Linear.Quaternion:$ctan from linear-1.19.1.3

Percentage Accurate: 84.7% → 98.9%

Time: 8.2s

Alternatives: 14

Speedup: 1.0×

• 63.4% 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: 84.7% 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: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+126} \lor \neg \left(y \leq 2.5 \cdot 10^{+89}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot \cosh x}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+126) (not (<= y 2.5e+89)))
   (* (cosh x) (/ (/ y z) x))
   (/ (/ (* y (cosh x)) x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+126) || !(y <= 2.5e+89)) {
		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 <= (-1d+126)) .or. (.not. (y <= 2.5d+89))) 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 <= -1e+126) || !(y <= 2.5e+89)) {
		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 <= -1e+126) or not (y <= 2.5e+89):
		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 <= -1e+126) || !(y <= 2.5e+89))
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	else
		tmp = Float64(Float64(Float64(y * cosh(x)) / x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+126) || ~((y <= 2.5e+89)))
		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, -1e+126], N[Not[LessEqual[y, 2.5e+89]], $MachinePrecision]], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[Cosh[x], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999925e125 or 2.49999999999999992e89 < y

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/l/ 82.9%

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

      3. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   if -9.99999999999999925e125 < y < 2.49999999999999992e89

   1. Initial program 87.7%

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

      1. associate-*r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+126} \lor \neg \left(y \leq 2.5 \cdot 10^{+89}\right):\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot \cosh x}{x}}{z}\\ \end{array} \]

Alternative 2: 91.8% 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 95.1%

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

   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/ 68.4%

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

      3. associate-*l/ 68.4%

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

      4. *-commutative 68.4%

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

      5. *-commutative 68.4%

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

   3. Simplified 68.4%

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

4. Final simplification 93.2%

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

Alternative 3: 88.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \frac{\cosh x}{z}\\ t_1 := \cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ y x) (/ (cosh x) z))) (t_1 (* (cosh x) (/ (/ y z) x))))
   (if (<= y -1e+124)
     t_1
     (if (<= y -1.9e-143)
       t_0
       (if (<= y 3.2e-296)
         (* y (/ (cosh x) (* x z)))
         (if (<= y 1.4e+89) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = (y / x) * (cosh(x) / z);
	double t_1 = cosh(x) * ((y / z) / x);
	double tmp;
	if (y <= -1e+124) {
		tmp = t_1;
	} else if (y <= -1.9e-143) {
		tmp = t_0;
	} else if (y <= 3.2e-296) {
		tmp = y * (cosh(x) / (x * z));
	} else if (y <= 1.4e+89) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (y / x) * (cosh(x) / z)
    t_1 = cosh(x) * ((y / z) / x)
    if (y <= (-1d+124)) then
        tmp = t_1
    else if (y <= (-1.9d-143)) then
        tmp = t_0
    else if (y <= 3.2d-296) then
        tmp = y * (cosh(x) / (x * z))
    else if (y <= 1.4d+89) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y / x) * (Math.cosh(x) / z);
	double t_1 = Math.cosh(x) * ((y / z) / x);
	double tmp;
	if (y <= -1e+124) {
		tmp = t_1;
	} else if (y <= -1.9e-143) {
		tmp = t_0;
	} else if (y <= 3.2e-296) {
		tmp = y * (Math.cosh(x) / (x * z));
	} else if (y <= 1.4e+89) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / x) * (math.cosh(x) / z)
	t_1 = math.cosh(x) * ((y / z) / x)
	tmp = 0
	if y <= -1e+124:
		tmp = t_1
	elif y <= -1.9e-143:
		tmp = t_0
	elif y <= 3.2e-296:
		tmp = y * (math.cosh(x) / (x * z))
	elif y <= 1.4e+89:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / x) * Float64(cosh(x) / z))
	t_1 = Float64(cosh(x) * Float64(Float64(y / z) / x))
	tmp = 0.0
	if (y <= -1e+124)
		tmp = t_1;
	elseif (y <= -1.9e-143)
		tmp = t_0;
	elseif (y <= 3.2e-296)
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	elseif (y <= 1.4e+89)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / x) * (cosh(x) / z);
	t_1 = cosh(x) * ((y / z) / x);
	tmp = 0.0;
	if (y <= -1e+124)
		tmp = t_1;
	elseif (y <= -1.9e-143)
		tmp = t_0;
	elseif (y <= 3.2e-296)
		tmp = y * (cosh(x) / (x * z));
	elseif (y <= 1.4e+89)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] * N[(N[Cosh[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+124], t$95$1, If[LessEqual[y, -1.9e-143], t$95$0, If[LessEqual[y, 3.2e-296], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+89], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.99999999999999948e123 or 1.3999999999999999e89 < y

   1. Initial program 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-/l/ 82.9%

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

      3. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   if -9.99999999999999948e123 < y < -1.89999999999999991e-143 or 3.20000000000000013e-296 < y < 1.3999999999999999e89

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   if -1.89999999999999991e-143 < y < 3.20000000000000013e-296

   1. Initial program 47.5%

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

      1. associate-*r/ 99.9%

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

      2. associate-/l/ 67.3%

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

      3. associate-*l/ 67.3%

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

      4. *-commutative 67.3%

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

      5. *-commutative 67.3%

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

   3. Simplified 67.3%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+124}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-296}:\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{\cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 4: 83.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.25 \cdot 10^{+161}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-47} \lor \neg \left(x \leq 2.6 \cdot 10^{-160}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.25e+161)
   (/ (* y (* x 0.5)) (* x (/ z x)))
   (if (or (<= x -2.7e-47) (not (<= x 2.6e-160)))
     (* y (/ (cosh x) (* x z)))
     (+ (/ (/ y z) x) (* 0.5 (* x (/ y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.25e+161) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else if ((x <= -2.7e-47) || !(x <= 2.6e-160)) {
		tmp = y * (cosh(x) / (x * z));
	} else {
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.25d+161)) then
        tmp = (y * (x * 0.5d0)) / (x * (z / x))
    else if ((x <= (-2.7d-47)) .or. (.not. (x <= 2.6d-160))) then
        tmp = y * (cosh(x) / (x * z))
    else
        tmp = ((y / z) / x) + (0.5d0 * (x * (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.25e+161) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else if ((x <= -2.7e-47) || !(x <= 2.6e-160)) {
		tmp = y * (Math.cosh(x) / (x * z));
	} else {
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.25e+161:
		tmp = (y * (x * 0.5)) / (x * (z / x))
	elif (x <= -2.7e-47) or not (x <= 2.6e-160):
		tmp = y * (math.cosh(x) / (x * z))
	else:
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.25e+161)
		tmp = Float64(Float64(y * Float64(x * 0.5)) / Float64(x * Float64(z / x)));
	elseif ((x <= -2.7e-47) || !(x <= 2.6e-160))
		tmp = Float64(y * Float64(cosh(x) / Float64(x * z)));
	else
		tmp = Float64(Float64(Float64(y / z) / x) + Float64(0.5 * Float64(x * Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.25e+161)
		tmp = (y * (x * 0.5)) / (x * (z / x));
	elseif ((x <= -2.7e-47) || ~((x <= 2.6e-160)))
		tmp = y * (cosh(x) / (x * z));
	else
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.25e+161], N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.7e-47], N[Not[LessEqual[x, 2.6e-160]], $MachinePrecision]], N[(y * N[(N[Cosh[x], $MachinePrecision] / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] + N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.25000000000000004e161

   1. Initial program 76.3%

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

   2. Taylor expanded in x around 0 62.3%

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

      1. +-commutative 62.3%

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

      2. associate-/l* 55.1%

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

      3. associate-/r* 55.1%

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

   4. Simplified 55.1%

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

      1. +-commutative 55.1%

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

      2. associate-*r/ 55.1%

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

      3. *-commutative 55.1%

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

      4. frac-add 69.5%

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

      5. *-commutative 69.5%

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

      6. associate-*l* 69.5%

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

      7. *-commutative 69.5%

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

   6. Applied egg-rr 69.5%

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

   7. Taylor expanded in x around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*r* 72.1%

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

   9. Simplified 72.1%

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

   if -4.25000000000000004e161 < x < -2.6999999999999998e-47 or 2.60000000000000003e-160 < x

   1. Initial program 90.9%

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

      1. associate-*r/ 97.9%

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

      2. associate-/l/ 84.7%

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

      3. associate-*l/ 83.8%

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

      4. *-commutative 83.8%

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

      5. *-commutative 83.8%

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

   3. Simplified 83.8%

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

   if -2.6999999999999998e-47 < x < 2.60000000000000003e-160

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 82.8%

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

      3. associate-/r* 97.4%

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

   4. Simplified 97.4%

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

      1. associate-/r/ 97.4%

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

   6. Applied egg-rr 97.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.25 \cdot 10^{+161}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-47} \lor \neg \left(x \leq 2.6 \cdot 10^{-160}\right):\\ \;\;\;\;y \cdot \frac{\cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 5: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+234}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e+234)
   (/ (* y (* x 0.5)) (* x (/ z x)))
   (* (cosh x) (/ (/ y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+234) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = cosh(x) * ((y / z) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-8.2d+234)) then
        tmp = (y * (x * 0.5d0)) / (x * (z / x))
    else
        tmp = cosh(x) * ((y / z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e+234) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = Math.cosh(x) * ((y / z) / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.2e+234:
		tmp = (y * (x * 0.5)) / (x * (z / x))
	else:
		tmp = math.cosh(x) * ((y / z) / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e+234)
		tmp = Float64(Float64(y * Float64(x * 0.5)) / Float64(x * Float64(z / x)));
	else
		tmp = Float64(cosh(x) * Float64(Float64(y / z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.2e+234)
		tmp = (y * (x * 0.5)) / (x * (z / x));
	else
		tmp = cosh(x) * ((y / z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e+234], N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999948e234

   1. Initial program 77.8%

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

   2. Taylor expanded in x around 0 68.2%

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

      1. +-commutative 68.2%

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

      2. associate-/l* 62.9%

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

      3. associate-/r* 62.9%

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

   4. Simplified 62.9%

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

      1. +-commutative 62.9%

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

      2. associate-*r/ 62.9%

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

      3. *-commutative 62.9%

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

      4. frac-add 73.1%

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

      5. *-commutative 73.1%

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

      6. associate-*l* 73.1%

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

      7. *-commutative 73.1%

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

   6. Applied egg-rr 73.1%

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

   7. Taylor expanded in x around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. associate-*r* 78.7%

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

   9. Simplified 78.7%

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

   if -8.19999999999999948e234 < x

   1. Initial program 88.9%

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

      1. associate-*r/ 81.7%

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

      2. associate-/l/ 78.3%

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

      3. associate-/r* 87.8%

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

   3. Simplified 87.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+234}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array} \]

Alternative 6: 69.7% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+24} \lor \neg \left(x \leq 10000000000\right):\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e+24) (not (<= x 10000000000.0)))
   (/ (* y (* x 0.5)) (* x (/ z x)))
   (+ (/ (/ y z) x) (* 0.5 (* x (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e+24) || !(x <= 10000000000.0)) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2d+24)) .or. (.not. (x <= 10000000000.0d0))) then
        tmp = (y * (x * 0.5d0)) / (x * (z / x))
    else
        tmp = ((y / z) / x) + (0.5d0 * (x * (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e+24) || !(x <= 10000000000.0)) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e+24) or not (x <= 10000000000.0):
		tmp = (y * (x * 0.5)) / (x * (z / x))
	else:
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e+24) || !(x <= 10000000000.0))
		tmp = Float64(Float64(y * Float64(x * 0.5)) / Float64(x * Float64(z / x)));
	else
		tmp = Float64(Float64(Float64(y / z) / x) + Float64(0.5 * Float64(x * Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2e+24) || ~((x <= 10000000000.0)))
		tmp = (y * (x * 0.5)) / (x * (z / x));
	else
		tmp = ((y / z) / x) + (0.5 * (x * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e+24], N[Not[LessEqual[x, 10000000000.0]], $MachinePrecision]], N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] + N[(0.5 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2e24 or 1e10 < x

   1. Initial program 85.3%

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

   2. Taylor expanded in x around 0 49.4%

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

      1. +-commutative 49.4%

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

      2. associate-/l* 48.8%

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

      3. associate-/r* 48.8%

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

   4. Simplified 48.8%

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

      1. +-commutative 48.8%

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

      2. associate-*r/ 48.8%

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

      3. *-commutative 48.8%

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

      4. frac-add 48.1%

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

      5. *-commutative 48.1%

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

      6. associate-*l* 48.1%

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

      7. *-commutative 48.1%

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

   6. Applied egg-rr 48.1%

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

   7. Taylor expanded in x around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-*r* 57.4%

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

   9. Simplified 57.4%

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

   if -2e24 < x < 1e10

   1. Initial program 90.9%

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

   2. Taylor expanded in x around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. associate-/l* 84.7%

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

      3. associate-/r* 91.6%

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

   4. Simplified 91.6%

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

      1. associate-/r/ 91.6%

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

   6. Applied egg-rr 91.6%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+24} \lor \neg \left(x \leq 10000000000\right):\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} + 0.5 \cdot \left(x \cdot \frac{y}{z}\right)\\ \end{array} \]

Alternative 7: 69.5% accurate, 7.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.42)) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} 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 <= 1.42d0))) then
        tmp = (y * (x * 0.5d0)) / (x * (z / x))
    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 <= 1.42)) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.42))
		tmp = Float64(Float64(y * Float64(x * 0.5)) / Float64(x * Float64(z / x)));
	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 <= 1.42)))
		tmp = (y * (x * 0.5)) / (x * (z / x));
	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, 1.42]], $MachinePrecision]], N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.4199999999999999 < x

   1. Initial program 86.1%

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

   2. Taylor expanded in x around 0 48.2%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   3. 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* 47.6%

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

      3. associate-/r* 47.6%

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

   4. Simplified 47.6%

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

      1. +-commutative 47.6%

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

      2. associate-*r/ 47.6%

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

      3. *-commutative 47.6%

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

      4. frac-add 47.0%

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

      5. *-commutative 47.0%

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

      6. associate-*l* 47.0%

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

      7. *-commutative 47.0%

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

   6. Applied egg-rr 47.0%

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

   7. Taylor expanded in x around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-*r* 55.8%

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

   9. Simplified 55.8%

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

   if -1.3999999999999999 < x < 1.4199999999999999

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 88.4%

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

      1. associate-/r* 95.8%

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

   4. Simplified 95.8%

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

4. Final simplification 74.4%

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

Alternative 8: 67.7% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e+49)
   (/ (* y (* x 0.5)) (* x (/ z x)))
   (+ (/ (/ y z) x) (* 0.5 (/ y (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+49) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = ((y / z) / x) + (0.5 * (y / (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2d+49)) then
        tmp = (y * (x * 0.5d0)) / (x * (z / x))
    else
        tmp = ((y / z) / x) + (0.5d0 * (y / (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e+49) {
		tmp = (y * (x * 0.5)) / (x * (z / x));
	} else {
		tmp = ((y / z) / x) + (0.5 * (y / (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e+49:
		tmp = (y * (x * 0.5)) / (x * (z / x))
	else:
		tmp = ((y / z) / x) + (0.5 * (y / (z / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e+49)
		tmp = Float64(Float64(y * Float64(x * 0.5)) / Float64(x * Float64(z / x)));
	else
		tmp = Float64(Float64(Float64(y / z) / x) + Float64(0.5 * Float64(y / Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e+49)
		tmp = (y * (x * 0.5)) / (x * (z / x));
	else
		tmp = ((y / z) / x) + (0.5 * (y / (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e+49], N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / N[(x * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision] + N[(0.5 * N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999989e49

   1. Initial program 86.2%

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

   2. Taylor expanded in x around 0 48.5%

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

      1. +-commutative 48.5%

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

      2. associate-/l* 42.7%

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

      3. associate-/r* 42.7%

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

   4. Simplified 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-*r/ 42.7%

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

      3. *-commutative 42.7%

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

      4. frac-add 51.0%

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

      5. *-commutative 51.0%

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

      6. associate-*l* 51.0%

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

      7. *-commutative 51.0%

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

   6. Applied egg-rr 51.0%

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

   7. Taylor expanded in x around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. associate-*r* 55.6%

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

   9. Simplified 55.6%

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

   if -1.99999999999999989e49 < x

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-/l* 74.8%

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

      3. associate-/r* 79.3%

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

   4. Simplified 79.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\frac{y \cdot \left(x \cdot 0.5\right)}{x \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} + 0.5 \cdot \frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 9: 62.3% accurate, 9.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.42)) {
		tmp = x * (y * (0.5 / 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 <= 1.42d0))) then
        tmp = x * (y * (0.5d0 / 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 <= 1.42)) {
		tmp = x * (y * (0.5 / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.42))
		tmp = Float64(x * Float64(y * Float64(0.5 / 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 <= 1.42)))
		tmp = x * (y * (0.5 / 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, 1.42]], $MachinePrecision]], N[(x * N[(y * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.4199999999999999 < x

   1. Initial program 86.1%

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

   2. Taylor expanded in x around 0 48.2%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   3. 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* 47.6%

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

      3. associate-/r* 47.6%

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

   4. Simplified 47.6%

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

      1. associate-/r/ 40.1%

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

      2. div-inv 40.1%

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

      3. associate-*l* 47.6%

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

   6. Applied egg-rr 47.6%

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

   7. Taylor expanded in x around inf 48.2%

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

      1. associate-*r/ 48.2%

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

      2. *-commutative 48.2%

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

      3. associate-*r/ 48.2%

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

      4. associate-*r* 47.6%

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

      5. *-commutative 47.6%

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

      6. associate-*l* 40.1%

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

   9. Simplified 40.1%

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

   if -1.3999999999999999 < x < 1.4199999999999999

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 88.4%

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

      1. associate-/r* 95.8%

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

   4. Simplified 95.8%

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

4. Final simplification 66.0%

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

Alternative 10: 66.1% accurate, 9.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.42)) {
		tmp = y * (x * (0.5 / 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 <= 1.42d0))) then
        tmp = y * (x * (0.5d0 / 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 <= 1.42)) {
		tmp = y * (x * (0.5 / z));
	} else {
		tmp = (y / z) / x;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.42))
		tmp = Float64(y * Float64(x * Float64(0.5 / 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 <= 1.42)))
		tmp = y * (x * (0.5 / 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, 1.42]], $MachinePrecision]], N[(y * N[(x * N[(0.5 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999 or 1.4199999999999999 < x

   1. Initial program 86.1%

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

   2. Taylor expanded in x around 0 48.2%

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} + 0.5 \cdot \frac{y \cdot x}{z}} \]
   3. 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* 47.6%

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

      3. associate-/r* 47.6%

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

   4. Simplified 47.6%

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

   5. Taylor expanded in x around inf 48.2%

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

      1. associate-*r/ 48.2%

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

      2. *-commutative 48.2%

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

      3. associate-*r* 48.2%

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

      4. associate-*r/ 47.6%

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

      5. associate-*r/ 47.6%

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

   7. Simplified 47.6%

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

   if -1.3999999999999999 < x < 1.4199999999999999

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 88.4%

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

      1. associate-/r* 95.8%

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

   4. Simplified 95.8%

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

4. Final simplification 70.0%

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

Alternative 11: 66.2% accurate, 9.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4) {
		tmp = (y * (x * 0.5)) / z;
	} else if (x <= 1.42) {
		tmp = (y / z) / x;
	} else {
		tmp = y * (x * (0.5 / 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 = (y * (x * 0.5d0)) / z
    else if (x <= 1.42d0) then
        tmp = (y / z) / x
    else
        tmp = y * (x * (0.5d0 / 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 = (y * (x * 0.5)) / z;
	} else if (x <= 1.42) {
		tmp = (y / z) / x;
	} else {
		tmp = y * (x * (0.5 / z));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999

   1. Initial program 87.7%

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

   2. Taylor expanded in x around 0 49.0%

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

   3. Taylor expanded in x around inf 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-*l* 49.0%

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

   5. Simplified 49.0%

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

   if -1.3999999999999999 < x < 1.4199999999999999

   1. Initial program 90.3%

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

   2. Taylor expanded in x around 0 88.4%

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

      1. associate-/r* 95.8%

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

   4. Simplified 95.8%

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

   if 1.4199999999999999 < x

   1. Initial program 84.4%

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

   2. Taylor expanded in x around 0 47.3%

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

      1. +-commutative 47.3%

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

      2. associate-/l* 51.9%

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

      3. associate-/r* 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in x around inf 47.3%

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

      1. associate-*r/ 47.3%

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

      2. *-commutative 47.3%

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

      3. associate-*r* 47.3%

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

      4. associate-*r/ 51.9%

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

      5. associate-*r/ 51.9%

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

   7. Simplified 51.9%

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

4. Final simplification 71.5%

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

Alternative 12: 53.8% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+34} \lor \neg \left(z \leq 2.2 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+34) (not (<= z 2.2e-69))) (/ y (* x z)) (/ (/ y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+34) || !(z <= 2.2e-69)) {
		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 <= (-1.8d+34)) .or. (.not. (z <= 2.2d-69))) 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 <= -1.8e+34) || !(z <= 2.2e-69)) {
		tmp = y / (x * z);
	} else {
		tmp = (y / x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+34) or not (z <= 2.2e-69):
		tmp = y / (x * z)
	else:
		tmp = (y / x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+34) || !(z <= 2.2e-69))
		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 ((z <= -1.8e+34) || ~((z <= 2.2e-69)))
		tmp = y / (x * z);
	else
		tmp = (y / x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+34], N[Not[LessEqual[z, 2.2e-69]], $MachinePrecision]], N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e34 or 2.2e-69 < z

   1. Initial program 85.8%

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

   2. Taylor expanded in x around 0 46.9%

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

   if -1.8e34 < z < 2.2e-69

   1. Initial program 90.7%

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

   2. Taylor expanded in x around 0 57.8%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+34} \lor \neg \left(z \leq 2.2 \cdot 10^{-69}\right):\\ \;\;\;\;\frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x}}{z}\\ \end{array} \]

Alternative 13: 50.2% 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 88.1%

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

2. Taylor expanded in x around 0 46.7%

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

3. Final simplification 46.7%

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

Alternative 14: 53.8% 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 88.1%

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

2. Taylor expanded in x around 0 46.7%

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

   1. associate-/r* 53.8%

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

4. Simplified 53.8%

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

5. Final simplification 53.8%

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

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(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))