Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 85.7% → 95.9%

Time: 8.0s

Alternatives: 15

Speedup: 1.0×

• 64.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% 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: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.1%

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

   1. associate-*r/ 96.2%

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

   2. associate-/l/ 81.1%

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

   3. associate-*l/ 80.7%

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

   4. *-commutative 80.7%

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

   5. *-commutative 80.7%

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

3. Simplified 80.7%

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

   1. *-commutative 80.7%

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

   2. associate-/r* 94.0%

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

   3. associate-*l/ 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 2: 92.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cosh x) (/ y x))))
   (if (<= t_0 INFINITY) (/ t_0 z) (* y (/ (cosh x) (* x z))))))

C

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

Java

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

Python

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

Julia

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.5%

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

   if +inf.0 < (*.f64 (cosh.f64 x) (/.f64 y x))

   1. Initial program 0.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 61.1%

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

      3. associate-*l/ 61.1%

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

      4. *-commutative 61.1%

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

      5. *-commutative 61.1%

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

   3. Simplified 61.1%

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

4. Final simplification 90.7%

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

Alternative 3: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-86} \lor \neg \left(x \leq 10^{-70}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.2e-86) (not (<= x 1e-70)))
   (* y (/ (cosh x) (* x z)))
   (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-86) || !(x <= 1e-70)) {
		tmp = y * (cosh(x) / (x * z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.2d-86)) .or. (.not. (x <= 1d-70))) then
        tmp = y * (cosh(x) / (x * z))
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.2e-86) || !(x <= 1e-70)) {
		tmp = y * (Math.cosh(x) / (x * z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.2e-86) or not (x <= 1e-70):
		tmp = y * (math.cosh(x) / (x * z))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.2e-86) || !(x <= 1e-70))
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.2e-86) || ~((x <= 1e-70)))
		tmp = y * (cosh(x) / (x * z));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.2e-86], N[Not[LessEqual[x, 1e-70]], $MachinePrecision]], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000007e-86 or 9.99999999999999996e-71 < x

   1. Initial program 76.7%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l/ 78.0%

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

      3. associate-*l/ 78.0%

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

      4. *-commutative 78.0%

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

      5. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   if -1.20000000000000007e-86 < x < 9.99999999999999996e-71

   1. Initial program 90.3%

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

      1. associate-*r/ 90.3%

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

      2. associate-/l/ 85.9%

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

      3. associate-*l/ 85.0%

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

      4. *-commutative 85.0%

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

      5. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in x around 0 85.0%

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

      1. div-inv 85.9%

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

      2. associate-/r* 95.4%

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

   6. Applied egg-rr 95.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-86} \lor \neg \left(x \leq 10^{-70}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 4: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{-181} \lor \neg \left(z \leq 3.8 \cdot 10^{+163}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 2.4e-181) (not (<= z 3.8e+163)))
   (* (cosh x) (/ (/ y z) x))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 2.4e-181) || !(z <= 3.8e+163)) {
		tmp = cosh(x) * ((y / z) / x);
	} else {
		tmp = y * (cosh(x) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= 2.4d-181) .or. (.not. (z <= 3.8d+163))) then
        tmp = cosh(x) * ((y / z) / x)
    else
        tmp = y * (cosh(x) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= 2.4e-181) || !(z <= 3.8e+163)) {
		tmp = Math.cosh(x) * ((y / z) / x);
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 2.4e-181) or not (z <= 3.8e+163):
		tmp = math.cosh(x) * ((y / z) / x)
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 2.4e-181) || !(z <= 3.8e+163))
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= 2.4e-181) || ~((z <= 3.8e+163)))
		tmp = cosh(x) * ((y / z) / x);
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 2.4e-181], N[Not[LessEqual[z, 3.8e+163]], $MachinePrecision]], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.4000000000000001e-181 or 3.80000000000000008e163 < z

   1. Initial program 83.5%

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

      1. associate-*r/ 77.6%

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

      2. associate-/l/ 72.1%

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

      3. associate-/r* 83.6%

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

   3. Simplified 83.6%

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

   if 2.4000000000000001e-181 < z < 3.80000000000000008e163

   1. Initial program 78.3%

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

      1. associate-*r/ 97.2%

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

      2. associate-/l/ 97.0%

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

      3. associate-*l/ 96.9%

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

      4. *-commutative 96.9%

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

      5. *-commutative 96.9%

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

   3. Simplified 96.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.4 \cdot 10^{-181} \lor \neg \left(z \leq 3.8 \cdot 10^{+163}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 5: 68.8% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{y}{x}}{z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+41}:\\ \;\;\;\;0.5 \cdot \left(\frac{1}{z} \cdot \frac{y}{\frac{1}{x}}\right) + t_0\\ \mathbf{elif}\;y \leq 2000000:\\ \;\;\;\;t_0 + \frac{1}{\frac{\frac{z}{x}}{y \cdot 0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} - x \cdot \frac{-0.5}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (/ y x) z)))
   (if (<= y -1e+41)
     (+ (* 0.5 (* (/ 1.0 z) (/ y (/ 1.0 x)))) t_0)
     (if (<= y 2000000.0)
       (+ t_0 (/ 1.0 (/ (/ z x) (* y 0.5))))
       (- (/ y (* x z)) (* x (/ -0.5 (/ z y))))))))

C

double code(double x, double y, double z) {
	double t_0 = (y / x) / z;
	double tmp;
	if (y <= -1e+41) {
		tmp = (0.5 * ((1.0 / z) * (y / (1.0 / x)))) + t_0;
	} else if (y <= 2000000.0) {
		tmp = t_0 + (1.0 / ((z / x) / (y * 0.5)));
	} else {
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / x) / z
    if (y <= (-1d+41)) then
        tmp = (0.5d0 * ((1.0d0 / z) * (y / (1.0d0 / x)))) + t_0
    else if (y <= 2000000.0d0) then
        tmp = t_0 + (1.0d0 / ((z / x) / (y * 0.5d0)))
    else
        tmp = (y / (x * z)) - (x * ((-0.5d0) / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y / x) / z;
	double tmp;
	if (y <= -1e+41) {
		tmp = (0.5 * ((1.0 / z) * (y / (1.0 / x)))) + t_0;
	} else if (y <= 2000000.0) {
		tmp = t_0 + (1.0 / ((z / x) / (y * 0.5)));
	} else {
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / x) / z
	tmp = 0
	if y <= -1e+41:
		tmp = (0.5 * ((1.0 / z) * (y / (1.0 / x)))) + t_0
	elif y <= 2000000.0:
		tmp = t_0 + (1.0 / ((z / x) / (y * 0.5)))
	else:
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / x) / z)
	tmp = 0.0
	if (y <= -1e+41)
		tmp = Float64(Float64(0.5 * Float64(Float64(1.0 / z) * Float64(y / Float64(1.0 / x)))) + t_0);
	elseif (y <= 2000000.0)
		tmp = Float64(t_0 + Float64(1.0 / Float64(Float64(z / x) / Float64(y * 0.5))));
	else
		tmp = Float64(Float64(y / Float64(x * z)) - Float64(x * Float64(-0.5 / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / x) / z;
	tmp = 0.0;
	if (y <= -1e+41)
		tmp = (0.5 * ((1.0 / z) * (y / (1.0 / x)))) + t_0;
	elseif (y <= 2000000.0)
		tmp = t_0 + (1.0 / ((z / x) / (y * 0.5)));
	else
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1e+41], N[(N[(0.5 * N[(N[(1.0 / z), $MachinePrecision] * N[(y / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[y, 2000000.0], N[(t$95$0 + N[(1.0 / N[(N[(z / x), $MachinePrecision] / N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(-0.5 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000001e41

   1. Initial program 93.6%

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

      1. associate-*r/ 93.6%

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

      2. associate-/l/ 84.9%

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

      3. associate-*l/ 84.8%

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

      4. *-commutative 84.8%

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

      5. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in x around 0 88.8%

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

      1. +-commutative 88.8%

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

      2. associate-/l* 68.5%

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

      3. *-commutative 68.5%

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

      4. associate-/r* 62.2%

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

   6. Simplified 62.2%

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

      1. *-un-lft-identity 62.2%

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

      2. div-inv 62.2%

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

      3. times-frac 82.5%

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

   8. Applied egg-rr 82.5%

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

   if -1.00000000000000001e41 < y < 2e6

   1. Initial program 72.2%

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

      1. associate-*r/ 99.1%

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

      2. associate-/l/ 75.2%

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

      3. associate-*l/ 74.5%

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

      4. *-commutative 74.5%

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

      5. *-commutative 74.5%

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

   3. Simplified 74.5%

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

   4. Taylor expanded in x around 0 43.4%

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

      1. +-commutative 43.4%

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

      2. associate-/l* 53.9%

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

      3. *-commutative 53.9%

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

      4. associate-/r* 63.6%

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

   6. Simplified 63.6%

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

      1. associate-*r/ 63.6%

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

      2. clear-num 63.6%

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

      3. *-commutative 63.6%

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

   8. Applied egg-rr 63.6%

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

   if 2e6 < y

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 73.9%

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

   3. Taylor expanded in y around -inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-/l* 75.5%

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

      3. *-commutative 75.5%

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

   5. Simplified 75.5%

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

      1. div-sub 75.5%

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

      2. *-un-lft-identity 75.5%

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

      3. times-frac 75.5%

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

      4. /-rgt-identity 75.5%

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

      5. associate-/r/ 75.5%

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

      6. associate-/l/ 75.5%

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

      7. associate-*l/ 75.5%

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

      8. *-un-lft-identity 75.5%

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

   7. Applied egg-rr 75.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+41}:\\ \;\;\;\;0.5 \cdot \left(\frac{1}{z} \cdot \frac{y}{\frac{1}{x}}\right) + \frac{\frac{y}{x}}{z}\\ \mathbf{elif}\;y \leq 2000000:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + \frac{1}{\frac{\frac{z}{x}}{y \cdot 0.5}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} - x \cdot \frac{-0.5}{\frac{z}{y}}\\ \end{array} \]

Alternative 6: 67.8% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+132}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+132)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (if (<= y 1.15e-116)
     (+ (/ (/ y x) z) (* 0.5 (/ y (/ z x))))
     (/ (- (/ 1.0 x) (* x -0.5)) (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+132) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (y <= 1.15e-116) {
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	} else {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6d+132)) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else if (y <= 1.15d-116) then
        tmp = ((y / x) / z) + (0.5d0 * (y / (z / x)))
    else
        tmp = ((1.0d0 / x) - (x * (-0.5d0))) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+132) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (y <= 1.15e-116) {
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	} else {
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+132:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	elif y <= 1.15e-116:
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)))
	else:
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+132)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	elseif (y <= 1.15e-116)
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y / Float64(z / x))));
	else
		tmp = Float64(Float64(Float64(1.0 / x) - Float64(x * -0.5)) / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+132)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	elseif (y <= 1.15e-116)
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	else
		tmp = ((1.0 / x) - (x * -0.5)) / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+132], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.15e-116], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / x), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999996e132

   1. Initial program 90.9%

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

   2. Taylor expanded in x around 0 81.9%

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

   if -5.9999999999999996e132 < y < 1.15000000000000001e-116

   1. Initial program 70.7%

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

      1. associate-*r/ 99.0%

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

      2. associate-/l/ 76.4%

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

      3. associate-*l/ 75.6%

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

      4. *-commutative 75.6%

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

      5. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in x around 0 47.2%

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

      1. +-commutative 47.2%

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

      2. associate-/l* 58.9%

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

      3. *-commutative 58.9%

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

      4. associate-/r* 68.2%

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

   6. Simplified 68.2%

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

   if 1.15000000000000001e-116 < y

   1. Initial program 92.7%

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

   2. Taylor expanded in x around 0 68.4%

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

   3. Taylor expanded in y around -inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. associate-/l* 69.5%

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

      3. *-commutative 69.5%

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

   5. Simplified 69.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+132}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} - x \cdot -0.5}{\frac{z}{y}}\\ \end{array} \]

Alternative 7: 68.4% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+119}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;y \leq 400000:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} - x \cdot \frac{-0.5}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.9e+119)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (if (<= y 400000.0)
     (+ (/ (/ y x) z) (* 0.5 (/ y (/ z x))))
     (- (/ y (* x z)) (* x (/ -0.5 (/ z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.9e+119) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (y <= 400000.0) {
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	} else {
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.9d+119)) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else if (y <= 400000.0d0) then
        tmp = ((y / x) / z) + (0.5d0 * (y / (z / x)))
    else
        tmp = (y / (x * z)) - (x * ((-0.5d0) / (z / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.9e+119) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else if (y <= 400000.0) {
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	} else {
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.9e+119:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	elif y <= 400000.0:
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)))
	else:
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.9e+119)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	elseif (y <= 400000.0)
		tmp = Float64(Float64(Float64(y / x) / z) + Float64(0.5 * Float64(y / Float64(z / x))));
	else
		tmp = Float64(Float64(y / Float64(x * z)) - Float64(x * Float64(-0.5 / Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.9e+119)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	elseif (y <= 400000.0)
		tmp = ((y / x) / z) + (0.5 * (y / (z / x)));
	else
		tmp = (y / (x * z)) - (x * (-0.5 / (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.9e+119], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 400000.0], N[(N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision] + N[(0.5 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(x * N[(-0.5 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9000000000000001e119

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 80.5%

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

   if -5.9000000000000001e119 < y < 4e5

   1. Initial program 75.2%

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

      1. associate-*r/ 99.2%

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

      2. associate-/l/ 77.2%

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

      3. associate-*l/ 76.5%

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

      4. *-commutative 76.5%

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

      5. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around 0 48.2%

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

      1. +-commutative 48.2%

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

      2. associate-/l* 57.5%

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

      3. *-commutative 57.5%

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

      4. associate-/r* 66.2%

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

   6. Simplified 66.2%

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

   if 4e5 < y

   1. Initial program 92.2%

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

   2. Taylor expanded in x around 0 73.9%

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

   3. Taylor expanded in y around -inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-/l* 75.5%

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

      3. *-commutative 75.5%

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

   5. Simplified 75.5%

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

      1. div-sub 75.5%

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

      2. *-un-lft-identity 75.5%

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

      3. times-frac 75.5%

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

      4. /-rgt-identity 75.5%

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

      5. associate-/r/ 75.5%

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

      6. associate-/l/ 75.5%

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

      7. associate-*l/ 75.5%

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

      8. *-un-lft-identity 75.5%

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

   7. Applied egg-rr 75.5%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+119}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;y \leq 400000:\\ \;\;\;\;\frac{\frac{y}{x}}{z} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} - x \cdot \frac{-0.5}{\frac{z}{y}}\\ \end{array} \]

Alternative 8: 66.0% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{-181}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{x \cdot z} + 0.5 \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.1e-181)
   (/ (+ (/ y x) (* 0.5 (* x y))) z)
   (* y (+ (/ 1.0 (* x z)) (* 0.5 (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.1e-181) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1.1d-181) then
        tmp = ((y / x) + (0.5d0 * (x * y))) / z
    else
        tmp = y * ((1.0d0 / (x * z)) + (0.5d0 * (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.1e-181) {
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	} else {
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.1e-181:
		tmp = ((y / x) + (0.5 * (x * y))) / z
	else:
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.1e-181)
		tmp = Float64(Float64(Float64(y / x) + Float64(0.5 * Float64(x * y))) / z);
	else
		tmp = Float64(y * Float64(Float64(1.0 / Float64(x * z)) + Float64(0.5 * Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.1e-181)
		tmp = ((y / x) + (0.5 * (x * y))) / z;
	else
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.1e-181], N[(N[(N[(y / x), $MachinePrecision] + N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * N[(N[(1.0 / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.09999999999999999e-181

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0 69.7%

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

   if 1.09999999999999999e-181 < z

   1. Initial program 74.7%

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

      1. associate-*r/ 92.8%

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

      2. associate-/l/ 83.9%

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

      3. associate-*l/ 83.9%

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

      4. *-commutative 83.9%

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

      5. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in x around 0 61.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.1 \cdot 10^{-181}:\\ \;\;\;\;\frac{\frac{y}{x} + 0.5 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{x \cdot z} + 0.5 \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 9: 61.9% accurate, 9.6× speedup

Math

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

FPCore

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

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 / 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)) .or. (.not. (x <= 1.4d0))) then
        tmp = 0.5d0 * (x * (y / z))
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 72.3%

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

   2. Taylor expanded in x around 0 38.2%

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

   3. Taylor expanded in x around inf 38.7%

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

      1. associate-/l* 37.3%

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

      2. associate-/r/ 26.4%

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

   5. Applied egg-rr 26.4%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 92.2%

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

      1. associate-*r/ 92.2%

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

      2. associate-/l/ 88.6%

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

      3. associate-*l/ 87.8%

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

      4. *-commutative 87.8%

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

      5. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around 0 87.8%

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

      1. div-inv 88.6%

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

      2. associate-/r* 95.5%

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

   6. Applied egg-rr 95.5%

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

4. Final simplification 60.4%

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

Alternative 10: 66.0% accurate, 9.6× speedup

Math

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

FPCore

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

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 / 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)) .or. (.not. (x <= 1.4d0))) then
        tmp = 0.5d0 * ((x * y) / z)
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

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

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.3999999999999999 < x

   1. Initial program 72.3%

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

   2. Taylor expanded in x around 0 38.2%

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

   3. Taylor expanded in x around inf 38.7%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 92.2%

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

      1. associate-*r/ 92.2%

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

      2. associate-/l/ 88.6%

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

      3. associate-*l/ 87.8%

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

      4. *-commutative 87.8%

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

      5. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around 0 87.8%

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

      1. div-inv 88.6%

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

      2. associate-/r* 95.5%

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

   6. Applied egg-rr 95.5%

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

4. Final simplification 66.7%

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

Alternative 11: 65.9% accurate, 9.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 33.5%

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

   3. Taylor expanded in x around inf 34.6%

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

   if -1.3999999999999999 < x < 1.3999999999999999

   1. Initial program 92.2%

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

      1. associate-*r/ 92.2%

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

      2. associate-/l/ 88.6%

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

      3. associate-*l/ 87.8%

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

      4. *-commutative 87.8%

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

      5. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in x around 0 87.8%

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

      1. div-inv 88.6%

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

      2. associate-/r* 95.5%

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

   6. Applied egg-rr 95.5%

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

   if 1.3999999999999999 < x

   1. Initial program 72.1%

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

   2. Taylor expanded in x around 0 43.5%

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

   3. Taylor expanded in x around inf 43.5%

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

      1. associate-/l* 45.0%

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

      2. associate-*r/ 45.0%

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

      3. *-commutative 45.0%

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

      4. associate-*l/ 45.0%

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

      5. associate-/l* 43.5%

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

      6. associate-*r/ 45.0%

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

      7. associate-*l* 45.0%

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

   5. Simplified 45.0%

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

4. Final simplification 67.1%

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

Alternative 12: 66.0% accurate, 9.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.1%

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

2. Taylor expanded in x around 0 64.8%

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

3. Final simplification 64.8%

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

Alternative 13: 50.8% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.0245:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.0245) (/ (/ y x) z) (/ y (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.0245) {
		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 (z <= 0.0245d0) 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 (z <= 0.0245) {
		tmp = (y / x) / z;
	} else {
		tmp = y / (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.0245:
		tmp = (y / x) / z
	else:
		tmp = y / (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.0245)
		tmp = Float64(Float64(y / x) / z);
	else
		tmp = Float64(y / Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.0245)
		tmp = (y / x) / z;
	else
		tmp = y / (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.0245], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.024500000000000001

   1. Initial program 84.9%

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

      1. associate-*r/ 98.5%

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

      2. associate-/l/ 83.3%

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

      3. associate-*l/ 82.8%

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

      4. *-commutative 82.8%

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

      5. *-commutative 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in x around 0 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-/r* 52.1%

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

   6. Simplified 52.1%

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

   if 0.024500000000000001 < z

   1. Initial program 72.3%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l/ 73.5%

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

      3. associate-*l/ 73.5%

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

      4. *-commutative 73.5%

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

      5. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in x around 0 48.3%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.0245:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z}\\ \end{array} \]

Alternative 14: 49.0% 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 82.1%

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

   1. associate-*r/ 96.2%

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

   2. associate-/l/ 81.1%

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

   3. associate-*l/ 80.7%

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

   4. *-commutative 80.7%

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

   5. *-commutative 80.7%

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

3. Simplified 80.7%

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

4. Taylor expanded in x around 0 46.9%

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

5. Final simplification 46.9%

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

Alternative 15: 52.8% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.1%

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

   1. associate-*r/ 96.2%

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

   2. associate-/l/ 81.1%

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

   3. associate-*l/ 80.7%

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

   4. *-commutative 80.7%

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

   5. *-commutative 80.7%

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

3. Simplified 80.7%

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

4. Taylor expanded in x around 0 46.5%

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

   1. div-inv 46.9%

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

   2. associate-/r* 53.5%

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

6. Applied egg-rr 53.5%

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

7. Final simplification 53.5%

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

Developer target: 96.8% 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 2023200 
(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))