Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.4% → 99.8%

Time: 12.9s

Alternatives: 19

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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cosh x \cdot \frac{y}{x}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+304} \lor \neg \left(t_0 \leq 5 \cdot 10^{+206}\right):\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cosh x) (/ y x))))
   (if (or (<= t_0 -1e+304) (not (<= t_0 5e+206)))
     (/ (* y (/ (cosh x) z)) x)
     (/ t_0 z))))

C

double code(double x, double y, double z) {
	double t_0 = cosh(x) * (y / x);
	double tmp;
	if ((t_0 <= -1e+304) || !(t_0 <= 5e+206)) {
		tmp = (y * (cosh(x) / z)) / x;
	} else {
		tmp = t_0 / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cosh(x) * (y / x)
    if ((t_0 <= (-1d+304)) .or. (.not. (t_0 <= 5d+206))) then
        tmp = (y * (cosh(x) / z)) / x
    else
        tmp = t_0 / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cosh(x) * (y / x);
	double tmp;
	if ((t_0 <= -1e+304) || !(t_0 <= 5e+206)) {
		tmp = (y * (Math.cosh(x) / z)) / x;
	} else {
		tmp = t_0 / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cosh(x) * (y / x)
	tmp = 0
	if (t_0 <= -1e+304) or not (t_0 <= 5e+206):
		tmp = (y * (math.cosh(x) / z)) / x
	else:
		tmp = t_0 / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cosh(x) * Float64(y / x))
	tmp = 0.0
	if ((t_0 <= -1e+304) || !(t_0 <= 5e+206))
		tmp = Float64(Float64(y * Float64(cosh(x) / z)) / x);
	else
		tmp = Float64(t_0 / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cosh(x) * (y / x);
	tmp = 0.0;
	if ((t_0 <= -1e+304) || ~((t_0 <= 5e+206)))
		tmp = (y * (cosh(x) / z)) / x;
	else
		tmp = t_0 / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cosh[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+304], N[Not[LessEqual[t$95$0, 5e+206]], $MachinePrecision]], N[(N[(y * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(t$95$0 / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (cosh.f64 x) (/.f64 y x)) < -9.9999999999999994e303 or 5.0000000000000002e206 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 76.4%

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

      1. associate-*r/ 66.6%

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

      2. associate-/r* 75.1%

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

   3. Simplified 75.1%

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

      1. associate-*r/ 82.9%

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

      2. *-commutative 82.9%

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

      3. frac-times 76.4%

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

      4. associate-*l/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -9.9999999999999994e303 < (*.f64 (cosh.f64 x) (/.f64 y x)) < 5.0000000000000002e206

   1. Initial program 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \leq -1 \cdot 10^{+304} \lor \neg \left(\cosh x \cdot \frac{y}{x} \leq 5 \cdot 10^{+206}\right):\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array} \]

Alternative 2: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{+222}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot 0.5 + \frac{z}{x \cdot x}}{z \cdot \frac{z}{x \cdot y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 3.1e+222)
   (* (cosh x) (/ y (* x z)))
   (/ (+ (* z 0.5) (/ z (* x x))) (* z (/ z (* x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.1e+222) {
		tmp = cosh(x) * (y / (x * z));
	} else {
		tmp = ((z * 0.5) + (z / (x * x))) / (z * (z / (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 3.1d+222) then
        tmp = cosh(x) * (y / (x * z))
    else
        tmp = ((z * 0.5d0) + (z / (x * x))) / (z * (z / (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.1e+222) {
		tmp = Math.cosh(x) * (y / (x * z));
	} else {
		tmp = ((z * 0.5) + (z / (x * x))) / (z * (z / (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3.1e+222:
		tmp = math.cosh(x) * (y / (x * z))
	else:
		tmp = ((z * 0.5) + (z / (x * x))) / (z * (z / (x * y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.1e+222)
		tmp = Float64(cosh(x) * Float64(y / Float64(x * z)));
	else
		tmp = Float64(Float64(Float64(z * 0.5) + Float64(z / Float64(x * x))) / Float64(z * Float64(z / Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.1e+222)
		tmp = cosh(x) * (y / (x * z));
	else
		tmp = ((z * 0.5) + (z / (x * x))) / (z * (z / (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.1e+222], N[(N[Cosh[x], $MachinePrecision] * N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * 0.5), $MachinePrecision] + N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.0999999999999998e222

   1. Initial program 88.1%

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

      1. associate-*r/ 83.5%

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

      2. associate-/r* 84.4%

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

   3. Simplified 84.4%

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

   if 3.0999999999999998e222 < x

   1. Initial program 52.9%

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

      1. associate-*r/ 29.4%

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

      2. associate-/r* 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in x around 0 48.9%

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

      1. associate-/l/ 48.9%

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

      2. +-commutative 48.9%

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

      3. associate-/l* 32.1%

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

   6. Simplified 32.1%

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

      1. *-un-lft-identity 32.1%

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

      2. associate-*l/ 32.1%

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

      3. +-commutative 32.1%

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

      4. associate-*l/ 32.1%

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

      5. *-un-lft-identity 32.1%

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

      6. frac-2neg 32.1%

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

      7. associate-*r/ 32.1%

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

      8. frac-add 48.1%

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

   8. Applied egg-rr 48.1%

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

      1. +-commutative 48.1%

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

      2. *-commutative 48.1%

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

      3. distribute-rgt-neg-out 48.1%

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

      4. unsub-neg 48.1%

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

      5. distribute-lft-neg-out 48.1%

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

      6. distribute-rgt-neg-in 48.1%

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

      7. *-commutative 48.1%

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

      8. distribute-rgt-neg-in 48.1%

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

      9. metadata-eval 48.1%

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

      10. associate-*r/ 48.1%

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

      11. *-commutative 48.1%

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

      12. *-lft-identity 48.1%

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

      13. times-frac 48.1%

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

      14. /-rgt-identity 48.1%

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

      15. associate-/r* 48.1%

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

      16. associate-*r/ 30.3%

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

      17. associate-/l* 48.1%

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

   10. Simplified 48.1%

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

   11. Taylor expanded in y around -inf 30.3%

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

       1. associate-/l* 30.5%

          \[\leadsto \color{blue}{\frac{0.5 \cdot z - -1 \cdot \frac{z}{{x}^{2}}}{\frac{{z}^{2}}{y \cdot x}}} \]

       2. associate-*r/ 30.5%

          \[\leadsto \frac{0.5 \cdot z - \color{blue}{\frac{-1 \cdot z}{{x}^{2}}}}{\frac{{z}^{2}}{y \cdot x}} \]

       3. neg-mul-1 30.5%

          \[\leadsto \frac{0.5 \cdot z - \frac{\color{blue}{-z}}{{x}^{2}}}{\frac{{z}^{2}}{y \cdot x}} \]

       4. unpow2 30.5%

          \[\leadsto \frac{0.5 \cdot z - \frac{-z}{\color{blue}{x \cdot x}}}{\frac{{z}^{2}}{y \cdot x}} \]

       5. unpow2 30.5%

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

       6. associate-*r/ 54.2%

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

       7. *-commutative 54.2%

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

   13. Simplified 54.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{+222}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot 0.5 + \frac{z}{x \cdot x}}{z \cdot \frac{z}{x \cdot y}}\\ \end{array} \]

Alternative 3: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+125}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e+125) (* (cosh x) (/ y (* x z))) (* (/ y x) (/ (cosh x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+125) {
		tmp = cosh(x) * (y / (x * z));
	} 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 (y <= (-8.2d+125)) then
        tmp = cosh(x) * (y / (x * z))
    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 (y <= -8.2e+125) {
		tmp = Math.cosh(x) * (y / (x * z));
	} else {
		tmp = (y / x) * (Math.cosh(x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.2e+125:
		tmp = math.cosh(x) * (y / (x * z))
	else:
		tmp = (y / x) * (math.cosh(x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e+125)
		tmp = Float64(cosh(x) * Float64(y / Float64(x * z)));
	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 (y <= -8.2e+125)
		tmp = cosh(x) * (y / (x * z));
	else
		tmp = (y / x) * (cosh(x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e+125], N[(N[Cosh[x], $MachinePrecision] * N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999983e125

   1. Initial program 81.1%

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

      1. associate-*r/ 81.1%

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

      2. associate-/r* 93.1%

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

   3. Simplified 93.1%

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

   if -8.19999999999999983e125 < y

   1. Initial program 86.7%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+125}:\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \]

Alternative 4: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+39}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.9e+39) (/ (cosh x) (* x (/ z y))) (* (/ y x) (/ (cosh x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.9e+39) {
		tmp = cosh(x) / (x * (z / y));
	} 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 (y <= (-6.9d+39)) then
        tmp = cosh(x) / (x * (z / y))
    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 (y <= -6.9e+39) {
		tmp = Math.cosh(x) / (x * (z / y));
	} else {
		tmp = (y / x) * (Math.cosh(x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.9e+39:
		tmp = math.cosh(x) / (x * (z / y))
	else:
		tmp = (y / x) * (math.cosh(x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.9e+39)
		tmp = Float64(cosh(x) / Float64(x * Float64(z / y)));
	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 (y <= -6.9e+39)
		tmp = cosh(x) / (x * (z / y));
	else
		tmp = (y / x) * (cosh(x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.9e+39], N[(N[Cosh[x], $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.90000000000000005e39

   1. Initial program 83.7%

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

      1. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -6.90000000000000005e39 < y

   1. Initial program 86.4%

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

      1. associate-*l/ 86.4%

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

   3. Simplified 86.4%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+39}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \end{array} \]

Alternative 5: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   3. frac-times 85.7%

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

   4. associate-*l/ 94.8%

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

5. Applied egg-rr 94.8%

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

6. Final simplification 94.8%

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

Alternative 6: 68.6% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-58} \lor \neg \left(z \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} - \frac{-1}{x \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.6e-58) (not (<= z 5e-17)))
   (* y (- (* 0.5 (/ x z)) (/ -1.0 (* x z))))
   (+ (/ (/ y x) z) (* 0.5 (/ y (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.6e-58) || !(z <= 5e-17)) {
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)));
	} else {
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.6d-58)) .or. (.not. (z <= 5d-17))) then
        tmp = y * ((0.5d0 * (x / z)) - ((-1.0d0) / (x * z)))
    else
        tmp = ((y / x) / z) + (0.5d0 * (y / (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.6e-58) || !(z <= 5e-17)) {
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)));
	} else {
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.6e-58) or not (z <= 5e-17):
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)))
	else:
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.6e-58) || !(z <= 5e-17))
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) - Float64(-1.0 / Float64(x * z))));
	else
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y / Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.6e-58) || ~((z <= 5e-17)))
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)));
	else
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.6e-58], N[Not[LessEqual[z, 5e-17]], $MachinePrecision]], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(-1.0 / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6000000000000002e-58 or 4.9999999999999999e-17 < z

   1. Initial program 82.8%

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

      1. associate-*r/ 72.7%

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

      2. associate-/r* 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in x around 0 68.0%

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

      1. associate-/l/ 58.6%

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

      2. +-commutative 58.6%

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

      3. associate-/l* 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in y around 0 65.5%

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

   if -9.6000000000000002e-58 < z < 4.9999999999999999e-17

   1. Initial program 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-/r* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in x around 0 71.5%

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

      1. associate-/l/ 81.4%

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

      2. +-commutative 81.4%

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

      3. associate-/l* 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-58} \lor \neg \left(z \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} - \frac{-1}{x \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 73.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-37} \lor \neg \left(y \leq 5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e-37) (not (<= y 5e-30)))
   (+ (/ y (* x z)) (* 0.5 (/ (* x y) z)))
   (+ (* y (/ 0.5 (/ z x))) (/ (/ y x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-37) || !(y <= 5e-30)) {
		tmp = (y / (x * z)) + (0.5 * ((x * y) / z));
	} else {
		tmp = (y * (0.5 / (z / x))) + ((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 <= (-1d-37)) .or. (.not. (y <= 5d-30))) then
        tmp = (y / (x * z)) + (0.5d0 * ((x * y) / z))
    else
        tmp = (y * (0.5d0 / (z / x))) + ((y / x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e-37) || !(y <= 5e-30)) {
		tmp = (y / (x * z)) + (0.5 * ((x * y) / z));
	} else {
		tmp = (y * (0.5 / (z / x))) + ((y / x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e-37) or not (y <= 5e-30):
		tmp = (y / (x * z)) + (0.5 * ((x * y) / z))
	else:
		tmp = (y * (0.5 / (z / x))) + ((y / x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e-37) || !(y <= 5e-30))
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(Float64(x * y) / z)));
	else
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / x))) + Float64(Float64(y / x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e-37) || ~((y <= 5e-30)))
		tmp = (y / (x * z)) + (0.5 * ((x * y) / z));
	else
		tmp = (y * (0.5 / (z / x))) + ((y / x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e-37], N[Not[LessEqual[y, 5e-30]], $MachinePrecision]], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000007e-37 or 4.99999999999999972e-30 < y

   1. Initial program 89.9%

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

      1. associate-*r/ 84.2%

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

      2. associate-/r* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around 0 80.0%

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

   if -1.00000000000000007e-37 < y < 4.99999999999999972e-30

   1. Initial program 80.7%

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

      1. associate-*r/ 74.6%

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

      2. associate-/r* 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in x around 0 56.6%

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

      1. associate-/l/ 66.0%

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

      2. +-commutative 66.0%

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

      3. associate-/l* 70.9%

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

   6. Simplified 70.9%

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

      1. clear-num 70.9%

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

      2. un-div-inv 70.9%

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

   8. Applied egg-rr 70.9%

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

      1. associate-/r/ 73.3%

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

   10. Applied egg-rr 73.3%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-37} \lor \neg \left(y \leq 5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 8: 65.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;\frac{x}{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;x \leq 175:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4)
   (* (/ x z) (* y 0.5))
   (if (<= x 175.0) (/ y (* x z)) (/ (* z (* y 0.5)) (* z (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = (x / z) * (y * 0.5);
	} else if (x <= 175.0) {
		tmp = y / (x * z);
	} else {
		tmp = (z * (y * 0.5)) / (z * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.4d0)) then
        tmp = (x / z) * (y * 0.5d0)
    else if (x <= 175.0d0) then
        tmp = y / (x * z)
    else
        tmp = (z * (y * 0.5d0)) / (z * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = (x / z) * (y * 0.5);
	} else if (x <= 175.0) {
		tmp = y / (x * z);
	} else {
		tmp = (z * (y * 0.5)) / (z * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4:
		tmp = (x / z) * (y * 0.5)
	elif x <= 175.0:
		tmp = y / (x * z)
	else:
		tmp = (z * (y * 0.5)) / (z * (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4)
		tmp = Float64(Float64(x / z) * Float64(y * 0.5));
	elseif (x <= 175.0)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(z * Float64(y * 0.5)) / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4)
		tmp = (x / z) * (y * 0.5);
	elseif (x <= 175.0)
		tmp = y / (x * z);
	else
		tmp = (z * (y * 0.5)) / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4], N[(N[(x / z), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 175.0], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999

   1. Initial program 88.5%

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

      1. associate-*r/ 75.0%

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

      2. associate-/r* 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in x around 0 42.7%

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

      1. associate-/l/ 42.7%

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

      2. +-commutative 42.7%

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

      3. associate-/l* 44.5%

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

   6. Simplified 44.5%

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

   7. Taylor expanded in y around 0 46.3%

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

   8. Taylor expanded in x around inf 42.7%

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

      1. associate-*r/ 42.7%

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

      2. associate-*r* 42.7%

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

      3. associate-*r/ 46.3%

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

      4. *-commutative 46.3%

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

   10. Simplified 46.3%

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

   if -1.3999999999999999 < x < 175

   1. Initial program 90.5%

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

      1. associate-*r/ 90.4%

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

      2. associate-/r* 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around 0 90.1%

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

   if 175 < x

   1. Initial program 69.2%

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

      1. associate-*r/ 53.8%

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

      2. associate-/r* 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in x around 0 35.1%

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

      1. associate-/l/ 35.1%

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

      2. +-commutative 35.1%

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

      3. associate-/l* 33.3%

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

   6. Simplified 33.3%

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

      1. *-un-lft-identity 33.3%

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

      2. associate-*l/ 33.3%

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

      3. +-commutative 33.3%

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

      4. associate-*l/ 33.3%

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

      5. *-un-lft-identity 33.3%

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

      6. associate-*r/ 33.3%

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

      7. frac-add 39.8%

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

   8. Applied egg-rr 39.8%

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

   9. Taylor expanded in x around inf 39.8%

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

       1. associate-*r* 39.8%

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

       2. *-commutative 39.8%

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

   11. Simplified 39.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;\frac{x}{z} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;x \leq 175:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 9: 65.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 - \frac{-1}{x}\right)}{z}\\ \mathbf{elif}\;x \leq 195:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.22e-175)
   (/ (* y (- (* x 0.5) (/ -1.0 x))) z)
   (if (<= x 195.0) (/ y (* x z)) (/ (* z (* y 0.5)) (* z (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.22e-175) {
		tmp = (y * ((x * 0.5) - (-1.0 / x))) / z;
	} else if (x <= 195.0) {
		tmp = y / (x * z);
	} else {
		tmp = (z * (y * 0.5)) / (z * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.22d-175)) then
        tmp = (y * ((x * 0.5d0) - ((-1.0d0) / x))) / z
    else if (x <= 195.0d0) then
        tmp = y / (x * z)
    else
        tmp = (z * (y * 0.5d0)) / (z * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.22e-175) {
		tmp = (y * ((x * 0.5) - (-1.0 / x))) / z;
	} else if (x <= 195.0) {
		tmp = y / (x * z);
	} else {
		tmp = (z * (y * 0.5)) / (z * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.22e-175:
		tmp = (y * ((x * 0.5) - (-1.0 / x))) / z
	elif x <= 195.0:
		tmp = y / (x * z)
	else:
		tmp = (z * (y * 0.5)) / (z * (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.22e-175)
		tmp = Float64(Float64(y * Float64(Float64(x * 0.5) - Float64(-1.0 / x))) / z);
	elseif (x <= 195.0)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(z * Float64(y * 0.5)) / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.22e-175)
		tmp = (y * ((x * 0.5) - (-1.0 / x))) / z;
	elseif (x <= 195.0)
		tmp = y / (x * z);
	else
		tmp = (z * (y * 0.5)) / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.22e-175], N[(N[(y * N[(N[(x * 0.5), $MachinePrecision] - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 195.0], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2200000000000001e-175

   1. Initial program 92.2%

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

      1. associate-*r/ 84.6%

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

      2. associate-/r* 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around 0 62.1%

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

      1. associate-/l/ 65.7%

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

      2. +-commutative 65.7%

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

      3. associate-/l* 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in z around 0 65.6%

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

   if -1.2200000000000001e-175 < x < 195

   1. Initial program 88.1%

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

      1. associate-*r/ 88.1%

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

      2. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around 0 91.0%

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

   if 195 < x

   1. Initial program 69.2%

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

      1. associate-*r/ 53.8%

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

      2. associate-/r* 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in x around 0 35.1%

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

      1. associate-/l/ 35.1%

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

      2. +-commutative 35.1%

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

      3. associate-/l* 33.3%

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

   6. Simplified 33.3%

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

      1. *-un-lft-identity 33.3%

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

      2. associate-*l/ 33.3%

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

      3. +-commutative 33.3%

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

      4. associate-*l/ 33.3%

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

      5. *-un-lft-identity 33.3%

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

      6. associate-*r/ 33.3%

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

      7. frac-add 39.8%

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

   8. Applied egg-rr 39.8%

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

   9. Taylor expanded in x around inf 39.8%

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

       1. associate-*r* 39.8%

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

       2. *-commutative 39.8%

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

   11. Simplified 39.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-175}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 - \frac{-1}{x}\right)}{z}\\ \mathbf{elif}\;x \leq 195:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 10: 65.6% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;x \leq 150:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e-175)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (if (<= x 150.0) (/ y (* x z)) (/ (* z (* y 0.5)) (* z (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-175) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (x <= 150.0) {
		tmp = y / (x * z);
	} else {
		tmp = (z * (y * 0.5)) / (z * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1d-175)) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else if (x <= 150.0d0) then
        tmp = y / (x * z)
    else
        tmp = (z * (y * 0.5d0)) / (z * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-175) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (x <= 150.0) {
		tmp = y / (x * z);
	} else {
		tmp = (z * (y * 0.5)) / (z * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e-175:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	elif x <= 150.0:
		tmp = y / (x * z)
	else:
		tmp = (z * (y * 0.5)) / (z * (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e-175)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	elseif (x <= 150.0)
		tmp = Float64(y / Float64(x * z));
	else
		tmp = Float64(Float64(z * Float64(y * 0.5)) / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e-175)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	elseif (x <= 150.0)
		tmp = y / (x * z);
	else
		tmp = (z * (y * 0.5)) / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e-175], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[x, 150.0], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e-175

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 65.7%

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

   if -1e-175 < x < 150

   1. Initial program 88.1%

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

      1. associate-*r/ 88.1%

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

      2. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around 0 91.0%

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

   if 150 < x

   1. Initial program 69.2%

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

      1. associate-*r/ 53.8%

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

      2. associate-/r* 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in x around 0 35.1%

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

      1. associate-/l/ 35.1%

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

      2. +-commutative 35.1%

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

      3. associate-/l* 33.3%

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

   6. Simplified 33.3%

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

      1. *-un-lft-identity 33.3%

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

      2. associate-*l/ 33.3%

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

      3. +-commutative 33.3%

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

      4. associate-*l/ 33.3%

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

      5. *-un-lft-identity 33.3%

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

      6. associate-*r/ 33.3%

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

      7. frac-add 39.8%

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

   8. Applied egg-rr 39.8%

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

   9. Taylor expanded in x around inf 39.8%

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

       1. associate-*r* 39.8%

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

       2. *-commutative 39.8%

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

   11. Simplified 39.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;x \leq 150:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot 0.5\right)}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 11: 65.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} - \frac{-1}{x \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e-43)
   (* y (- (* 0.5 (/ x z)) (/ -1.0 (* x z))))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e-43) {
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (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 (y <= (-2.4d-43)) then
        tmp = y * ((0.5d0 * (x / z)) - ((-1.0d0) / (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 (y <= -2.4e-43) {
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)));
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e-43:
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)))
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e-43)
		tmp = Float64(y * Float64(Float64(0.5 * Float64(x / z)) - Float64(-1.0 / 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 (y <= -2.4e-43)
		tmp = y * ((0.5 * (x / z)) - (-1.0 / (x * z)));
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e-43], N[(y * N[(N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(-1.0 / 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 y < -2.4000000000000002e-43

   1. Initial program 87.4%

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

      1. associate-*r/ 83.7%

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

      2. associate-/r* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 77.6%

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

      1. associate-/l/ 65.1%

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

      2. +-commutative 65.1%

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

      3. associate-/l* 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in y around 0 76.4%

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

   if -2.4000000000000002e-43 < y

   1. Initial program 85.0%

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

   2. Taylor expanded in x around 0 69.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{z} - \frac{-1}{x \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 12: 67.1% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-5)
   (/ (- (/ 1.0 x) (* x -0.5)) (/ z y))
   (+ (* y (/ 0.5 (/ z x))) (/ (/ y x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-5) {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	} else {
		tmp = (y * (0.5 / (z / x))) + ((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 <= (-1d-5)) then
        tmp = ((1.0d0 / x) - (x * (-0.5d0))) / (z / y)
    else
        tmp = (y * (0.5d0 / (z / x))) + ((y / x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-5) {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	} else {
		tmp = (y * (0.5 / (z / x))) + ((y / x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1e-5:
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y)
	else:
		tmp = (y * (0.5 / (z / x))) + ((y / x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-5)
		tmp = Float64(Float64(Float64(1.0 / x) - Float64(x * -0.5)) / Float64(z / y));
	else
		tmp = Float64(Float64(y * Float64(0.5 / Float64(z / x))) + Float64(Float64(y / x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1e-5)
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	else
		tmp = (y * (0.5 / (z / x))) + ((y / x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e-5], N[(N[(N[(1.0 / x), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(0.5 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000008e-5

   1. Initial program 85.3%

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

      1. associate-*r/ 83.8%

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

      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 80.5%

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

      1. associate-/l/ 66.0%

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

      2. +-commutative 66.0%

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

      3. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in y around 0 77.9%

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

   8. Taylor expanded in z around -inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 78.0%

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

      3. *-commutative 78.0%

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

   10. Simplified 78.0%

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

   if -1.00000000000000008e-5 < y

   1. Initial program 85.9%

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

      1. associate-*r/ 78.4%

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

      2. associate-/r* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in x around 0 65.3%

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

      1. associate-/l/ 69.1%

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

      2. +-commutative 69.1%

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

      3. associate-/l* 70.1%

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

   6. Simplified 70.1%

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

      1. clear-num 70.1%

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

      2. un-div-inv 70.1%

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

   8. Applied egg-rr 70.1%

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

      1. associate-/r/ 71.6%

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

   10. Applied egg-rr 71.6%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{\frac{z}{x}} + \frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 13: 65.3% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e-6)
   (/ (- (/ 1.0 x) (* x -0.5)) (/ z y))
   (/ (+ (/ y x) (* 0.5 (* x y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-6) {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	} 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 <= (-6d-6)) then
        tmp = ((1.0d0 / x) - (x * (-0.5d0))) / (z / y)
    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 <= -6e-6) {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	} else {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e-6:
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y)
	else:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e-6)
		tmp = Float64(Float64(Float64(1.0 / x) - Float64(x * -0.5)) / Float64(z / y));
	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 <= -6e-6)
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	else
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e-6], N[(N[(N[(1.0 / x), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision] / N[(z / y), $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 < -6.0000000000000002e-6

   1. Initial program 85.3%

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

      1. associate-*r/ 83.8%

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

      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 80.5%

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

      1. associate-/l/ 66.0%

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

      2. +-commutative 66.0%

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

      3. associate-/l* 63.4%

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

   6. Simplified 63.4%

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

   7. Taylor expanded in y around 0 77.9%

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

   8. Taylor expanded in z around -inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 78.0%

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

      3. *-commutative 78.0%

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

   10. Simplified 78.0%

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

   if -6.0000000000000002e-6 < y

   1. Initial program 85.9%

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

   2. Taylor expanded in x around 0 69.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \end{array} \]

Alternative 14: 61.4% accurate, 9.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.4))
		tmp = Float64(0.5 * Float64(x * Float64(y / z)));
	else
		tmp = Float64(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[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 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%

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

      1. associate-/l/ 38.1%

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

      2. +-commutative 38.1%

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

      3. associate-/l* 38.1%

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

   6. Simplified 38.1%

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

   7. Taylor expanded in y around 0 40.7%

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

   8. Taylor expanded in x around inf 38.1%

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

      1. associate-*l/ 32.8%

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

   10. Simplified 32.8%

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

   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%

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

4. Final simplification 67.1%

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

Alternative 15: 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%

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

      1. associate-/l/ 38.1%

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

      2. +-commutative 38.1%

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

      3. associate-/l* 38.1%

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

   6. Simplified 38.1%

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

   7. Taylor expanded in y around 0 40.7%

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

   8. Taylor expanded in x around inf 38.1%

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

   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%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x}} \]
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 16: 65.4% accurate, 9.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.4)) {
		tmp = (x / z) * (y * 0.5);
	} 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 = (x / z) * (y * 0.5d0)
    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 = (x / z) * (y * 0.5);
	} 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 = (x / z) * (y * 0.5)
	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(Float64(x / z) * Float64(y * 0.5));
	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 = (x / z) * (y * 0.5);
	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[(N[(x / z), $MachinePrecision] * N[(y * 0.5), $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%

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

      1. associate-/l/ 38.1%

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

      2. +-commutative 38.1%

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

      3. associate-/l* 38.1%

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

   6. Simplified 38.1%

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

   7. Taylor expanded in y around 0 40.7%

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

   8. Taylor expanded in x around inf 38.1%

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

      1. associate-*r/ 38.1%

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

      2. associate-*r* 38.1%

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

      3. associate-*r/ 40.7%

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

      4. *-commutative 40.7%

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

   10. Simplified 40.7%

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

   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%

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

4. Final simplification 70.4%

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

Alternative 17: 56.3% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.54 \cdot 10^{+38} \lor \neg \left(y \leq 2.3 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.54e+38) (not (<= y 2.3e-67))) (/ (/ y z) x) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.54e+38) || !(y <= 2.3e-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 <= (-1.54d+38)) .or. (.not. (y <= 2.3d-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 <= -1.54e+38) || !(y <= 2.3e-67)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.54e+38) or not (y <= 2.3e-67):
		tmp = (y / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.54e+38) || !(y <= 2.3e-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 <= -1.54e+38) || ~((y <= 2.3e-67)))
		tmp = (y / z) / x;
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.54e+38], N[Not[LessEqual[y, 2.3e-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 < -1.54000000000000004e38 or 2.3e-67 < y

   1. Initial program 89.3%

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

      1. associate-*r/ 83.2%

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

      2. associate-/r* 86.4%

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

   3. Simplified 86.4%

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

      1. associate-*r/ 86.4%

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

      2. *-commutative 86.4%

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

      3. frac-times 89.2%

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

      4. associate-*l/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 68.1%

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

   if -1.54000000000000004e38 < y < 2.3e-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%

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

      1. associate-/l/ 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.54 \cdot 10^{+38} \lor \neg \left(y \leq 2.3 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 18: 50.2% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.85e-41) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.85e-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 <= (-1.85d-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 <= -1.85e-41) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.85e-41:
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.85e-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 <= -1.85e-41)
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.85e-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 < -1.8500000000000001e-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%

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

   if -1.8500000000000001e-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%

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

      1. associate-/l/ 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 19: 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%

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

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))