Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.0% → 96.0%

Time: 8.3s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-8} \lor \neg \left(y \leq 6.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.25e-8) (not (<= y 6.4e-11)))
   (* (/ (sin y) z) (/ x y))
   (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.25e-8) || !(y <= 6.4e-11)) {
		tmp = (sin(y) / z) * (x / y);
	} else {
		tmp = 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 <= (-2.25d-8)) .or. (.not. (y <= 6.4d-11))) then
        tmp = (sin(y) / z) * (x / y)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.25e-8) || !(y <= 6.4e-11)) {
		tmp = (Math.sin(y) / z) * (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.25e-8) or not (y <= 6.4e-11):
		tmp = (math.sin(y) / z) * (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.25e-8) || !(y <= 6.4e-11))
		tmp = Float64(Float64(sin(y) / z) * Float64(x / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.25e-8) || ~((y <= 6.4e-11)))
		tmp = (sin(y) / z) * (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.25e-8], N[Not[LessEqual[y, 6.4e-11]], $MachinePrecision]], N[(N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.24999999999999996e-8 or 6.39999999999999987e-11 < y

   1. Initial program 96.7%

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

      1. associate-*r/ 96.8%

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

      2. associate-/l/ 89.5%

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

      3. *-commutative 89.5%

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

      4. times-frac 96.8%

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

   3. Simplified 96.8%

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

   if -2.24999999999999996e-8 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. times-frac 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-*r/ 73.9%

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

      5. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-8} \lor \neg \left(y \leq 6.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 2: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-8} \lor \neg \left(y \leq 3 \cdot 10^{-21}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.35e-8) (not (<= y 3e-21)))
   (* (sin y) (/ x (* y z)))
   (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e-8) || !(y <= 3e-21)) {
		tmp = sin(y) * (x / (y * z));
	} else {
		tmp = 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 <= (-2.35d-8)) .or. (.not. (y <= 3d-21))) then
        tmp = sin(y) * (x / (y * z))
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.35e-8) || !(y <= 3e-21)) {
		tmp = Math.sin(y) * (x / (y * z));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.35e-8) or not (y <= 3e-21):
		tmp = math.sin(y) * (x / (y * z))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.35e-8) || !(y <= 3e-21))
		tmp = Float64(sin(y) * Float64(x / Float64(y * z)));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.35e-8) || ~((y <= 3e-21)))
		tmp = sin(y) * (x / (y * z));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.35e-8], N[Not[LessEqual[y, 3e-21]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3499999999999999e-8 or 2.99999999999999991e-21 < y

   1. Initial program 96.7%

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

      1. associate-*l/ 92.5%

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

      2. times-frac 89.6%

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

      3. *-commutative 89.6%

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

      4. associate-*r/ 89.6%

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

      5. *-commutative 89.6%

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

   3. Simplified 89.6%

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

   if -2.3499999999999999e-8 < y < 2.99999999999999991e-21

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. times-frac 75.1%

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

      3. *-commutative 75.1%

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

      4. associate-*r/ 73.7%

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

      5. *-commutative 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in y around 0 100.0%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-8} \lor \neg \left(y \leq 3 \cdot 10^{-21}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 3: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

2. Final simplification 98.3%

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

Alternative 4: 66.3% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7200000000:\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7200000000.0)
   (* (/ x (* y z)) (/ 6.0 y))
   (if (<= y 6.4e-11) (/ x z) (* 6.0 (* (/ (/ x z) y) (/ 1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7200000000.0) {
		tmp = (x / (y * z)) * (6.0 / y);
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = 6.0 * (((x / z) / y) * (1.0 / 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 <= (-7200000000.0d0)) then
        tmp = (x / (y * z)) * (6.0d0 / y)
    else if (y <= 6.4d-11) then
        tmp = x / z
    else
        tmp = 6.0d0 * (((x / z) / y) * (1.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7200000000.0) {
		tmp = (x / (y * z)) * (6.0 / y);
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = 6.0 * (((x / z) / y) * (1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7200000000.0:
		tmp = (x / (y * z)) * (6.0 / y)
	elif y <= 6.4e-11:
		tmp = x / z
	else:
		tmp = 6.0 * (((x / z) / y) * (1.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7200000000.0)
		tmp = Float64(Float64(x / Float64(y * z)) * Float64(6.0 / y));
	elseif (y <= 6.4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(6.0 * Float64(Float64(Float64(x / z) / y) * Float64(1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7200000000.0)
		tmp = (x / (y * z)) * (6.0 / y);
	elseif (y <= 6.4e-11)
		tmp = x / z;
	else
		tmp = 6.0 * (((x / z) / y) * (1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7200000000.0], N[(N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(6.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-11], N[(x / z), $MachinePrecision], N[(6.0 * N[(N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2e9

   1. Initial program 97.9%

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

      1. associate-/l* 90.1%

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

      2. associate-/r/ 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in y around 0 36.8%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 36.8%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 36.8%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 36.8%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 36.8%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 36.8%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 36.8%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{{y}^{2} \cdot z}} \]

      2. *-commutative 36.8%

         \[\leadsto \frac{\color{blue}{x \cdot 6}}{{y}^{2} \cdot z} \]

      3. unpow2 36.8%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      4. *-commutative 36.8%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      5. associate-/l* 36.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y \cdot y\right)}{6}}} \]

      6. associate-*r* 36.8%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(z \cdot y\right) \cdot y}}{6}} \]

      7. associate-/l* 36.8%

         \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot y}{\frac{6}{y}}}} \]

   10. Simplified 36.8%

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

       1. associate-/r/ 38.4%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y} \cdot \frac{6}{y}} \]

       2. *-commutative 38.4%

          \[\leadsto \frac{x}{\color{blue}{y \cdot z}} \cdot \frac{6}{y} \]

   12. Applied egg-rr 38.4%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z} \cdot \frac{6}{y}} \]

   if -7.2e9 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*r/ 74.7%

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

      5. *-commutative 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in y around 0 98.7%

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

   if 6.39999999999999987e-11 < y

   1. Initial program 95.5%

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

      1. associate-/l* 88.3%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 30.7%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 30.7%

      \[\leadsto 6 \cdot \color{blue}{\frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      3. associate-/r* 32.0%

         \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{z}}{y \cdot y}} \]

   10. Simplified 32.0%

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

       1. associate-/r* 32.2%

          \[\leadsto 6 \cdot \color{blue}{\frac{\frac{\frac{x}{z}}{y}}{y}} \]

       2. div-inv 32.2%

          \[\leadsto 6 \cdot \color{blue}{\left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)} \]

   12. Applied egg-rr 32.2%

       \[\leadsto 6 \cdot \color{blue}{\left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7200000000:\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)\\ \end{array} \]

Alternative 5: 66.4% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3700000:\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3700000.0)
   (* (/ x (* y z)) (/ 6.0 y))
   (if (<= y 6.4e-11)
     (/ (* x (+ 1.0 (* -0.16666666666666666 (* y y)))) z)
     (* 6.0 (* (/ (/ x z) y) (/ 1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3700000.0) {
		tmp = (x / (y * z)) * (6.0 / y);
	} else if (y <= 6.4e-11) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = 6.0 * (((x / z) / y) * (1.0 / 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 <= (-3700000.0d0)) then
        tmp = (x / (y * z)) * (6.0d0 / y)
    else if (y <= 6.4d-11) then
        tmp = (x * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))) / z
    else
        tmp = 6.0d0 * (((x / z) / y) * (1.0d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3700000.0) {
		tmp = (x / (y * z)) * (6.0 / y);
	} else if (y <= 6.4e-11) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = 6.0 * (((x / z) / y) * (1.0 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3700000.0:
		tmp = (x / (y * z)) * (6.0 / y)
	elif y <= 6.4e-11:
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z
	else:
		tmp = 6.0 * (((x / z) / y) * (1.0 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3700000.0)
		tmp = Float64(Float64(x / Float64(y * z)) * Float64(6.0 / y));
	elseif (y <= 6.4e-11)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))) / z);
	else
		tmp = Float64(6.0 * Float64(Float64(Float64(x / z) / y) * Float64(1.0 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3700000.0)
		tmp = (x / (y * z)) * (6.0 / y);
	elseif (y <= 6.4e-11)
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	else
		tmp = 6.0 * (((x / z) / y) * (1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3700000.0], N[(N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(6.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-11], N[(N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(6.0 * N[(N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7e6

   1. Initial program 98.0%

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

      1. associate-/l* 90.6%

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

      2. associate-/r/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around 0 38.4%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 38.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 38.4%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 38.4%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 38.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 38.4%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 38.4%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{{y}^{2} \cdot z}} \]

      2. *-commutative 38.4%

         \[\leadsto \frac{\color{blue}{x \cdot 6}}{{y}^{2} \cdot z} \]

      3. unpow2 38.4%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      4. *-commutative 38.4%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      5. associate-/l* 38.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y \cdot y\right)}{6}}} \]

      6. associate-*r* 38.4%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(z \cdot y\right) \cdot y}}{6}} \]

      7. associate-/l* 38.4%

         \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot y}{\frac{6}{y}}}} \]

   10. Simplified 38.4%

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

       1. associate-/r/ 39.9%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y} \cdot \frac{6}{y}} \]

       2. *-commutative 39.9%

          \[\leadsto \frac{x}{\color{blue}{y \cdot z}} \cdot \frac{6}{y} \]

   12. Applied egg-rr 39.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z} \cdot \frac{6}{y}} \]

   if -3.7e6 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.4%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot {y}^{2}\right)}}{z} \]
   3. Step-by-step derivation

      1. unpow2 99.4%

         \[\leadsto \frac{x \cdot \left(1 + -0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)}\right)}{z} \]

   4. Simplified 99.4%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}}{z} \]

   if 6.39999999999999987e-11 < y

   1. Initial program 95.5%

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

      1. associate-/l* 88.3%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 30.7%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 30.7%

      \[\leadsto 6 \cdot \color{blue}{\frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      3. associate-/r* 32.0%

         \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{z}}{y \cdot y}} \]

   10. Simplified 32.0%

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

       1. associate-/r* 32.2%

          \[\leadsto 6 \cdot \color{blue}{\frac{\frac{\frac{x}{z}}{y}}{y}} \]

       2. div-inv 32.2%

          \[\leadsto 6 \cdot \color{blue}{\left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)} \]

   12. Applied egg-rr 32.2%

       \[\leadsto 6 \cdot \color{blue}{\left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3700000:\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\frac{\frac{x}{z}}{y} \cdot \frac{1}{y}\right)\\ \end{array} \]

Alternative 6: 66.3% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8000000000 \lor \neg \left(y \leq 6.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8000000000.0) (not (<= y 6.4e-11)))
   (* (/ x (* y z)) (/ 6.0 y))
   (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8000000000.0) || !(y <= 6.4e-11)) {
		tmp = (x / (y * z)) * (6.0 / y);
	} else {
		tmp = 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 <= (-8000000000.0d0)) .or. (.not. (y <= 6.4d-11))) then
        tmp = (x / (y * z)) * (6.0d0 / y)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8000000000.0) || !(y <= 6.4e-11)) {
		tmp = (x / (y * z)) * (6.0 / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8000000000.0) or not (y <= 6.4e-11):
		tmp = (x / (y * z)) * (6.0 / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8000000000.0) || !(y <= 6.4e-11))
		tmp = Float64(Float64(x / Float64(y * z)) * Float64(6.0 / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8000000000.0) || ~((y <= 6.4e-11)))
		tmp = (x / (y * z)) * (6.0 / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8000000000.0], N[Not[LessEqual[y, 6.4e-11]], $MachinePrecision]], N[(N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(6.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e9 or 6.39999999999999987e-11 < y

   1. Initial program 96.6%

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

      1. associate-/l* 89.1%

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

      2. associate-/r/ 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around 0 33.5%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 33.5%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 33.5%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 33.5%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 33.5%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 33.5%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 33.5%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{{y}^{2} \cdot z}} \]

      2. *-commutative 33.5%

         \[\leadsto \frac{\color{blue}{x \cdot 6}}{{y}^{2} \cdot z} \]

      3. unpow2 33.5%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      4. *-commutative 33.5%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      5. associate-/l* 33.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y \cdot y\right)}{6}}} \]

      6. associate-*r* 33.5%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(z \cdot y\right) \cdot y}}{6}} \]

      7. associate-/l* 33.5%

         \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot y}{\frac{6}{y}}}} \]

   10. Simplified 33.5%

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

       1. associate-/r/ 35.0%

          \[\leadsto \color{blue}{\frac{x}{z \cdot y} \cdot \frac{6}{y}} \]

       2. *-commutative 35.0%

          \[\leadsto \frac{x}{\color{blue}{y \cdot z}} \cdot \frac{6}{y} \]

   12. Applied egg-rr 35.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot z} \cdot \frac{6}{y}} \]

   if -8e9 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 76.0%

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

      3. *-commutative 76.0%

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

      4. associate-*r/ 74.7%

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

      5. *-commutative 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in y around 0 98.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8000000000 \lor \neg \left(y \leq 6.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y \cdot z} \cdot \frac{6}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 7: 66.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{z}}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e+32)
   (* 6.0 (/ x (* z (* y y))))
   (if (<= y 6.4e-11) (/ x z) (* 6.0 (/ (/ x z) (* y y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+32) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = 6.0 * ((x / z) / (y * 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 <= (-2.1d+32)) then
        tmp = 6.0d0 * (x / (z * (y * y)))
    else if (y <= 6.4d-11) then
        tmp = x / z
    else
        tmp = 6.0d0 * ((x / z) / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+32) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = 6.0 * ((x / z) / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e+32:
		tmp = 6.0 * (x / (z * (y * y)))
	elif y <= 6.4e-11:
		tmp = x / z
	else:
		tmp = 6.0 * ((x / z) / (y * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e+32)
		tmp = Float64(6.0 * Float64(x / Float64(z * Float64(y * y))));
	elseif (y <= 6.4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(6.0 * Float64(Float64(x / z) / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.1e+32)
		tmp = 6.0 * (x / (z * (y * y)));
	elseif (y <= 6.4e-11)
		tmp = x / z;
	else
		tmp = 6.0 * ((x / z) / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e+32], N[(6.0 * N[(x / N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-11], N[(x / z), $MachinePrecision], N[(6.0 * N[(N[(x / z), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1000000000000001e32

   1. Initial program 97.6%

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

      1. associate-/l* 88.6%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 38.0%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 38.0%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   if -2.1000000000000001e32 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 77.4%

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

      3. *-commutative 77.4%

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

      4. associate-*r/ 76.1%

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

      5. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in y around 0 95.2%

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

   if 6.39999999999999987e-11 < y

   1. Initial program 95.5%

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

      1. associate-/l* 88.3%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 30.7%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 30.7%

      \[\leadsto 6 \cdot \color{blue}{\frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      3. associate-/r* 32.0%

         \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{z}}{y \cdot y}} \]

   10. Simplified 32.0%

       \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{z}}{y \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+32}:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{z}}{y \cdot y}\\ \end{array} \]

Alternative 8: 66.0% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{\frac{6}{y}}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{z}}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+32)
   (* x (/ (/ 6.0 y) (* y z)))
   (if (<= y 6.4e-11) (/ x z) (* 6.0 (/ (/ x z) (* y y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+32) {
		tmp = x * ((6.0 / y) / (y * z));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = 6.0 * ((x / z) / (y * 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 <= (-7d+32)) then
        tmp = x * ((6.0d0 / y) / (y * z))
    else if (y <= 6.4d-11) then
        tmp = x / z
    else
        tmp = 6.0d0 * ((x / z) / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+32) {
		tmp = x * ((6.0 / y) / (y * z));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = 6.0 * ((x / z) / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+32:
		tmp = x * ((6.0 / y) / (y * z))
	elif y <= 6.4e-11:
		tmp = x / z
	else:
		tmp = 6.0 * ((x / z) / (y * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+32)
		tmp = Float64(x * Float64(Float64(6.0 / y) / Float64(y * z)));
	elseif (y <= 6.4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(6.0 * Float64(Float64(x / z) / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+32)
		tmp = x * ((6.0 / y) / (y * z));
	elseif (y <= 6.4e-11)
		tmp = x / z;
	else
		tmp = 6.0 * ((x / z) / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+32], N[(x * N[(N[(6.0 / y), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-11], N[(x / z), $MachinePrecision], N[(6.0 * N[(N[(x / z), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000002e32

   1. Initial program 97.6%

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

      1. associate-/l* 88.6%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 38.0%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 38.0%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. associate-*r/ 38.0%

         \[\leadsto \color{blue}{\frac{6 \cdot x}{{y}^{2} \cdot z}} \]

      2. *-commutative 38.0%

         \[\leadsto \frac{\color{blue}{x \cdot 6}}{{y}^{2} \cdot z} \]

      3. unpow2 38.0%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      4. *-commutative 38.0%

         \[\leadsto \frac{x \cdot 6}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      5. associate-/l* 38.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot \left(y \cdot y\right)}{6}}} \]

      6. associate-*r* 38.0%

         \[\leadsto \frac{x}{\frac{\color{blue}{\left(z \cdot y\right) \cdot y}}{6}} \]

      7. associate-/l* 38.0%

         \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot y}{\frac{6}{y}}}} \]

   10. Simplified 38.0%

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

       1. div-inv 38.0%

          \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z \cdot y}{\frac{6}{y}}}} \]

       2. clear-num 38.0%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{6}{y}}{z \cdot y}} \]

       3. *-commutative 38.0%

          \[\leadsto x \cdot \frac{\frac{6}{y}}{\color{blue}{y \cdot z}} \]

   12. Applied egg-rr 38.0%

       \[\leadsto \color{blue}{x \cdot \frac{\frac{6}{y}}{y \cdot z}} \]

   if -7.0000000000000002e32 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 77.4%

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

      3. *-commutative 77.4%

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

      4. associate-*r/ 76.1%

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

      5. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in y around 0 95.2%

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

   if 6.39999999999999987e-11 < y

   1. Initial program 95.5%

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

      1. associate-/l* 88.3%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 30.7%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 30.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   8. Taylor expanded in x around 0 30.7%

      \[\leadsto 6 \cdot \color{blue}{\frac{x}{{y}^{2} \cdot z}} \]
   9. Step-by-step derivation

      1. unpow2 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{\left(y \cdot y\right)} \cdot z} \]

      2. *-commutative 30.7%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot \left(y \cdot y\right)}} \]

      3. associate-/r* 32.0%

         \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{z}}{y \cdot y}} \]

   10. Simplified 32.0%

       \[\leadsto 6 \cdot \color{blue}{\frac{\frac{x}{z}}{y \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{\frac{6}{y}}{y \cdot z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \frac{\frac{x}{z}}{y \cdot y}\\ \end{array} \]

Alternative 9: 66.0% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49} \lor \neg \left(y \leq 5 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+49) (not (<= y 5e+25))) (* y (/ x (* y z))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+49) || !(y <= 5e+25)) {
		tmp = y * (x / (y * z));
	} else {
		tmp = 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 <= (-5d+49)) .or. (.not. (y <= 5d+25))) then
        tmp = y * (x / (y * z))
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+49) || !(y <= 5e+25)) {
		tmp = y * (x / (y * z));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+49) or not (y <= 5e+25):
		tmp = y * (x / (y * z))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+49) || !(y <= 5e+25))
		tmp = Float64(y * Float64(x / Float64(y * z)));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e+49) || ~((y <= 5e+25)))
		tmp = y * (x / (y * z));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+49], N[Not[LessEqual[y, 5e+25]], $MachinePrecision]], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000004e49 or 5.00000000000000024e25 < y

   1. Initial program 96.0%

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

      1. associate-*r/ 96.1%

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

      2. associate-/l/ 87.9%

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

      3. *-commutative 87.9%

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

      4. times-frac 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around 0 21.1%

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

      1. *-commutative 21.1%

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

      2. clear-num 21.1%

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

      3. frac-times 34.5%

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

      4. *-un-lft-identity 34.5%

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

   6. Applied egg-rr 34.5%

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

      1. div-inv 34.5%

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

      2. associate-*l/ 34.6%

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

      3. *-commutative 34.6%

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

      4. clear-num 33.1%

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

      5. *-commutative 33.1%

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

   8. Applied egg-rr 33.1%

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

   if -5.0000000000000004e49 < y < 5.00000000000000024e25

   1. Initial program 99.9%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*r/ 77.9%

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

      5. *-commutative 77.9%

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

   3. Simplified 77.9%

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

   4. Taylor expanded in y around 0 88.4%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49} \lor \neg \left(y \leq 5 \cdot 10^{+25}\right):\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 10: 66.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49} \lor \neg \left(y \leq 2.3 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+49) (not (<= y 2.3e-32))) (/ y (* z (/ y x))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+49) || !(y <= 2.3e-32)) {
		tmp = y / (z * (y / x));
	} else {
		tmp = 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 <= (-5d+49)) .or. (.not. (y <= 2.3d-32))) then
        tmp = y / (z * (y / x))
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+49) || !(y <= 2.3e-32)) {
		tmp = y / (z * (y / x));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+49) or not (y <= 2.3e-32):
		tmp = y / (z * (y / x))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+49) || !(y <= 2.3e-32))
		tmp = Float64(y / Float64(z * Float64(y / x)));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e+49) || ~((y <= 2.3e-32)))
		tmp = y / (z * (y / x));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+49], N[Not[LessEqual[y, 2.3e-32]], $MachinePrecision]], N[(y / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000004e49 or 2.3000000000000001e-32 < y

   1. Initial program 96.4%

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

      1. associate-*r/ 96.5%

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

      2. associate-/l/ 87.5%

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

      3. *-commutative 87.5%

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

      4. times-frac 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around 0 23.7%

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

      1. *-commutative 23.7%

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

      2. clear-num 23.7%

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

      3. frac-times 36.2%

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

      4. *-un-lft-identity 36.2%

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

   6. Applied egg-rr 36.2%

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

   if -5.0000000000000004e49 < y < 2.3000000000000001e-32

   1. Initial program 99.9%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*r/ 77.3%

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

      5. *-commutative 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in y around 0 92.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+49} \lor \neg \left(y \leq 2.3 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 11: 66.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+49)
   (/ y (* z (/ y x)))
   (if (<= y 6.4e-11) (/ x z) (/ y (/ z (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+49) {
		tmp = y / (z * (y / x));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = y / (z / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7.5d+49)) then
        tmp = y / (z * (y / x))
    else if (y <= 6.4d-11) then
        tmp = x / z
    else
        tmp = y / (z / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+49) {
		tmp = y / (z * (y / x));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = y / (z / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+49:
		tmp = y / (z * (y / x))
	elif y <= 6.4e-11:
		tmp = x / z
	else:
		tmp = y / (z / (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+49)
		tmp = Float64(y / Float64(z * Float64(y / x)));
	elseif (y <= 6.4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(z / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.5e+49)
		tmp = y / (z * (y / x));
	elseif (y <= 6.4e-11)
		tmp = x / z;
	else
		tmp = y / (z / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+49], N[(y / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-11], N[(x / z), $MachinePrecision], N[(y / N[(z / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999995e49

   1. Initial program 97.4%

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

      1. associate-*r/ 97.5%

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

      2. associate-/l/ 87.2%

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

      3. *-commutative 87.2%

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

      4. times-frac 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around 0 18.8%

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

      1. *-commutative 18.8%

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

      2. clear-num 18.8%

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

      3. frac-times 39.1%

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

      4. *-un-lft-identity 39.1%

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

   6. Applied egg-rr 39.1%

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

   if -7.4999999999999995e49 < y < 6.39999999999999987e-11

   1. Initial program 99.9%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*r/ 77.1%

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

      5. *-commutative 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in y around 0 92.2%

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

   if 6.39999999999999987e-11 < y

   1. Initial program 95.5%

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

      1. associate-*r/ 95.7%

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

      2. associate-/l/ 88.5%

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

      3. *-commutative 88.5%

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

      4. times-frac 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 23.7%

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

      1. *-commutative 23.7%

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

      2. clear-num 23.7%

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

      3. frac-times 31.5%

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

      4. *-un-lft-identity 31.5%

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

   6. Applied egg-rr 31.5%

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

      1. *-commutative 31.5%

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

      2. clear-num 31.5%

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

      3. un-div-inv 31.5%

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

   8. Applied egg-rr 31.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{y}}}\\ \end{array} \]

Alternative 12: 66.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+32}:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+32)
   (* 6.0 (/ x (* z (* y y))))
   (if (<= y 6.4e-11) (/ x z) (/ y (/ z (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+32) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = y / (z / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-7d+32)) then
        tmp = 6.0d0 * (x / (z * (y * y)))
    else if (y <= 6.4d-11) then
        tmp = x / z
    else
        tmp = y / (z / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+32) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 6.4e-11) {
		tmp = x / z;
	} else {
		tmp = y / (z / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e+32:
		tmp = 6.0 * (x / (z * (y * y)))
	elif y <= 6.4e-11:
		tmp = x / z
	else:
		tmp = y / (z / (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+32)
		tmp = Float64(6.0 * Float64(x / Float64(z * Float64(y * y))));
	elseif (y <= 6.4e-11)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(z / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e+32)
		tmp = 6.0 * (x / (z * (y * y)));
	elseif (y <= 6.4e-11)
		tmp = x / z;
	else
		tmp = y / (z / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+32], N[(6.0 * N[(x / N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e-11], N[(x / z), $MachinePrecision], N[(y / N[(z / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000002e32

   1. Initial program 97.6%

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

      1. associate-/l* 88.6%

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

      2. associate-/r/ 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around 0 38.0%

      \[\leadsto \frac{x}{\color{blue}{\left(0.16666666666666666 \cdot \left(y \cdot z\right) + \frac{z}{y}\right)} \cdot y} \]

   5. Taylor expanded in y around inf 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{{y}^{2} \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto 6 \cdot \frac{x}{\color{blue}{z \cdot {y}^{2}}} \]

      2. unpow2 38.0%

         \[\leadsto 6 \cdot \frac{x}{z \cdot \color{blue}{\left(y \cdot y\right)}} \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]

   if -7.0000000000000002e32 < y < 6.39999999999999987e-11

   1. Initial program 100.0%

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

      1. associate-*l/ 99.3%

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

      2. times-frac 77.4%

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

      3. *-commutative 77.4%

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

      4. associate-*r/ 76.1%

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

      5. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in y around 0 95.2%

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

   if 6.39999999999999987e-11 < y

   1. Initial program 95.5%

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

      1. associate-*r/ 95.7%

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

      2. associate-/l/ 88.5%

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

      3. *-commutative 88.5%

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

      4. times-frac 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around 0 23.7%

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

      1. *-commutative 23.7%

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

      2. clear-num 23.7%

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

      3. frac-times 31.5%

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

      4. *-un-lft-identity 31.5%

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

   6. Applied egg-rr 31.5%

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

      1. *-commutative 31.5%

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

      2. clear-num 31.5%

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

      3. un-div-inv 31.5%

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

   8. Applied egg-rr 31.5%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+32}:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{y}}}\\ \end{array} \]

Alternative 13: 58.4% accurate, 35.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. associate-*l/ 96.1%

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

   2. times-frac 82.6%

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

   3. *-commutative 82.6%

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

   4. associate-*r/ 82.0%

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

   5. *-commutative 82.0%

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

3. Simplified 82.0%

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

4. Taylor expanded in y around 0 58.7%

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

5. Final simplification 58.7%

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

Developer target: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\sin y}\\ t_1 := \frac{x \cdot \frac{1}{t_0}}{z}\\ \mathbf{if}\;z < -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (sin y))) (t_1 (/ (* x (/ 1.0 t_0)) z)))
   (if (< z -4.2173720203427147e-29)
     t_1
     (if (< z 4.446702369113811e+64) (/ x (* z t_0)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = y / sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * 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 / sin(y)
    t_1 = (x * (1.0d0 / t_0)) / z
    if (z < (-4.2173720203427147d-29)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x / (z * 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 / Math.sin(y);
	double t_1 = (x * (1.0 / t_0)) / z;
	double tmp;
	if (z < -4.2173720203427147e-29) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x / (z * t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / math.sin(y)
	t_1 = (x * (1.0 / t_0)) / z
	tmp = 0
	if z < -4.2173720203427147e-29:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x / (z * t_0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / sin(y))
	t_1 = Float64(Float64(x * Float64(1.0 / t_0)) / z)
	tmp = 0.0
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x / Float64(z * t_0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / sin(y);
	t_1 = (x * (1.0 / t_0)) / z;
	tmp = 0.0;
	if (z < -4.2173720203427147e-29)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x / (z * t_0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[Less[z, -4.2173720203427147e-29], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x / N[(z * t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))