Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.3% → 97.3%

Time: 7.6s

Alternatives: 14

Speedup: 1.0×

• 64.0% 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: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.4e+67) (/ (* y (/ (cosh x) x)) z) (/ (cosh x) (* x (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e+67) {
		tmp = (y * (cosh(x) / x)) / z;
	} else {
		tmp = cosh(x) / (x * (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 <= 1.4d+67) then
        tmp = (y * (cosh(x) / x)) / z
    else
        tmp = cosh(x) / (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e+67) {
		tmp = (y * (Math.cosh(x) / x)) / z;
	} else {
		tmp = Math.cosh(x) / (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.4e+67:
		tmp = (y * (math.cosh(x) / x)) / z
	else:
		tmp = math.cosh(x) / (x * (z / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.4e+67)
		tmp = Float64(Float64(y * Float64(cosh(x) / x)) / z);
	else
		tmp = Float64(cosh(x) / Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.4e+67)
		tmp = (y * (cosh(x) / x)) / z;
	else
		tmp = cosh(x) / (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.4e+67], N[(N[(y * N[(N[Cosh[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] / N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3999999999999999e67

   1. Initial program 84.2%

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

      1. associate-*r/ 75.3%

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

      2. associate-/l/ 74.8%

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

      3. associate-/r* 80.2%

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

   3. Simplified 80.2%

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

      1. associate-/l/ 74.8%

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

      2. associate-*r/ 82.2%

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

      3. associate-*l/ 81.6%

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

      4. associate-/r* 94.4%

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

      5. associate-*l/ 97.5%

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

   5. Applied egg-rr 97.5%

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

   if 1.3999999999999999e67 < y

   1. Initial program 82.3%

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

      1. associate-/l* 82.2%

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

      2. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{y \cdot \frac{\cosh x}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{x \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 2: 92.1% 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 93.7%

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

   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/ 77.8%

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

      3. associate-*l/ 77.8%

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

      4. *-commutative 77.8%

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

      5. *-commutative 77.8%

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

   3. Simplified 77.8%

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

4. Final simplification 92.0%

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

Alternative 3: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-157} \lor \neg \left(y \leq 8.2 \cdot 10^{-52}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e-157) (not (<= y 8.2e-52)))
   (* (cosh x) (/ (/ y z) x))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e-157) || !(y <= 8.2e-52)) {
		tmp = cosh(x) * ((y / z) / x);
	} else {
		tmp = y * (cosh(x) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.35d-157)) .or. (.not. (y <= 8.2d-52))) then
        tmp = cosh(x) * ((y / z) / x)
    else
        tmp = y * (cosh(x) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e-157) || !(y <= 8.2e-52)) {
		tmp = Math.cosh(x) * ((y / z) / x);
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e-157) or not (y <= 8.2e-52):
		tmp = math.cosh(x) * ((y / z) / x)
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e-157) || !(y <= 8.2e-52))
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.35e-157) || ~((y <= 8.2e-52)))
		tmp = cosh(x) * ((y / z) / x);
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e-157], N[Not[LessEqual[y, 8.2e-52]], $MachinePrecision]], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e-157 or 8.19999999999999977e-52 < y

   1. Initial program 91.1%

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

      1. associate-*r/ 85.4%

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

      2. associate-/l/ 82.2%

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

      3. associate-/r* 93.5%

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

   3. Simplified 93.5%

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

   if -1.35e-157 < y < 8.19999999999999977e-52

   1. Initial program 68.5%

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

      1. associate-*r/ 99.8%

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

      2. associate-/l/ 84.9%

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

      3. associate-*l/ 83.6%

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

      4. *-commutative 83.6%

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

      5. *-commutative 83.6%

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

   3. Simplified 83.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-157} \lor \neg \left(y \leq 8.2 \cdot 10^{-52}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+158)
   (+ (/ y (* x z)) (* 0.5 (/ (* y x) z)))
   (* y (/ (cosh x) (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+158) {
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z));
	} else {
		tmp = y * (cosh(x) / (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6d+158)) then
        tmp = (y / (x * z)) + (0.5d0 * ((y * x) / z))
    else
        tmp = y * (cosh(x) / (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+158) {
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z));
	} else {
		tmp = y * (Math.cosh(x) / (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+158:
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z))
	else:
		tmp = y * (math.cosh(x) / (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+158)
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(Float64(y * x) / z)));
	else
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+158)
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z));
	else
		tmp = y * (cosh(x) / (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+158], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6e158

   1. Initial program 94.0%

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

      1. associate-*r/ 90.9%

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

      2. associate-/l/ 71.9%

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

      3. associate-/r* 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around 0 94.1%

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

   if -6e158 < y

   1. Initial program 82.3%

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

      1. associate-*r/ 94.4%

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

      2. associate-/l/ 85.2%

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

      3. associate-*l/ 84.6%

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

      4. *-commutative 84.6%

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

      5. *-commutative 84.6%

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

   3. Simplified 84.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \end{array} \]

Alternative 5: 69.2% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-58} \lor \neg \left(y \leq 5.6 \cdot 10^{-179}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{x \cdot z} + 0.5 \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-58) (not (<= y 5.6e-179)))
   (+ (/ y (* x z)) (* 0.5 (/ (* y x) z)))
   (* y (+ (/ 1.0 (* x z)) (* 0.5 (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-58) || !(y <= 5.6e-179)) {
		tmp = (y / (x * z)) + (0.5 * ((y * x) / 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 ((y <= (-3.4d-58)) .or. (.not. (y <= 5.6d-179))) then
        tmp = (y / (x * z)) + (0.5d0 * ((y * x) / 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 ((y <= -3.4e-58) || !(y <= 5.6e-179)) {
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z));
	} else {
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-58) or not (y <= 5.6e-179):
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z))
	else:
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-58) || !(y <= 5.6e-179))
		tmp = Float64(Float64(y / Float64(x * z)) + Float64(0.5 * Float64(Float64(y * x) / 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 ((y <= -3.4e-58) || ~((y <= 5.6e-179)))
		tmp = (y / (x * z)) + (0.5 * ((y * x) / z));
	else
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-58], N[Not[LessEqual[y, 5.6e-179]], $MachinePrecision]], N[(N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $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 y < -3.39999999999999973e-58 or 5.6000000000000001e-179 < y

   1. Initial program 91.2%

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

      1. associate-*r/ 83.8%

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

      2. associate-/l/ 81.0%

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

      3. associate-/r* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 77.3%

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

   if -3.39999999999999973e-58 < y < 5.6000000000000001e-179

   1. Initial program 67.7%

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

      1. associate-*r/ 99.8%

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

      2. associate-/l/ 81.4%

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

      3. associate-*l/ 80.9%

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

      4. *-commutative 80.9%

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

      5. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in x around 0 55.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-58} \lor \neg \left(y \leq 5.6 \cdot 10^{-179}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{x \cdot z} + 0.5 \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 6: 68.9% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x \cdot z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-54} \lor \neg \left(y \leq 5.6 \cdot 10^{-179}\right):\\ \;\;\;\;t_0 + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{y \cdot 0.5}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (* x z))))
   (if (or (<= y -1e-54) (not (<= y 5.6e-179)))
     (+ t_0 (* 0.5 (/ (* y x) z)))
     (+ t_0 (/ (* y 0.5) (/ z x))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (x * z);
	double tmp;
	if ((y <= -1e-54) || !(y <= 5.6e-179)) {
		tmp = t_0 + (0.5 * ((y * x) / z));
	} else {
		tmp = t_0 + ((y * 0.5) / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (x * z)
    if ((y <= (-1d-54)) .or. (.not. (y <= 5.6d-179))) then
        tmp = t_0 + (0.5d0 * ((y * x) / z))
    else
        tmp = t_0 + ((y * 0.5d0) / (z / x))
    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-54) || !(y <= 5.6e-179)) {
		tmp = t_0 + (0.5 * ((y * x) / z));
	} else {
		tmp = t_0 + ((y * 0.5) / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (x * z)
	tmp = 0
	if (y <= -1e-54) or not (y <= 5.6e-179):
		tmp = t_0 + (0.5 * ((y * x) / z))
	else:
		tmp = t_0 + ((y * 0.5) / (z / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(x * z))
	tmp = 0.0
	if ((y <= -1e-54) || !(y <= 5.6e-179))
		tmp = Float64(t_0 + Float64(0.5 * Float64(Float64(y * x) / z)));
	else
		tmp = Float64(t_0 + Float64(Float64(y * 0.5) / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (x * z);
	tmp = 0.0;
	if ((y <= -1e-54) || ~((y <= 5.6e-179)))
		tmp = t_0 + (0.5 * ((y * x) / z));
	else
		tmp = t_0 + ((y * 0.5) / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -1e-54], N[Not[LessEqual[y, 5.6e-179]], $MachinePrecision]], N[(t$95$0 + N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(y * 0.5), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1e-54 or 5.6000000000000001e-179 < y

   1. Initial program 91.2%

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

      1. associate-*r/ 83.8%

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

      2. associate-/l/ 81.0%

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

      3. associate-/r* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around 0 77.3%

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

   if -1e-54 < y < 5.6000000000000001e-179

   1. Initial program 67.7%

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

      1. associate-*r/ 61.5%

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

      2. associate-/l/ 70.3%

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

      3. associate-/r* 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in x around 0 41.3%

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

      1. associate-/l* 56.4%

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

      2. associate-*r/ 56.4%

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

      3. *-commutative 56.4%

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

   6. Applied egg-rr 56.4%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-54} \lor \neg \left(y \leq 5.6 \cdot 10^{-179}\right):\\ \;\;\;\;\frac{y}{x \cdot z} + 0.5 \cdot \frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x \cdot z} + \frac{y \cdot 0.5}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 66.4% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-128}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{x \cdot z} + 0.5 \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.05e-128)
   (/ (* y (+ (* x 0.5) (/ 1.0 x))) z)
   (* y (+ (/ 1.0 (* x z)) (* 0.5 (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.05e-128) {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / 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 (y <= (-3.05d-128)) then
        tmp = (y * ((x * 0.5d0) + (1.0d0 / x))) / 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 (y <= -3.05e-128) {
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	} else {
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.05e-128:
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z
	else:
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.05e-128)
		tmp = Float64(Float64(y * Float64(Float64(x * 0.5) + Float64(1.0 / x))) / 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 (y <= -3.05e-128)
		tmp = (y * ((x * 0.5) + (1.0 / x))) / z;
	else
		tmp = y * ((1.0 / (x * z)) + (0.5 * (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.05e-128], N[(N[(y * N[(N[(x * 0.5), $MachinePrecision] + N[(1.0 / x), $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 y < -3.0499999999999999e-128

   1. Initial program 94.9%

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

      1. associate-*r/ 86.6%

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

      2. associate-/l/ 77.4%

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

      3. associate-/r* 90.5%

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

   3. Simplified 90.5%

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

      1. associate-/l/ 77.4%

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

      2. associate-*r/ 78.4%

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

      3. associate-*l/ 78.4%

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

      4. associate-/r* 96.0%

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

      5. associate-*l/ 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in x around 0 74.1%

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

   if -3.0499999999999999e-128 < y

   1. Initial program 77.1%

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

      1. associate-*r/ 94.0%

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

      2. associate-/l/ 86.6%

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

      3. associate-*l/ 85.8%

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

      4. *-commutative 85.8%

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

      5. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in x around 0 63.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-128}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5 + \frac{1}{x}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\frac{1}{x \cdot z} + 0.5 \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 8: 62.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.42) (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 <= -1.42) || !(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 <= (-1.42d0)) .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 <= -1.42) || !(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 <= -1.42) 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 <= -1.42) || !(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 <= -1.42) || ~((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, -1.42], 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 < -1.4199999999999999 or 1.3999999999999999 < x

   1. Initial program 78.9%

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

   2. Taylor expanded in x around 0 40.0%

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

      1. associate-*r* 40.0%

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

   4. Simplified 40.0%

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

   5. Taylor expanded in x around inf 40.6%

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

      1. div-inv 40.6%

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

      2. *-commutative 40.6%

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

      3. associate-*l* 31.1%

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

      4. div-inv 31.1%

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

   7. Applied egg-rr 31.1%

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

   if -1.4199999999999999 < x < 1.3999999999999999

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/l/ 92.0%

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

      3. associate-*l/ 91.1%

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

      4. *-commutative 91.1%

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

      5. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 89.9%

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

      1. div-inv 90.9%

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

      2. associate-/r* 91.6%

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

   6. Applied egg-rr 91.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 9: 66.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.42) (not (<= x 1.4))) (* 0.5 (* y (/ x z))) (/ (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42) || !(x <= 1.4)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.42d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = 0.5d0 * (y * (x / z))
    else
        tmp = (y / z) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.42) || !(x <= 1.4)) {
		tmp = 0.5 * (y * (x / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.42) or not (x <= 1.4):
		tmp = 0.5 * (y * (x / z))
	else:
		tmp = (y / z) / x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.42) || !(x <= 1.4))
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	else
		tmp = Float64(Float64(y / z) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.42) || ~((x <= 1.4)))
		tmp = 0.5 * (y * (x / z));
	else
		tmp = (y / z) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.42], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4199999999999999 or 1.3999999999999999 < x

   1. Initial program 78.9%

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

   2. Taylor expanded in x around 0 40.0%

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

      1. associate-*r* 40.0%

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

   4. Simplified 40.0%

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

   5. Taylor expanded in x around inf 40.6%

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

      1. associate-*r/ 40.7%

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

   7. Simplified 40.7%

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

   if -1.4199999999999999 < x < 1.3999999999999999

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/l/ 92.0%

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

      3. associate-*l/ 91.1%

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

      4. *-commutative 91.1%

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

      5. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 89.9%

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

      1. div-inv 90.9%

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

      2. associate-/r* 91.6%

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

   6. Applied egg-rr 91.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 10: 65.9% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.42)
   (* 0.5 (* y (/ x z)))
   (if (<= x 1.4) (/ (/ y z) x) (* 0.5 (/ (* y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 1.4) {
		tmp = (y / z) / x;
	} else {
		tmp = 0.5 * ((y * x) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.42d0)) then
        tmp = 0.5d0 * (y * (x / z))
    else if (x <= 1.4d0) then
        tmp = (y / z) / x
    else
        tmp = 0.5d0 * ((y * x) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.42) {
		tmp = 0.5 * (y * (x / z));
	} else if (x <= 1.4) {
		tmp = (y / z) / x;
	} else {
		tmp = 0.5 * ((y * x) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.42:
		tmp = 0.5 * (y * (x / z))
	elif x <= 1.4:
		tmp = (y / z) / x
	else:
		tmp = 0.5 * ((y * x) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.42)
		tmp = Float64(0.5 * Float64(y * Float64(x / z)));
	elseif (x <= 1.4)
		tmp = Float64(Float64(y / z) / x);
	else
		tmp = Float64(0.5 * Float64(Float64(y * x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.42)
		tmp = 0.5 * (y * (x / z));
	elseif (x <= 1.4)
		tmp = (y / z) / x;
	else
		tmp = 0.5 * ((y * x) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.42], N[(0.5 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision], N[(0.5 * N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4199999999999999

   1. Initial program 76.8%

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

   2. Taylor expanded in x around 0 36.6%

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

      1. associate-*r* 36.6%

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

   4. Simplified 36.6%

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

   5. Taylor expanded in x around inf 36.6%

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

      1. associate-*r/ 41.6%

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

   7. Simplified 41.6%

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

   if -1.4199999999999999 < x < 1.3999999999999999

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/l/ 92.0%

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

      3. associate-*l/ 91.1%

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

      4. *-commutative 91.1%

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

      5. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 89.9%

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

      1. div-inv 90.9%

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

      2. associate-/r* 91.6%

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

   6. Applied egg-rr 91.6%

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

   if 1.3999999999999999 < x

   1. Initial program 80.6%

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

   2. Taylor expanded in x around 0 42.6%

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

      1. associate-*r* 42.6%

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

   4. Simplified 42.6%

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

   5. Taylor expanded in x around inf 43.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;x \leq 1.4:\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{z}\\ \end{array} \]

Alternative 11: 65.7% accurate, 9.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y * ((x * 0.5) + (1.0 / 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 * 0.5d0) + (1.0d0 / x))) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. associate-*r/ 76.8%

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

   2. associate-/l/ 77.6%

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

   3. associate-/r* 84.3%

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

3. Simplified 84.3%

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

   1. associate-/l/ 77.6%

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

   2. associate-*r/ 83.5%

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

   3. associate-*l/ 83.0%

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

   4. associate-/r* 95.5%

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

   5. associate-*l/ 94.3%

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

5. Applied egg-rr 94.3%

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

6. Taylor expanded in x around 0 63.9%

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

7. Final simplification 63.9%

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

Alternative 12: 53.9% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-47} \lor \neg \left(y \leq 2500000000000\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e-47) (not (<= y 2500000000000.0)))
   (/ y (* x z))
   (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e-47) || !(y <= 2500000000000.0)) {
		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 <= (-5.9d-47)) .or. (.not. (y <= 2500000000000.0d0))) 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 <= -5.9e-47) || !(y <= 2500000000000.0)) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e-47) or not (y <= 2500000000000.0):
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e-47) || !(y <= 2500000000000.0))
		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 <= -5.9e-47) || ~((y <= 2500000000000.0)))
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e-47], N[Not[LessEqual[y, 2500000000000.0]], $MachinePrecision]], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.89999999999999973e-47 or 2.5e12 < y

   1. Initial program 89.8%

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

      1. associate-*r/ 86.2%

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

      2. associate-/l/ 84.9%

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

      3. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around 0 54.0%

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

   if -5.89999999999999973e-47 < y < 2.5e12

   1. Initial program 76.5%

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

      1. associate-*r/ 65.3%

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

      2. associate-/l/ 68.8%

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

      3. associate-/r* 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in x around 0 39.8%

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

      1. *-commutative 39.8%

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

      2. associate-/r* 48.3%

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

   6. Simplified 48.3%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-47} \lor \neg \left(y \leq 2500000000000\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 13: 57.1% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-47} \lor \neg \left(y \leq 1.02 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e-47) (not (<= y 1.02e-168))) (/ (/ y z) x) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e-47) || !(y <= 1.02e-168)) {
		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 <= (-6.8d-47)) .or. (.not. (y <= 1.02d-168))) 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 <= -6.8e-47) || !(y <= 1.02e-168)) {
		tmp = (y / z) / x;
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.8e-47) or not (y <= 1.02e-168):
		tmp = (y / z) / x
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e-47) || !(y <= 1.02e-168))
		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 <= -6.8e-47) || ~((y <= 1.02e-168)))
		tmp = (y / z) / x;
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.8e-47], N[Not[LessEqual[y, 1.02e-168]], $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 < -6.8000000000000003e-47 or 1.01999999999999999e-168 < y

   1. Initial program 90.8%

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

      1. associate-*r/ 91.4%

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

      2. associate-/l/ 84.8%

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

      3. associate-*l/ 84.3%

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

      4. *-commutative 84.3%

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

      5. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in x around 0 51.9%

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

      1. div-inv 52.4%

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

      2. associate-/r* 61.5%

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

   6. Applied egg-rr 61.5%

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

   if -6.8000000000000003e-47 < y < 1.01999999999999999e-168

   1. Initial program 70.9%

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

      1. associate-*r/ 62.0%

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

      2. associate-/l/ 68.9%

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

      3. associate-/r* 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in x around 0 38.8%

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

      1. *-commutative 38.8%

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

      2. associate-/r* 47.4%

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

   6. Simplified 47.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-47} \lor \neg \left(y \leq 1.02 \cdot 10^{-168}\right):\\ \;\;\;\;\frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 14: 50.5% accurate, 21.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. associate-*r/ 76.8%

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

   2. associate-/l/ 77.6%

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

   3. associate-/r* 84.3%

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

3. Simplified 84.3%

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

4. Taylor expanded in x around 0 47.6%

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

5. Final simplification 47.6%

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

Developer target: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023192 
(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))