Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 85.1% → 98.1%

Time: 14.0s

Alternatives: 16

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: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* (cosh x) (/ y x)) z) 2e-5)
   (* (/ y x) (/ (cosh x) z))
   (/ (/ (* (cosh x) y) z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((cosh(x) * (y / x)) / z) <= 2e-5) {
		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 (((cosh(x) * (y / x)) / z) <= 2d-5) 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 (((Math.cosh(x) * (y / x)) / z) <= 2e-5) {
		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 ((math.cosh(x) * (y / x)) / z) <= 2e-5:
		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 (Float64(Float64(cosh(x) * Float64(y / x)) / z) <= 2e-5)
		tmp = Float64(Float64(y / x) * Float64(cosh(x) / z));
	else
		tmp = Float64(Float64(Float64(cosh(x) * y) / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((cosh(x) * (y / x)) / z) <= 2e-5)
		tmp = (y / x) * (cosh(x) / z);
	else
		tmp = ((cosh(x) * y) / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 2e-5], N[(N[(y / x), $MachinePrecision] * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Cosh[x], $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 2.00000000000000016e-5

   1. Initial program 98.9%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   if 2.00000000000000016e-5 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 70.0%

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

      1. associate-*r/ 61.4%

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

      2. associate-/r* 71.0%

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

   3. Simplified 71.0%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

      3. frac-times 70.0%

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

      4. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. associate-*r/ 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\cosh x}{z}\\ \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{x} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t_0}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (cosh x) z)))
   (if (<= (/ (* (cosh x) (/ y x)) z) 4e+113)
     (* (/ y x) t_0)
     (/ (* y t_0) x))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) / z;
	double tmp;
	if (((cosh(x) * (y / x)) / z) <= 4e+113) {
		tmp = (y / x) * t_0;
	} else {
		tmp = (y * t_0) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cosh(x) / z
    if (((cosh(x) * (y / x)) / z) <= 4d+113) then
        tmp = (y / x) * t_0
    else
        tmp = (y * t_0) / x
    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 (((Math.cosh(x) * (y / x)) / z) <= 4e+113) {
		tmp = (y / x) * t_0;
	} else {
		tmp = (y * t_0) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) / z
	tmp = 0
	if ((math.cosh(x) * (y / x)) / z) <= 4e+113:
		tmp = (y / x) * t_0
	else:
		tmp = (y * t_0) / x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) / z)
	tmp = 0.0
	if (Float64(Float64(cosh(x) * Float64(y / x)) / z) <= 4e+113)
		tmp = Float64(Float64(y / x) * t_0);
	else
		tmp = Float64(Float64(y * t_0) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) / z;
	tmp = 0.0;
	if (((cosh(x) * (y / x)) / z) <= 4e+113)
		tmp = (y / x) * t_0;
	else
		tmp = (y * t_0) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 4e+113], N[(N[(y / x), $MachinePrecision] * t$95$0), $MachinePrecision], N[(N[(y * t$95$0), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z) < 4e113

   1. Initial program 99.0%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

   if 4e113 < (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

   1. Initial program 67.5%

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

      1. associate-*r/ 58.1%

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

      2. associate-/r* 68.5%

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

   3. Simplified 68.5%

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

      1. associate-*r/ 76.3%

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

      2. *-commutative 76.3%

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

      3. frac-times 67.5%

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

      4. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cosh x \cdot \frac{y}{x}}{z} \leq 4 \cdot 10^{+113}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{z}}{x}\\ \end{array} \]

Alternative 3: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+154} \lor \neg \left(x \leq 1.95 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e+154) (not (<= x 1.95e+121)))
   (/ (* y (/ 0.5 (/ z (* x x)))) x)
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e+154) || !(x <= 1.95e+121)) {
		tmp = (y * (0.5 / (z / (x * x)))) / 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 ((x <= (-1.3d+154)) .or. (.not. (x <= 1.95d+121))) then
        tmp = (y * (0.5d0 / (z / (x * x)))) / 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 ((x <= -1.3e+154) || !(x <= 1.95e+121)) {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e+154) or not (x <= 1.95e+121):
		tmp = (y * (0.5 / (z / (x * x)))) / x
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e+154) || !(x <= 1.95e+121))
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / Float64(x * x)))) / 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 ((x <= -1.3e+154) || ~((x <= 1.95e+121)))
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e+154], N[Not[LessEqual[x, 1.95e+121]], $MachinePrecision]], N[(N[(y * N[(0.5 / N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.29999999999999994e154 or 1.94999999999999992e121 < x

   1. Initial program 56.6%

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

      1. associate-*r/ 43.4%

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

      2. associate-/r* 52.6%

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

   3. Simplified 52.6%

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

      1. associate-*r/ 59.2%

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

      2. *-commutative 59.2%

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

      3. frac-times 56.6%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 97.4%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 50.2%

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

   8. Simplified 97.4%

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

   9. Taylor expanded in x around inf 97.4%

      \[\leadsto \frac{y \cdot \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{z}\right)}}{x} \]
   10. Step-by-step derivation

       1. unpow2 97.4%

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

       2. associate-*r/ 97.4%

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

       3. associate-/l* 97.4%

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

   11. Simplified 97.4%

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

   if -1.29999999999999994e154 < x < 1.94999999999999992e121

   1. Initial program 94.5%

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

      1. associate-*r/ 90.1%

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

      2. associate-/r* 91.4%

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

   3. Simplified 91.4%

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

      1. associate-/r* 90.1%

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

      2. associate-*r/ 94.5%

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

      3. associate-/l* 88.6%

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

      4. add-log-exp 53.4%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\cosh x}{\frac{z}{\frac{y}{x}}}}\right)} \]

      5. *-un-lft-identity 53.4%

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

      6. log-prod 53.4%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\cosh x}{\frac{z}{\frac{y}{x}}}}\right)} \]

      7. metadata-eval 53.4%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\cosh x}{\frac{z}{\frac{y}{x}}}}\right) \]

      8. add-log-exp 88.6%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x}{\frac{z}{\frac{y}{x}}}} \]

      9. associate-/l* 94.5%

         \[\leadsto 0 + \color{blue}{\frac{\cosh x \cdot \frac{y}{x}}{z}} \]

      10. associate-*r/ 90.1%

          \[\leadsto 0 + \color{blue}{\cosh x \cdot \frac{\frac{y}{x}}{z}} \]

   5. Applied egg-rr 90.1%

      \[\leadsto \color{blue}{0 + \cosh x \cdot \frac{\frac{y}{x}}{z}} \]
   6. Step-by-step derivation

      1. +-lft-identity 90.1%

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

      2. *-commutative 90.1%

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

      3. associate-/r* 91.4%

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

      4. associate-*l/ 95.8%

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

      5. associate-*r/ 95.0%

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

   7. Simplified 95.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+154} \lor \neg \left(x \leq 1.95 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 4: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+182} \lor \neg \left(x \leq 5.5 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.3e+182) (not (<= x 5.5e+144)))
   (/ (* y (/ 0.5 (/ z (* x x)))) x)
   (* (/ y x) (/ (cosh x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.3e+182) || !(x <= 5.5e+144)) {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	} 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) :: tmp
    if ((x <= (-3.3d+182)) .or. (.not. (x <= 5.5d+144))) then
        tmp = (y * (0.5d0 / (z / (x * x)))) / x
    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 tmp;
	if ((x <= -3.3e+182) || !(x <= 5.5e+144)) {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	} else {
		tmp = (y / x) * (Math.cosh(x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.3e+182) or not (x <= 5.5e+144):
		tmp = (y * (0.5 / (z / (x * x)))) / x
	else:
		tmp = (y / x) * (math.cosh(x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.3e+182) || !(x <= 5.5e+144))
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / Float64(x * x)))) / x);
	else
		tmp = Float64(Float64(y / x) * Float64(cosh(x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.3e+182) || ~((x <= 5.5e+144)))
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	else
		tmp = (y / x) * (cosh(x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.3e+182], N[Not[LessEqual[x, 5.5e+144]], $MachinePrecision]], N[(N[(y * N[(0.5 / N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3000000000000001e182 or 5.50000000000000022e144 < x

   1. Initial program 50.7%

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

      1. associate-*r/ 40.3%

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

      2. associate-/r* 53.7%

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

   3. Simplified 53.7%

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

      1. associate-*r/ 59.7%

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

      2. *-commutative 59.7%

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

      3. frac-times 50.7%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 100.0%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 52.3%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around inf 100.0%

      \[\leadsto \frac{y \cdot \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{z}\right)}}{x} \]
   10. Step-by-step derivation

       1. unpow2 100.0%

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

       2. associate-*r/ 100.0%

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

       3. associate-/l* 100.0%

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

   11. Simplified 100.0%

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

   if -3.3000000000000001e182 < x < 5.50000000000000022e144

   1. Initial program 94.8%

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

      1. associate-*l/ 94.8%

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

   3. Simplified 94.8%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+182} \lor \neg \left(x \leq 5.5 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \]

Alternative 5: 79.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot \left(x \cdot 0.5\right)\right)}{x}}{z}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(x \cdot x\right)\right) \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5e+32)
   (/ (/ (* y (* x (* x 0.5))) x) z)
   (if (<= x 1.45e+47)
     (* (+ 1.0 (* 0.5 (* x x))) (/ y (* x z)))
     (/ (* y (/ 0.5 (/ z (* x x)))) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5e+32) {
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	} else if (x <= 1.45e+47) {
		tmp = (1.0 + (0.5 * (x * x))) * (y / (x * z));
	} else {
		tmp = (y * (0.5 / (z / (x * x)))) / 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 <= (-5d+32)) then
        tmp = ((y * (x * (x * 0.5d0))) / x) / z
    else if (x <= 1.45d+47) then
        tmp = (1.0d0 + (0.5d0 * (x * x))) * (y / (x * z))
    else
        tmp = (y * (0.5d0 / (z / (x * x)))) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5e+32) {
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	} else if (x <= 1.45e+47) {
		tmp = (1.0 + (0.5 * (x * x))) * (y / (x * z));
	} else {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5e+32:
		tmp = ((y * (x * (x * 0.5))) / x) / z
	elif x <= 1.45e+47:
		tmp = (1.0 + (0.5 * (x * x))) * (y / (x * z))
	else:
		tmp = (y * (0.5 / (z / (x * x)))) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5e+32)
		tmp = Float64(Float64(Float64(y * Float64(x * Float64(x * 0.5))) / x) / z);
	elseif (x <= 1.45e+47)
		tmp = Float64(Float64(1.0 + Float64(0.5 * Float64(x * x))) * Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / Float64(x * x)))) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5e+32)
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	elseif (x <= 1.45e+47)
		tmp = (1.0 + (0.5 * (x * x))) * (y / (x * z));
	else
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5e+32], N[(N[(N[(y * N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 1.45e+47], N[(N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.9999999999999997e32

   1. Initial program 77.2%

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

      1. associate-*r/ 57.9%

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

      2. associate-/r* 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in x around 0 41.2%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in x around inf 41.2%

      \[\leadsto \color{blue}{\left(0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   8. Step-by-step derivation

      1. unpow2 41.2%

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

   9. Simplified 41.2%

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

       1. associate-*r/ 44.6%

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

       2. associate-/r* 77.9%

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

       3. *-commutative 77.9%

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

       4. *-commutative 77.9%

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

       5. associate-*l* 77.9%

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

   11. Applied egg-rr 77.9%

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

   if -4.9999999999999997e32 < x < 1.4499999999999999e47

   1. Initial program 95.1%

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

      1. associate-*r/ 93.7%

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

      2. associate-/r* 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around 0 87.5%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 87.5%

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

   6. Simplified 87.5%

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

   if 1.4499999999999999e47 < x

   1. Initial program 60.3%

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

      1. associate-*r/ 51.7%

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

      2. associate-/r* 65.5%

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

   3. Simplified 65.5%

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

      1. associate-*r/ 75.9%

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

      2. *-commutative 75.9%

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

      3. frac-times 60.3%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.9%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 49.1%

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

   8. Simplified 79.9%

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

   9. Taylor expanded in x around inf 79.9%

      \[\leadsto \frac{y \cdot \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{z}\right)}}{x} \]
   10. Step-by-step derivation

       1. unpow2 79.9%

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

       2. associate-*r/ 79.9%

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

       3. associate-/l* 79.9%

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

   11. Simplified 79.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot \left(x \cdot 0.5\right)\right)}{x}}{z}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;\left(1 + 0.5 \cdot \left(x \cdot x\right)\right) \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \end{array} \]

Alternative 6: 79.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot \left(x \cdot 0.5\right)\right)}{x}}{z}\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+109}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e+32)
   (/ (/ (* y (* x (* x 0.5))) x) z)
   (if (<= x 9.6e+109)
     (+ (* 0.5 (/ (* x y) z)) (/ y (* x z)))
     (/ (* y (/ 0.5 (/ z (* x x)))) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+32) {
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	} else if (x <= 9.6e+109) {
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	} else {
		tmp = (y * (0.5 / (z / (x * x)))) / 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 <= (-2d+32)) then
        tmp = ((y * (x * (x * 0.5d0))) / x) / z
    else if (x <= 9.6d+109) then
        tmp = (0.5d0 * ((x * y) / z)) + (y / (x * z))
    else
        tmp = (y * (0.5d0 / (z / (x * x)))) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+32) {
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	} else if (x <= 9.6e+109) {
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	} else {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e+32:
		tmp = ((y * (x * (x * 0.5))) / x) / z
	elif x <= 9.6e+109:
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z))
	else:
		tmp = (y * (0.5 / (z / (x * x)))) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e+32)
		tmp = Float64(Float64(Float64(y * Float64(x * Float64(x * 0.5))) / x) / z);
	elseif (x <= 9.6e+109)
		tmp = Float64(Float64(0.5 * Float64(Float64(x * y) / z)) + Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / Float64(x * x)))) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e+32)
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	elseif (x <= 9.6e+109)
		tmp = (0.5 * ((x * y) / z)) + (y / (x * z));
	else
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e+32], N[(N[(N[(y * N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 9.6e+109], N[(N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.00000000000000011e32

   1. Initial program 77.2%

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

      1. associate-*r/ 57.9%

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

      2. associate-/r* 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in x around 0 41.2%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 41.2%

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

   6. Simplified 41.2%

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

   7. Taylor expanded in x around inf 41.2%

      \[\leadsto \color{blue}{\left(0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   8. Step-by-step derivation

      1. unpow2 41.2%

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

   9. Simplified 41.2%

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

       1. associate-*r/ 44.6%

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

       2. associate-/r* 77.9%

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

       3. *-commutative 77.9%

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

       4. *-commutative 77.9%

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

       5. associate-*l* 77.9%

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

   11. Applied egg-rr 77.9%

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

   if -2.00000000000000011e32 < x < 9.59999999999999949e109

   1. Initial program 94.8%

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

      1. associate-*r/ 92.9%

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

      2. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 83.4%

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

   if 9.59999999999999949e109 < x

   1. Initial program 52.2%

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

      1. associate-*r/ 43.5%

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

      2. associate-/r* 60.9%

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

   3. Simplified 60.9%

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

      1. associate-*r/ 71.7%

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

      2. *-commutative 71.7%

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

      3. frac-times 52.2%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 93.6%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 54.8%

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

   8. Simplified 93.6%

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

   9. Taylor expanded in x around inf 93.6%

      \[\leadsto \frac{y \cdot \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{z}\right)}}{x} \]
   10. Step-by-step derivation

       1. unpow2 93.6%

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

       2. associate-*r/ 93.6%

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

       3. associate-/l* 93.6%

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

   11. Simplified 93.6%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot \left(x \cdot 0.5\right)\right)}{x}}{z}\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+109}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \end{array} \]

Alternative 7: 76.1% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;\frac{0.5 \cdot \frac{x \cdot \left(x \cdot y\right)}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (not (<= x 1.4)))
   (/ (* 0.5 (/ (* x (* x y)) z)) x)
   (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 1.4)) {
		tmp = (0.5 * ((x * (x * 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 ((x <= (-1.45d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = (0.5d0 * ((x * (x * 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 ((x <= -1.45) || !(x <= 1.4)) {
		tmp = (0.5 * ((x * (x * y)) / z)) / x;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45) or not (x <= 1.4):
		tmp = (0.5 * ((x * (x * y)) / z)) / x
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45) || !(x <= 1.4))
		tmp = Float64(Float64(0.5 * Float64(Float64(x * Float64(x * y)) / z)) / x);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((x <= 1.4)))
		tmp = (0.5 * ((x * (x * y)) / z)) / x;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(N[(0.5 * N[(N[(x * N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 1.3999999999999999 < x

   1. Initial program 72.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/r* 62.8%

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

   3. Simplified 62.8%

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

      1. associate-*r/ 72.9%

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

      2. *-commutative 72.9%

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

      3. frac-times 72.1%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 70.1%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 40.8%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in x around inf 70.9%

      \[\leadsto \frac{\color{blue}{0.5 \cdot \frac{{x}^{2} \cdot y}{z}}}{x} \]
   10. Step-by-step derivation

       1. unpow2 70.9%

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

       2. associate-*l* 63.3%

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

       3. *-commutative 63.3%

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

   11. Simplified 63.3%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;\frac{0.5 \cdot \frac{x \cdot \left(x \cdot y\right)}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 8: 80.4% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (not (<= x 1.4)))
   (/ (* y (/ 0.5 (/ z (* x x)))) x)
   (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45) || !(x <= 1.4)) {
		tmp = (y * (0.5 / (z / (x * x)))) / 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 ((x <= (-1.45d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = (y * (0.5d0 / (z / (x * x)))) / 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 ((x <= -1.45) || !(x <= 1.4)) {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45) or not (x <= 1.4):
		tmp = (y * (0.5 / (z / (x * x)))) / x
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45) || !(x <= 1.4))
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / Float64(x * x)))) / x);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((x <= 1.4)))
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(N[(y * N[(0.5 / N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 1.3999999999999999 < x

   1. Initial program 72.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/r* 62.8%

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

   3. Simplified 62.8%

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

      1. associate-*r/ 72.9%

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

      2. *-commutative 72.9%

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

      3. frac-times 72.1%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 70.1%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 40.8%

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

   8. Simplified 70.1%

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

   9. Taylor expanded in x around inf 70.1%

      \[\leadsto \frac{y \cdot \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{z}\right)}}{x} \]
   10. Step-by-step derivation

       1. unpow2 70.1%

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

       2. associate-*r/ 70.1%

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

       3. associate-/l* 70.1%

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

   11. Simplified 70.1%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 9: 64.3% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x \cdot z}\\ \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(x \cdot x\right)\right) \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (* x z))))
   (if (<= x -1.45)
     (* 0.5 (/ (* x y) z))
     (if (<= x 1.4) t_0 (* (* 0.5 (* x x)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if (x <= -1.45) {
		tmp = 0.5 * ((x * y) / z);
	} else if (x <= 1.4) {
		tmp = t_0;
	} else {
		tmp = (0.5 * (x * 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 = y / (x * z)
    if (x <= (-1.45d0)) then
        tmp = 0.5d0 * ((x * y) / z)
    else if (x <= 1.4d0) then
        tmp = t_0
    else
        tmp = (0.5d0 * (x * x)) * t_0
    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 (x <= -1.45) {
		tmp = 0.5 * ((x * y) / z);
	} else if (x <= 1.4) {
		tmp = t_0;
	} else {
		tmp = (0.5 * (x * x)) * t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (x * z)
	tmp = 0
	if x <= -1.45:
		tmp = 0.5 * ((x * y) / z)
	elif x <= 1.4:
		tmp = t_0
	else:
		tmp = (0.5 * (x * x)) * t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(x * z))
	tmp = 0.0
	if (x <= -1.45)
		tmp = Float64(0.5 * Float64(Float64(x * y) / z));
	elseif (x <= 1.4)
		tmp = t_0;
	else
		tmp = Float64(Float64(0.5 * Float64(x * x)) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (x * z);
	tmp = 0.0;
	if (x <= -1.45)
		tmp = 0.5 * ((x * y) / z);
	elseif (x <= 1.4)
		tmp = t_0;
	else
		tmp = (0.5 * (x * x)) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45], N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4], t$95$0, N[(N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999996

   1. Initial program 79.7%

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

      1. associate-*r/ 60.9%

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

      2. associate-/r* 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in x around 0 37.1%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in x around inf 45.9%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

   if 1.3999999999999999 < x

   1. Initial program 64.6%

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

      1. associate-*r/ 55.4%

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

      2. associate-/r* 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around 0 44.4%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in x around inf 44.4%

      \[\leadsto \color{blue}{\left(0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   8. Step-by-step derivation

      1. unpow2 44.4%

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

   9. Simplified 44.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \left(x \cdot x\right)\right) \cdot \frac{y}{x \cdot z}\\ \end{array} \]

Alternative 10: 79.8% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot \left(x \cdot 0.5\right)\right)}{x}}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45)
   (/ (/ (* y (* x (* x 0.5))) x) z)
   (if (<= x 1.4) (/ y (* x z)) (/ (* y (/ 0.5 (/ z (* x x)))) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45) {
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	} else if (x <= 1.4) {
		tmp = y / (x * z);
	} else {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.45d0)) then
        tmp = ((y * (x * (x * 0.5d0))) / x) / z
    else if (x <= 1.4d0) then
        tmp = y / (x * z)
    else
        tmp = (y * (0.5d0 / (z / (x * x)))) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.45) {
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	} else if (x <= 1.4) {
		tmp = y / (x * z);
	} else {
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.45:
		tmp = ((y * (x * (x * 0.5))) / x) / z
	elif x <= 1.4:
		tmp = y / (x * z)
	else:
		tmp = (y * (0.5 / (z / (x * x)))) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.45)
		tmp = Float64(Float64(Float64(y * Float64(x * Float64(x * 0.5))) / x) / z);
	elseif (x <= 1.4)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / Float64(x * x)))) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.45)
		tmp = ((y * (x * (x * 0.5))) / x) / z;
	elseif (x <= 1.4)
		tmp = y / (x * z);
	else
		tmp = (y * (0.5 / (z / (x * x)))) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.45], N[(N[(N[(y * N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 1.4], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999996

   1. Initial program 79.7%

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

      1. associate-*r/ 60.9%

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

      2. associate-/r* 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in x around 0 37.1%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in x around inf 37.1%

      \[\leadsto \color{blue}{\left(0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   8. Step-by-step derivation

      1. unpow2 37.1%

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

   9. Simplified 37.1%

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

       1. associate-*r/ 40.1%

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

       2. associate-/r* 69.8%

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

       3. *-commutative 69.8%

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

       4. *-commutative 69.8%

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

       5. associate-*l* 69.8%

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

   11. Applied egg-rr 69.8%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

   if 1.3999999999999999 < x

   1. Initial program 64.6%

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

      1. associate-*r/ 55.4%

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

      2. associate-/r* 67.7%

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

   3. Simplified 67.7%

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

      1. associate-*r/ 78.5%

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

      2. *-commutative 78.5%

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

      3. frac-times 64.6%

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

      4. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 71.9%

      \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
   7. Step-by-step derivation

      1. unpow2 44.4%

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

   8. Simplified 71.9%

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

   9. Taylor expanded in x around inf 71.9%

      \[\leadsto \frac{y \cdot \color{blue}{\left(0.5 \cdot \frac{{x}^{2}}{z}\right)}}{x} \]
   10. Step-by-step derivation

       1. unpow2 71.9%

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

       2. associate-*r/ 71.9%

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

       3. associate-/l* 71.9%

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

   11. Simplified 71.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;\frac{\frac{y \cdot \left(x \cdot \left(x \cdot 0.5\right)\right)}{x}}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{0.5}{\frac{z}{x \cdot x}}}{x}\\ \end{array} \]

Alternative 11: 80.8% accurate, 8.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

   1. associate-*r/ 76.2%

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

   2. associate-/r* 79.9%

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

3. Simplified 79.9%

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

   1. associate-*r/ 84.9%

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

   2. *-commutative 84.9%

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

   3. frac-times 83.3%

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

   4. associate-*l/ 97.2%

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

5. Applied egg-rr 97.2%

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

6. Taylor expanded in x around 0 81.8%

   \[\leadsto \frac{y \cdot \frac{\color{blue}{1 + 0.5 \cdot {x}^{2}}}{z}}{x} \]
7. Step-by-step derivation

   1. unpow2 68.5%

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

8. Simplified 81.8%

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

9. Final simplification 81.8%

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

Alternative 12: 61.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (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 <= -1.45) || !(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 <= (-1.45d0)) .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 <= -1.45) || !(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 <= -1.45) 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 <= -1.45) || !(x <= 1.4))
		tmp = Float64(0.5 * Float64(x * Float64(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 <= -1.45) || ~((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, -1.45], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 1.3999999999999999 < x

   1. Initial program 72.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/r* 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around 0 40.8%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 40.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in x around inf 43.3%

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

      1. div-inv 43.3%

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

      2. associate-*l* 34.5%

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

      3. *-commutative 34.5%

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

      4. associate-*l/ 34.5%

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

      5. *-un-lft-identity 34.5%

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

   9. Applied egg-rr 34.5%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 13: 65.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45) (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 <= -1.45) || !(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 <= (-1.45d0)) .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 <= -1.45) || !(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 <= -1.45) 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 <= -1.45) || !(x <= 1.4))
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45) || ~((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, -1.45], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999996 or 1.3999999999999999 < x

   1. Initial program 72.1%

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

      1. associate-*r/ 58.1%

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

      2. associate-/r* 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in x around 0 40.8%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 40.8%

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

   6. Simplified 40.8%

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

   7. Taylor expanded in x around inf 43.3%

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

      1. associate-*l/ 41.1%

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

      2. *-commutative 41.1%

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

   9. Simplified 41.1%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 14: 65.1% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.45)
   (* 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 <= -1.45) {
		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 <= (-1.45d0)) 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 <= -1.45) {
		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 <= -1.45:
		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 <= -1.45)
		tmp = Float64(0.5 * Float64(Float64(x * y) / z));
	elseif (x <= 1.4)
		tmp = Float64(y / Float64(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 <= -1.45)
		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, -1.45], N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.44999999999999996

   1. Initial program 79.7%

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

      1. associate-*r/ 60.9%

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

      2. associate-/r* 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in x around 0 37.1%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 37.1%

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

   6. Simplified 37.1%

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

   7. Taylor expanded in x around inf 45.9%

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

   if -1.44999999999999996 < x < 1.3999999999999999

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 96.6%

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

   if 1.3999999999999999 < x

   1. Initial program 64.6%

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

      1. associate-*r/ 55.4%

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

      2. associate-/r* 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around 0 44.4%

      \[\leadsto \color{blue}{\left(1 + 0.5 \cdot {x}^{2}\right)} \cdot \frac{y}{x \cdot z} \]
   5. Step-by-step derivation

      1. unpow2 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in x around inf 40.8%

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

      1. associate-*l/ 43.7%

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

      2. *-commutative 43.7%

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

   9. Simplified 43.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 15: 54.4% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.35e-107) (/ (/ y z) x) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.35e-107) {
		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 (z <= 1.35d-107) 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 (z <= 1.35e-107) {
		tmp = (y / z) / x;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.35e-107:
		tmp = (y / z) / x
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.35e-107)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.35e-107)
		tmp = (y / z) / x;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.35e-107], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.35e-107

   1. Initial program 82.2%

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

      1. associate-*r/ 76.3%

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

      2. associate-/r* 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in x around 0 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/r* 52.7%

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

   6. Simplified 52.7%

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

   if 1.35e-107 < z

   1. Initial program 85.3%

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

      1. associate-*r/ 76.1%

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

      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 60.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.35 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 16: 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 83.2%

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

   1. associate-*r/ 76.2%

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

   2. associate-/r* 79.9%

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

3. Simplified 79.9%

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

4. Taylor expanded in x around 0 52.0%

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

5. Final simplification 52.0%

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

Developer target: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023280 
(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))