.4%

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

      6. associate-*l/ 95.4%

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

      7. associate-*r/ 96.7%

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

   7. Simplified 96.7%

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

   if -7.19999999999999967e-121 < y < -3.2000000000000001e-223

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.5%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-121} \lor \neg \left(y \leq -3.2 \cdot 10^{-223}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 3: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x}{z}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+38} \lor \neg \left(y \leq -3.2 \cdot 10^{-227}\right):\\ \;\;\;\;y \cdot \frac{t_0}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (cosh x) z)))
   (if (or (<= y -1.1e+38) (not (<= y -3.2e-227)))
     (* y (/ t_0 x))
     (* (/ y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) / z;
	double tmp;
	if ((y <= -1.1e+38) || !(y <= -3.2e-227)) {
		tmp = y * (t_0 / x);
	} else {
		tmp = (y / x) * 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 = cosh(x) / z
    if ((y <= (-1.1d+38)) .or. (.not. (y <= (-3.2d-227)))) then
        tmp = y * (t_0 / x)
    else
        tmp = (y / x) * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(x) / z;
	double tmp;
	if ((y <= -1.1e+38) || !(y <= -3.2e-227)) {
		tmp = y * (t_0 / x);
	} else {
		tmp = (y / x) * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) / z
	tmp = 0
	if (y <= -1.1e+38) or not (y <= -3.2e-227):
		tmp = y * (t_0 / x)
	else:
		tmp = (y / x) * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) / z)
	tmp = 0.0
	if ((y <= -1.1e+38) || !(y <= -3.2e-227))
		tmp = Float64(y * Float64(t_0 / x));
	else
		tmp = Float64(Float64(y / x) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) / z;
	tmp = 0.0;
	if ((y <= -1.1e+38) || ~((y <= -3.2e-227)))
		tmp = y * (t_0 / x);
	else
		tmp = (y / x) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]}, If[Or[LessEqual[y, -1.1e+38], N[Not[LessEqual[y, -3.2e-227]], $MachinePrecision]], N[(y * N[(t$95$0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000003e38 or -3.2000000000000001e-227 < y

   1. Initial program 82.4%

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

      1. associate-*r/ 76.9%

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

      2. associate-/r* 80.6%

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

   3. Simplified 80.6%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. frac-times 82.3%

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

      4. expm1-log1p-u 47.7%

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

      5. expm1-udef 33.1%

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

      6. frac-times 36.2%

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

      7. *-commutative 36.2%

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

      8. associate-*r/ 33.7%

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

      9. associate-/r* 31.6%

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

   5. Applied egg-rr 31.6%

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

      1. expm1-def 46.2%

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

      2. expm1-log1p 76.9%

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

      3. associate-*r/ 82.4%

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

      4. associate-*l/ 82.3%

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

      5. *-commutative 82.3%

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

      6. associate-*l/ 95.1%

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

      7. associate-*r/ 97.1%

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

   7. Simplified 97.1%

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

   if -1.10000000000000003e38 < y < -3.2000000000000001e-227

   1. Initial program 98.1%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+38} \lor \neg \left(y \leq -3.2 \cdot 10^{-227}\right):\\ \;\;\;\;y \cdot \frac{\frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \]

Alternative 4: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{+254}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.3e+254)
   (+ (* 0.5 (/ (* x y) z)) (/ y (* x z)))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.3e+254) {
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	} 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 (z <= (-7.3d+254)) then
        tmp = (0.5d0 * ((x * y) / z)) + (y / (x * z))
    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 (z <= -7.3e+254) {
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.3e+254:
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z))
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.3e+254)
		tmp = Float64(Float64(0.5 * Float64(Float64(x * y) / z)) + Float64(y / Float64(x * z)));
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.3e+254)
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.3e+254], N[(N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.3000000000000002e254

   1. Initial program 77.6%

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

      1. associate-*r/ 48.1%

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

      2. associate-/r* 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in x around 0 71.1%

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

   if -7.3000000000000002e254 < z

   1. Initial program 86.3%

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

      1. associate-*r/ 82.1%

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

      2. associate-/r* 83.2%

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

   3. Simplified 83.2%

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

      1. associate-*r/ 88.2%

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

      2. *-commutative 88.2%

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

      3. frac-times 86.3%

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

      4. expm1-log1p-u 51.5%

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

      5. expm1-udef 35.9%

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

      6. frac-times 36.9%

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

      7. *-commutative 36.9%

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

      8. associate-*r/ 34.4%

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

      9. associate-/r* 33.8%

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

   5. Applied egg-rr 33.8%

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

      1. expm1-def 49.5%

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

      2. expm1-log1p 82.1%

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

      3. associate-*r/ 86.3%

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

      4. associate-*l/ 86.3%

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

      5. *-commutative 86.3%

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

      6. *-rgt-identity 86.3%

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

      7. associate-*r/ 86.2%

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

      8. associate-*r* 94.3%

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

      9. associate-*r/ 94.4%

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

      10. associate-*r/ 94.3%

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

      11. associate-*l/ 94.4%

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

      12. *-lft-identity 94.4%

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

      13. associate-/l/ 87.2%

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

   7. Simplified 87.2%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{+254}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 5: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

   1. associate-*r/ 79.9%

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

   2. associate-/r* 80.8%

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

3. Simplified 80.8%

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

   1. associate-*r/ 85.5%

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

   2. *-commutative 85.5%

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

   3. frac-times 85.7%

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

   4. expm1-log1p-u 50.1%

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

   5. expm1-udef 34.7%

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

   6. frac-times 35.5%

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

   7. *-commutative 35.5%

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

   8. associate-*r/ 33.2%

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

   9. associate-/r* 32.4%

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

5. Applied egg-rr 32.4%

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

   1. expm1-def 47.7%

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

   2. expm1-log1p 79.9%

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

   3. associate-*r/ 85.7%

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

   4. associate-*l/ 85.7%

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

   5. *-commutative 85.7%

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

   6. associate-*l/ 94.8%

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

   7. associate-*r/ 94.7%

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

7. Simplified 94.7%

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

   1. clear-num 94.7%

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

   2. un-div-inv 95.6%

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

   3. associate-/r/ 95.6%

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

9. Applied egg-rr 95.6%

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

10. Final simplification 95.6%

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

Alternative 6: 69.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{z}{x}}{y}\\ t_1 := \frac{z}{x \cdot y}\\ \mathbf{if}\;x \leq -0.0088:\\ \;\;\;\;\frac{\frac{y}{x} \cdot t_1 + z \cdot 0.5}{z \cdot t_1}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-264}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;x \leq 110:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\frac{x}{y} \cdot -0.5\right) - t_0}{\frac{-x}{\frac{\frac{y}{z}}{t_0}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (/ z x) y)) (t_1 (/ z (* x y))))
   (if (<= x -0.0088)
     (/ (+ (* (/ y x) t_1) (* z 0.5)) (* z t_1))
     (if (<= x -5e-264)
       (/ (/ y z) x)
       (if (<= x 110.0)
         (+ (/ y (* x z)) (* 0.5 (* x (/ y z))))
         (/ (- (* z (* (/ x y) -0.5)) t_0) (/ (- x) (/ (/ y z) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = (z / x) / y;
	double t_1 = z / (x * y);
	double tmp;
	if (x <= -0.0088) {
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1);
	} else if (x <= -5e-264) {
		tmp = (y / z) / x;
	} else if (x <= 110.0) {
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	} else {
		tmp = ((z * ((x / y) * -0.5)) - t_0) / (-x / ((y / z) / 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) :: t_1
    real(8) :: tmp
    t_0 = (z / x) / y
    t_1 = z / (x * y)
    if (x <= (-0.0088d0)) then
        tmp = (((y / x) * t_1) + (z * 0.5d0)) / (z * t_1)
    else if (x <= (-5d-264)) then
        tmp = (y / z) / x
    else if (x <= 110.0d0) then
        tmp = (y / (x * z)) + (0.5d0 * (x * (y / z)))
    else
        tmp = ((z * ((x / y) * (-0.5d0))) - t_0) / (-x / ((y / z) / t_0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z / x) / y;
	double t_1 = z / (x * y);
	double tmp;
	if (x <= -0.0088) {
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1);
	} else if (x <= -5e-264) {
		tmp = (y / z) / x;
	} else if (x <= 110.0) {
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	} else {
		tmp = ((z * ((x / y) * -0.5)) - t_0) / (-x / ((y / z) / t_0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z / x) / y
	t_1 = z / (x * y)
	tmp = 0
	if x <= -0.0088:
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1)
	elif x <= -5e-264:
		tmp = (y / z) / x
	elif x <= 110.0:
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)))
	else:
		tmp = ((z * ((x / y) * -0.5)) - t_0) / (-x / ((y / z) / t_0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z / x) / y)
	t_1 = Float64(z / Float64(x * y))
	tmp = 0.0
	if (x <= -0.0088)
		tmp = Float64(Float64(Float64(Float64(y / x) * t_1) + Float64(z * 0.5)) / Float64(z * t_1));
	elseif (x <= -5e-264)
		tmp = Float64(Float64(y / z) / x);
	elseif (x <= 110.0)
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(x * Float64(y / z))));
	else
		tmp = Float64(Float64(Float64(z * Float64(Float64(x / y) * -0.5)) - t_0) / Float64(Float64(-x) / Float64(Float64(y / z) / t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z / x) / y;
	t_1 = z / (x * y);
	tmp = 0.0;
	if (x <= -0.0088)
		tmp = (((y / x) * t_1) + (z * 0.5)) / (z * t_1);
	elseif (x <= -5e-264)
		tmp = (y / z) / x;
	elseif (x <= 110.0)
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	else
		tmp = ((z * ((x / y) * -0.5)) - t_0) / (-x / ((y / z) / t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z / x), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0088], N[(N[(N[(N[(y / x), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(z * 0.5), $MachinePrecision]), $MachinePrecision] / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e-264], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 110.0], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(N[(x / y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision] / N[((-x) / N[(N[(y / z), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.00880000000000000053

   1. Initial program 88.6%

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

      1. associate-*r/ 75.4%

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

      2. associate-/r* 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around 0 43.1%

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

      1. clear-num 43.1%

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

      2. un-div-inv 43.1%

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

      3. *-commutative 43.1%

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

   6. Applied egg-rr 43.1%

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

      1. +-commutative 43.1%

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

      2. associate-/r* 43.1%

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

      3. frac-add 51.9%

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

      4. *-commutative 51.9%

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

      5. *-commutative 51.9%

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

   8. Applied egg-rr 51.9%

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

   if -0.00880000000000000053 < x < -5.0000000000000001e-264

   1. Initial program 91.1%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 91.1%

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

      1. associate-*r/ 94.0%

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

      2. associate-*l/ 94.0%

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

      3. *-un-lft-identity 94.0%

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

   6. Applied egg-rr 94.0%

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

   if -5.0000000000000001e-264 < x < 110

   1. Initial program 89.8%

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

      1. associate-*r/ 89.7%

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

      2. associate-/r* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around 0 93.3%

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

      1. div-inv 93.3%

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

      2. associate-*l* 93.3%

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

      3. *-commutative 93.3%

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

      4. associate-*l/ 93.3%

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

      5. *-un-lft-identity 93.3%

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

   6. Applied egg-rr 93.3%

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

   if 110 < x

   1. Initial program 69.8%

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

      1. associate-*r/ 54.7%

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

      2. associate-/r* 60.4%

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

   3. Simplified 60.4%

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

   4. Taylor expanded in x around 0 34.6%

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

      1. clear-num 34.6%

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

      2. un-div-inv 34.6%

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

      3. *-commutative 34.6%

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

   6. Applied egg-rr 34.6%

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

      1. frac-2neg 34.6%

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

      2. associate-/l/ 34.6%

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

      3. clear-num 34.6%

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

      4. frac-add 20.6%

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

      5. metadata-eval 20.6%

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

      6. *-commutative 20.6%

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

      7. *-commutative 20.6%

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

   8. Applied egg-rr 20.6%

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

      1. fma-def 20.6%

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

      2. associate-/l* 28.1%

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

      3. *-rgt-identity 28.1%

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

      4. fma-neg 28.1%

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

      5. *-commutative 28.1%

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

      6. associate-*l/ 35.2%

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

      7. *-commutative 35.2%

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

      8. associate-*l* 35.2%

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

      9. associate-/r* 35.2%

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

      10. associate-*r/ 42.7%

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

      11. *-commutative 42.7%

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

      12. distribute-rgt-neg-out 42.7%

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

      13. distribute-lft-neg-out 42.7%

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

      14. associate-/l* 49.8%

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

      15. associate-/r* 48.0%

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

   10. Simplified 48.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0088:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \frac{z}{x \cdot y} + z \cdot 0.5}{z \cdot \frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-264}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;x \leq 110:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(\frac{x}{y} \cdot -0.5\right) - \frac{\frac{z}{x}}{y}}{\frac{-x}{\frac{\frac{y}{z}}{\frac{\frac{z}{x}}{y}}}}\\ \end{array} \]

Alternative 7: 70.3% accurate, 4.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;\frac{z \cdot \left(y + y \cdot \left(0.5 \cdot \left(x \cdot x\right)\right)\right)}{x \cdot \left(z \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 0.5 (/ (* x y) z)) (/ y (* x z)))))
   (if (<= z -1.7e+93)
     t_0
     (if (<= z 2.2e-68)
       (/ (+ (/ y x) (* 0.5 (* x y))) z)
       (if (<= z 1.15e+42)
         (/ (* z (+ y (* y (* 0.5 (* x x))))) (* x (* z z)))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (0.5 * ((x * y) / z)) + (y / (x * z));
	double tmp;
	if (z <= -1.7e+93) {
		tmp = t_0;
	} else if (z <= 2.2e-68) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (z <= 1.15e+42) {
		tmp = (z * (y + (y * (0.5 * (x * x))))) / (x * (z * 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 = (0.5d0 * ((x * y) / z)) + (y / (x * z))
    if (z <= (-1.7d+93)) then
        tmp = t_0
    else if (z <= 2.2d-68) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else if (z <= 1.15d+42) then
        tmp = (z * (y + (y * (0.5d0 * (x * x))))) / (x * (z * 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 = (0.5 * ((x * y) / z)) + (y / (x * z));
	double tmp;
	if (z <= -1.7e+93) {
		tmp = t_0;
	} else if (z <= 2.2e-68) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (z <= 1.15e+42) {
		tmp = (z * (y + (y * (0.5 * (x * x))))) / (x * (z * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.5 * ((x * y) / z)) + (y / (x * z))
	tmp = 0
	if z <= -1.7e+93:
		tmp = t_0
	elif z <= 2.2e-68:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	elif z <= 1.15e+42:
		tmp = (z * (y + (y * (0.5 * (x * x))))) / (x * (z * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.5 * Float64(Float64(x * y) / z)) + Float64(y / Float64(x * z)))
	tmp = 0.0
	if (z <= -1.7e+93)
		tmp = t_0;
	elseif (z <= 2.2e-68)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	elseif (z <= 1.15e+42)
		tmp = Float64(Float64(z * Float64(y + Float64(y * Float64(0.5 * Float64(x * x))))) / Float64(x * Float64(z * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.5 * ((x * y) / z)) + (y / (x * z));
	tmp = 0.0;
	if (z <= -1.7e+93)
		tmp = t_0;
	elseif (z <= 2.2e-68)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	elseif (z <= 1.15e+42)
		tmp = (z * (y + (y * (0.5 * (x * x))))) / (x * (z * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+93], t$95$0, If[LessEqual[z, 2.2e-68], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.15e+42], N[(N[(z * N[(y + N[(y * N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e93 or 1.15e42 < z

   1. Initial program 80.9%

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

      1. associate-*r/ 67.0%

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

      2. associate-/r* 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in x around 0 70.7%

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

   if -1.7e93 < z < 2.20000000000000002e-68

   1. Initial program 88.2%

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

   2. Taylor expanded in x around 0 78.0%

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

   if 2.20000000000000002e-68 < z < 1.15e42

   1. Initial program 92.5%

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

      1. associate-*r/ 92.5%

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

      2. associate-/r* 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in x around 0 63.3%

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

      1. associate-*r/ 63.3%

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

      2. frac-add 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*r* 78.5%

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

   6. Applied egg-rr 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 78.5%

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

      3. +-commutative 78.5%

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

      4. *-commutative 78.5%

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

      5. associate-*r* 78.5%

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

      6. distribute-rgt-out 78.5%

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

      7. associate-*l* 82.1%

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

      8. *-commutative 82.1%

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

      9. associate-*l* 82.1%

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

   8. Simplified 82.1%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+93}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;\frac{z \cdot \left(y + y \cdot \left(0.5 \cdot \left(x \cdot x\right)\right)\right)}{x \cdot \left(z \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \end{array} \]

Alternative 8: 65.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-54} \lor \neg \left(z \leq 5.7 \cdot 10^{-291}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e-54) (not (<= z 5.7e-291)))
   (+ (/ y (* x z)) (* 0.5 (* y (/ x z))))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-54) || !(z <= 5.7e-291)) {
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.6d-54)) .or. (.not. (z <= 5.7d-291))) then
        tmp = (y / (x * z)) + (0.5d0 * (y * (x / z)))
    else
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-54) || !(z <= 5.7e-291)) {
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e-54) or not (z <= 5.7e-291):
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)))
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.6e-54) || !(z <= 5.7e-291))
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(y * Float64(x / z))));
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.6e-54) || ~((z <= 5.7e-291)))
		tmp = (y / (x * z)) + (0.5 * (y * (x / z)));
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e-54], N[Not[LessEqual[z, 5.7e-291]], $MachinePrecision]], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999998e-54 or 5.70000000000000034e-291 < z

   1. Initial program 84.0%

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

      1. associate-*r/ 76.6%

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

      2. associate-/r* 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. associate-/l* 65.9%

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

      2. associate-/r/ 68.7%

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

   6. Applied egg-rr 68.7%

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

   if -4.5999999999999998e-54 < z < 5.70000000000000034e-291

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 87.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-54} \lor \neg \left(z \leq 5.7 \cdot 10^{-291}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 9: 67.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x \cdot z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+93}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + t_0\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0 + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (* x z))))
   (if (<= z -1.7e+93)
     (+ (* 0.5 (/ (* x y) z)) t_0)
     (if (<= z 2.35e-290)
       (/ (+ (/ y x) (* 0.5 (* x y))) z)
       (+ t_0 (* 0.5 (* y (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (z <= -1.7e+93) {
		tmp = (0.5 * ((x * y) / z)) + t_0;
	} else if (z <= 2.35e-290) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = t_0 + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (x * z)
    if (z <= (-1.7d+93)) then
        tmp = (0.5d0 * ((x * y) / z)) + t_0
    else if (z <= 2.35d-290) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = t_0 + (0.5d0 * (y * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (z <= -1.7e+93) {
		tmp = (0.5 * ((x * y) / z)) + t_0;
	} else if (z <= 2.35e-290) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = t_0 + (0.5 * (y * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (x * z)
	tmp = 0
	if z <= -1.7e+93:
		tmp = (0.5 * ((x * y) / z)) + t_0
	elif z <= 2.35e-290:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = t_0 + (0.5 * (y * (x / z)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(x * z))
	tmp = 0.0
	if (z <= -1.7e+93)
		tmp = Float64(Float64(0.5 * Float64(Float64(x * y) / z)) + t_0);
	elseif (z <= 2.35e-290)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(t_0 + Float64(0.5 * Float64(y * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (x * z);
	tmp = 0.0;
	if (z <= -1.7e+93)
		tmp = (0.5 * ((x * y) / z)) + t_0;
	elseif (z <= 2.35e-290)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = t_0 + (0.5 * (y * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+93], N[(N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[z, 2.35e-290], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(t$95$0 + N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e93

   1. Initial program 80.2%

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

      1. associate-*r/ 65.6%

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

      2. associate-/r* 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around 0 71.3%

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

   if -1.7e93 < z < 2.3500000000000001e-290

   1. Initial program 89.1%

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

   2. Taylor expanded in x around 0 79.0%

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

   if 2.3500000000000001e-290 < z

   1. Initial program 85.6%

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

      1. associate-*r/ 79.9%

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

      2. associate-/r* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around 0 68.8%

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

      1. associate-/l* 67.3%

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

      2. associate-/r/ 71.1%

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

   6. Applied egg-rr 71.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+93}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 10: 65.4% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.2e+92)
   (+ (/ y (* x z)) (* 0.5 (* x (/ y z))))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e+92) {
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.2d+92)) then
        tmp = (y / (x * z)) + (0.5d0 * (x * (y / z)))
    else
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.2e+92) {
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.2e+92:
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)))
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.2e+92)
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(x * Float64(y / z))));
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.2e+92)
		tmp = (y / (x * z)) + (0.5 * (x * (y / z)));
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.2e+92], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000004e92

   1. Initial program 80.2%

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

      1. associate-*r/ 65.6%

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

      2. associate-/r* 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around 0 71.3%

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

      1. div-inv 71.3%

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

      2. associate-*l* 63.4%

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

      3. *-commutative 63.4%

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

      4. associate-*l/ 63.4%

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

      5. *-un-lft-identity 63.4%

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

   6. Applied egg-rr 63.4%

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

   if -6.2000000000000004e92 < z

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0 72.0%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 11: 65.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+195}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.7e+195) (/ y (* x z)) (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.7e+195) {
		tmp = y / (x * z);
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.7d+195)) then
        tmp = y / (x * z)
    else
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.7e+195) {
		tmp = y / (x * z);
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.7e+195:
		tmp = y / (x * z)
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.7e+195)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.7e+195)
		tmp = y / (x * z);
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.7e+195], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6999999999999999e195

   1. Initial program 72.5%

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

      1. associate-*r/ 56.3%

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

      2. associate-/r* 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around 0 67.9%

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

   if -4.6999999999999999e195 < z

   1. Initial program 87.6%

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

   2. Taylor expanded in x around 0 70.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+195}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 12: 61.3% accurate, 9.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4) (not (<= x 1.4))) (* 0.5 (/ x (/ z y))) (/ 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 / (z / y));
	} 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 / (z / y))
    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 / (z / y));
	} 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 / (z / y))
	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(z / y)));
	else
		tmp = Float64(y / Float64(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 / (z / y));
	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[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 79.4%

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

      1. associate-*r/ 65.4%

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

      2. associate-/r* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 38.1%

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

   5. Taylor expanded in x around inf 38.1%

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

      1. associate-/l* 32.8%

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

   7. Simplified 32.8%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 90.3%

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

      1. associate-*r/ 90.3%

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

      2. associate-/r* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around 0 91.7%

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

4. Final simplification 67.1%

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

Alternative 13: 65.5% accurate, 9.6× speedup

Math

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

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(Float64(x * y) / z));
	else
		tmp = Float64(y / Float64(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[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 79.4%

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

      1. associate-*r/ 65.4%

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

      2. associate-/r* 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 38.1%

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

   5. Taylor expanded in x around inf 38.1%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 90.3%

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

      1. associate-*r/ 90.3%

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

      2. associate-/r* 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around 0 91.7%

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

4. Final simplification 69.3%

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

Alternative 14: 56.3% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+37} \lor \neg \left(y \leq 3.6 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.2e+37) (not (<= y 3.6e-67))) (/ (/ y z) x) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+37) || !(y <= 3.6e-67)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.2d+37)) .or. (.not. (y <= 3.6d-67))) then
        tmp = (y / z) / x
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.2e+37) || !(y <= 3.6e-67)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.2e+37) or not (y <= 3.6e-67):
		tmp = (y / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.2e+37) || !(y <= 3.6e-67))
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.2e+37) || ~((y <= 3.6e-67)))
		tmp = (y / z) / x;
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.2e+37], N[Not[LessEqual[y, 3.6e-67]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999995e37 or 3.59999999999999999e-67 < y

   1. Initial program 89.3%

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

      1. associate-*l/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 51.8%

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

      1. associate-*r/ 68.0%

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

      2. associate-*l/ 68.1%

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

      3. *-un-lft-identity 68.1%

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

   6. Applied egg-rr 68.1%

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

   if -7.19999999999999995e37 < y < 3.59999999999999999e-67

   1. Initial program 81.9%

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

      1. associate-*r/ 76.2%

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

      2. associate-/r* 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in x around 0 51.5%

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

      1. associate-/r* 59.5%

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

   6. Simplified 59.5%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+37} \lor \neg \left(y \leq 3.6 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 15: 50.2% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-41) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-41) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d-41)) then
        tmp = y / (x * z)
    else
        tmp = (y / x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-41) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e-41:
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e-41)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e-41)
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e-41], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999999e-41

   1. Initial program 87.2%

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

      1. associate-*r/ 84.8%

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

      2. associate-/r* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around 0 60.4%

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

   if -1.8999999999999999e-41 < y

   1. Initial program 85.0%

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

      1. associate-*r/ 77.6%

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

      2. associate-/r* 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in x around 0 55.2%

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

      1. associate-/r* 59.2%

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

   6. Simplified 59.2%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 16: 48.8% 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 85.7%

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

   1. associate-*r/ 79.9%

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

   2. associate-/r* 80.8%

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

3. Simplified 80.8%

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

4. Taylor expanded in x around 0 56.8%

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

5. Final simplification 56.8%

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

Developer target: 97.0% 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 2023279 
(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))