Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.0% → 97.5%

Time: 9.0s

Alternatives: 10

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: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0052:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0052) (* (/ (sin y) y) (/ x z)) (/ x (* z (/ y (sin y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0052) {
		tmp = (sin(y) / y) * (x / z);
	} else {
		tmp = x / (z * (y / sin(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 (z <= (-0.0052d0)) then
        tmp = (sin(y) / y) * (x / z)
    else
        tmp = x / (z * (y / sin(y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0052) {
		tmp = (Math.sin(y) / y) * (x / z);
	} else {
		tmp = x / (z * (y / Math.sin(y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0052:
		tmp = (math.sin(y) / y) * (x / z)
	else:
		tmp = x / (z * (y / math.sin(y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0052)
		tmp = Float64(Float64(sin(y) / y) * Float64(x / z));
	else
		tmp = Float64(x / Float64(z * Float64(y / sin(y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0052)
		tmp = (sin(y) / y) * (x / z);
	else
		tmp = x / (z * (y / sin(y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0052], N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0051999999999999998

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   if -0.0051999999999999998 < z

   1. Initial program 96.3%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

      1. div-inv 97.9%

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

      2. *-commutative 97.9%

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

      3. clear-num 97.9%

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

   5. Applied egg-rr 97.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0052:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array} \]

Alternative 2: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.6e-8) (/ x z) (* (sin y) (/ x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e-8) {
		tmp = x / z;
	} else {
		tmp = sin(y) * (x / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.6d-8) then
        tmp = x / z
    else
        tmp = sin(y) * (x / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.6e-8) {
		tmp = x / z;
	} else {
		tmp = Math.sin(y) * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.6e-8:
		tmp = x / z
	else:
		tmp = math.sin(y) * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.6e-8)
		tmp = Float64(x / z);
	else
		tmp = Float64(sin(y) * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.6e-8)
		tmp = x / z;
	else
		tmp = sin(y) * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.6e-8], N[(x / z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6000000000000001e-8

   1. Initial program 98.9%

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

      1. associate-*r/ 87.0%

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

      2. associate-/l/ 78.6%

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

      3. associate-/l* 83.6%

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

      4. associate-/r/ 77.3%

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

      5. *-commutative 77.3%

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

      6. *-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 74.3%

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

   if 1.6000000000000001e-8 < y

   1. Initial program 91.7%

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

      1. associate-*r/ 91.8%

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

      2. associate-/l/ 91.9%

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

      3. associate-/l* 91.8%

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

      4. associate-/r/ 91.9%

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

      5. *-commutative 91.9%

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

      6. *-commutative 91.9%

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

   3. Simplified 91.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 3: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. associate-*r/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 4: 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 97.2%

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

2. Final simplification 97.2%

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

Alternative 5: 61.3% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{y \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.8e+85) (/ x z) (* y (* x (/ 1.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.8e+85) {
		tmp = x / z;
	} else {
		tmp = y * (x * (1.0 / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.8d+85) then
        tmp = x / z
    else
        tmp = y * (x * (1.0d0 / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.8e+85) {
		tmp = x / z;
	} else {
		tmp = y * (x * (1.0 / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.8e+85:
		tmp = x / z
	else:
		tmp = y * (x * (1.0 / (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.8e+85)
		tmp = Float64(x / z);
	else
		tmp = Float64(y * Float64(x * Float64(1.0 / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.8e+85)
		tmp = x / z;
	else
		tmp = y * (x * (1.0 / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.8e+85], N[(x / z), $MachinePrecision], N[(y * N[(x * N[(1.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7999999999999999e85

   1. Initial program 98.9%

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

      1. associate-*r/ 88.0%

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

      2. associate-/l/ 79.5%

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

      3. associate-/l* 84.1%

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

      4. associate-/r/ 78.3%

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

      5. *-commutative 78.3%

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

      6. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in y around 0 69.9%

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

   if 1.7999999999999999e85 < y

   1. Initial program 88.5%

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

      1. associate-*r/ 88.6%

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

      2. associate-/l/ 93.0%

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

      3. associate-/l* 93.0%

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

      4. associate-/r/ 93.1%

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

      5. *-commutative 93.1%

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

      6. *-commutative 93.1%

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

   3. Simplified 93.1%

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

      1. associate-*r/ 93.0%

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

      2. frac-times 90.8%

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

      3. associate-*l/ 90.8%

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

   5. Applied egg-rr 90.8%

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

   6. Taylor expanded in y around 0 16.6%

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

      1. associate-/l* 16.4%

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

      2. associate-/r/ 16.8%

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

   8. Simplified 16.8%

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

      1. *-commutative 16.8%

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

      2. clear-num 16.8%

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

      3. un-div-inv 16.8%

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

   10. Applied egg-rr 16.8%

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

       1. associate-/r/ 16.4%

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

       2. associate-*r/ 20.6%

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

       3. times-frac 23.4%

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

       4. *-commutative 23.4%

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

       5. un-div-inv 23.4%

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

       6. *-commutative 23.4%

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

       7. associate-*r* 32.6%

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

   12. Applied egg-rr 32.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{y \cdot z}\right)\\ \end{array} \]

Alternative 6: 58.6% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.2e+132) (/ x z) (* (/ x y) (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.2e+132) {
		tmp = x / z;
	} else {
		tmp = (x / y) * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.2d+132) then
        tmp = x / z
    else
        tmp = (x / y) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.2e+132) {
		tmp = x / z;
	} else {
		tmp = (x / y) * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.2e+132:
		tmp = x / z
	else:
		tmp = (x / y) * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.2e+132)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x / y) * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.2e+132)
		tmp = x / z;
	else
		tmp = (x / y) * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.2e+132], N[(x / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2000000000000001e132

   1. Initial program 98.1%

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

      1. associate-*r/ 87.6%

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

      2. associate-/l/ 80.2%

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

      3. associate-/l* 84.7%

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

      4. associate-/r/ 79.0%

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

      5. *-commutative 79.0%

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

      6. *-commutative 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in y around 0 67.9%

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

   if 1.2000000000000001e132 < y

   1. Initial program 91.5%

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

      1. associate-*r/ 91.6%

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

      2. associate-/l/ 91.5%

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

      3. associate-/l* 91.5%

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

      4. associate-/r/ 91.6%

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

      5. *-commutative 91.6%

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

      6. *-commutative 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 91.5%

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

      2. frac-times 88.8%

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

      3. associate-*l/ 88.7%

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

   5. Applied egg-rr 88.7%

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

   6. Taylor expanded in y around 0 16.8%

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

      1. associate-/l* 16.7%

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

      2. associate-/r/ 17.0%

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

   8. Simplified 17.0%

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

      1. associate-*l/ 16.8%

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

      2. associate-/l/ 25.1%

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

      3. times-frac 21.9%

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

   10. Applied egg-rr 21.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{y}{z}\\ \end{array} \]

Alternative 7: 59.7% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+115}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1e+115) (/ x z) (* x (/ y (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e+115) {
		tmp = x / z;
	} else {
		tmp = x * (y / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1d+115) then
        tmp = x / z
    else
        tmp = x * (y / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e+115) {
		tmp = x / z;
	} else {
		tmp = x * (y / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1e+115:
		tmp = x / z
	else:
		tmp = x * (y / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1e+115)
		tmp = Float64(x / z);
	else
		tmp = Float64(x * Float64(y / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1e+115)
		tmp = x / z;
	else
		tmp = x * (y / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1e+115], N[(x / z), $MachinePrecision], N[(x * N[(y / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1e115

   1. Initial program 98.9%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l/ 79.7%

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

      3. associate-/l* 84.2%

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

      4. associate-/r/ 78.5%

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

      5. *-commutative 78.5%

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

      6. *-commutative 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in y around 0 69.3%

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

   if 1e115 < y

   1. Initial program 88.0%

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

      1. associate-*r/ 88.0%

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

      2. associate-/l/ 92.6%

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

      3. associate-/l* 92.7%

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

      4. associate-/r/ 92.8%

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

      5. *-commutative 92.8%

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

      6. *-commutative 92.8%

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

   3. Simplified 92.8%

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

      1. associate-*r/ 92.6%

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

      2. frac-times 90.4%

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

      3. associate-*l/ 90.4%

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

   5. Applied egg-rr 90.4%

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

   6. Taylor expanded in y around 0 17.3%

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

      1. associate-/l* 17.1%

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

      2. associate-/r/ 17.4%

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

   8. Simplified 17.4%

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

      1. *-commutative 17.4%

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

      2. clear-num 17.4%

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

      3. un-div-inv 17.4%

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

   10. Applied egg-rr 17.4%

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

       1. associate-/r/ 17.1%

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

       2. associate-*r/ 21.4%

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

       3. times-frac 24.3%

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

       4. *-commutative 24.3%

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

       5. un-div-inv 24.3%

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

       6. associate-*l* 24.7%

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

       7. *-commutative 24.7%

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

       8. un-div-inv 24.7%

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

   12. Applied egg-rr 24.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+115}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y \cdot z}\\ \end{array} \]

Alternative 8: 61.3% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2e+18) (/ x z) (* y (/ (/ x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2e+18) {
		tmp = x / z;
	} else {
		tmp = y * ((x / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2d+18) then
        tmp = x / z
    else
        tmp = y * ((x / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2e+18) {
		tmp = x / z;
	} else {
		tmp = y * ((x / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2e+18:
		tmp = x / z
	else:
		tmp = y * ((x / z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2e+18)
		tmp = Float64(x / z);
	else
		tmp = Float64(y * Float64(Float64(x / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2e+18)
		tmp = x / z;
	else
		tmp = y * ((x / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2e+18], N[(x / z), $MachinePrecision], N[(y * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2e18

   1. Initial program 98.9%

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

      1. associate-*r/ 87.3%

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

      2. associate-/l/ 79.2%

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

      3. associate-/l* 84.1%

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

      4. associate-/r/ 77.9%

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

      5. *-commutative 77.9%

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

      6. *-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 73.3%

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

   if 2e18 < y

   1. Initial program 90.9%

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

      1. associate-*r/ 90.9%

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

      2. associate-/l/ 91.0%

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

      3. associate-/l* 91.0%

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

      4. associate-/r/ 91.1%

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

      5. *-commutative 91.1%

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

      6. *-commutative 91.1%

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

   3. Simplified 91.1%

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

      1. associate-*r/ 91.0%

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

      2. frac-times 92.6%

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

      3. associate-*l/ 92.7%

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

   5. Applied egg-rr 92.7%

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

   6. Taylor expanded in y around 0 15.9%

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

      1. associate-/l* 15.7%

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

      2. associate-/r/ 16.0%

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

   8. Simplified 16.0%

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

      1. associate-/l* 16.1%

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

      2. associate-/r/ 28.2%

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

   10. Applied egg-rr 28.2%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 9: 61.6% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 400.0) (/ x z) (/ y (* z (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 400.0) {
		tmp = x / z;
	} else {
		tmp = y / (z * (y / 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 (y <= 400.0d0) then
        tmp = x / z
    else
        tmp = y / (z * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 400.0) {
		tmp = x / z;
	} else {
		tmp = y / (z * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 400.0:
		tmp = x / z
	else:
		tmp = y / (z * (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 400.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(y / Float64(z * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 400.0)
		tmp = x / z;
	else
		tmp = y / (z * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 400.0], N[(x / z), $MachinePrecision], N[(y / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 400

   1. Initial program 98.9%

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

      1. associate-*r/ 87.2%

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

      2. associate-/l/ 79.0%

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

      3. associate-/l* 84.0%

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

      4. associate-/r/ 77.7%

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

      5. *-commutative 77.7%

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

      6. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in y around 0 73.4%

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

   if 400 < y

   1. Initial program 91.2%

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

      1. associate-*r/ 91.2%

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

      2. associate-/l/ 91.3%

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

      3. associate-/l* 91.3%

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

      4. associate-/r/ 91.4%

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

      5. *-commutative 91.4%

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

      6. *-commutative 91.4%

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

   3. Simplified 91.4%

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

      1. associate-*r/ 91.3%

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

      2. frac-times 92.9%

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

      3. associate-*l/ 93.0%

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

   5. Applied egg-rr 93.0%

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

   6. Taylor expanded in y around 0 17.3%

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

      1. associate-/l* 17.1%

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

      2. associate-/r/ 17.4%

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

   8. Simplified 17.4%

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

      1. associate-*l/ 17.3%

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

      2. associate-/l/ 22.3%

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

      3. times-frac 20.3%

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

   10. Applied egg-rr 20.3%

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

       1. clear-num 20.3%

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

       2. frac-times 29.3%

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

       3. *-un-lft-identity 29.3%

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

   12. Applied egg-rr 29.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 400:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 10: 57.5% 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 97.2%

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

   1. associate-*r/ 88.1%

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

   2. associate-/l/ 81.7%

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

   3. associate-/l* 85.6%

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

   4. associate-/r/ 80.8%

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

   5. *-commutative 80.8%

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

   6. *-commutative 80.8%

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

3. Simplified 80.8%

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

4. Taylor expanded in y around 0 61.0%

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

5. Final simplification 61.0%

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

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 2023301 
(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))