Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.2% → 97.6%

Time: 8.5s

Alternatives: 11

Speedup: 0.5×

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: 96.2% 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: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ t_1 := x \cdot t_0\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-296}:\\ \;\;\;\;\frac{t_1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)) (t_1 (* x t_0)))
   (if (<= t_1 -5e-296) (/ t_1 z) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double t_1 = x * t_0;
	double tmp;
	if (t_1 <= -5e-296) {
		tmp = t_1 / z;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sin(y) / y
    t_1 = x * t_0
    if (t_1 <= (-5d-296)) then
        tmp = t_1 / z
    else
        tmp = x / (z / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) / y;
	double t_1 = x * t_0;
	double tmp;
	if (t_1 <= -5e-296) {
		tmp = t_1 / z;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	t_1 = x * t_0
	tmp = 0
	if t_1 <= -5e-296:
		tmp = t_1 / z
	else:
		tmp = x / (z / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	t_1 = Float64(x * t_0)
	tmp = 0.0
	if (t_1 <= -5e-296)
		tmp = Float64(t_1 / z);
	else
		tmp = Float64(x / Float64(z / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) / y;
	t_1 = x * t_0;
	tmp = 0.0;
	if (t_1 <= -5e-296)
		tmp = t_1 / z;
	else
		tmp = x / (z / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(x * t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-296], N[(t$95$1 / z), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (/.f64 (sin.f64 y) y)) < -5.0000000000000003e-296

   1. Initial program 99.9%

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

   if -5.0000000000000003e-296 < (*.f64 x (/.f64 (sin.f64 y) y))

   1. Initial program 92.6%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \leq -5 \cdot 10^{-296}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array} \]

Alternative 2: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-8} \lor \neg \left(y \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e-8) (not (<= y 5e-9))) (* (sin y) (/ x (* y z))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e-8) || !(y <= 5e-9)) {
		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 <= (-2.5d-8)) .or. (.not. (y <= 5d-9))) 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 <= -2.5e-8) || !(y <= 5e-9)) {
		tmp = Math.sin(y) * (x / (y * z));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e-8) or not (y <= 5e-9):
		tmp = math.sin(y) * (x / (y * z))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e-8) || !(y <= 5e-9))
		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 <= -2.5e-8) || ~((y <= 5e-9)))
		tmp = sin(y) * (x / (y * z));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e-8], N[Not[LessEqual[y, 5e-9]], $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 < -2.4999999999999999e-8 or 5.0000000000000001e-9 < y

   1. Initial program 91.6%

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

      1. associate-*l/ 92.8%

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

      2. times-frac 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-*r/ 94.1%

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

      5. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   if -2.4999999999999999e-8 < y < 5.0000000000000001e-9

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   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 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-8} \lor \neg \left(y \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 3: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (sin(y) / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 4: 66.9% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -950000000:\\ \;\;\;\;\frac{6}{y \cdot z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 6}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -950000000.0)
   (* (/ 6.0 (* y z)) (/ x y))
   (if (<= y 3e+24)
     (/ x (/ z (+ 1.0 (* -0.16666666666666666 (* y y)))))
     (/ (* (/ x z) 6.0) (* y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -950000000.0) {
		tmp = (6.0 / (y * z)) * (x / y);
	} else if (y <= 3e+24) {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	} else {
		tmp = ((x / z) * 6.0) / (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 <= (-950000000.0d0)) then
        tmp = (6.0d0 / (y * z)) * (x / y)
    else if (y <= 3d+24) then
        tmp = x / (z / (1.0d0 + ((-0.16666666666666666d0) * (y * y))))
    else
        tmp = ((x / z) * 6.0d0) / (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -950000000.0) {
		tmp = (6.0 / (y * z)) * (x / y);
	} else if (y <= 3e+24) {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	} else {
		tmp = ((x / z) * 6.0) / (y * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -950000000.0:
		tmp = (6.0 / (y * z)) * (x / y)
	elif y <= 3e+24:
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))))
	else:
		tmp = ((x / z) * 6.0) / (y * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -950000000.0)
		tmp = Float64(Float64(6.0 / Float64(y * z)) * Float64(x / y));
	elseif (y <= 3e+24)
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))));
	else
		tmp = Float64(Float64(Float64(x / z) * 6.0) / Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -950000000.0)
		tmp = (6.0 / (y * z)) * (x / y);
	elseif (y <= 3e+24)
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	else
		tmp = ((x / z) * 6.0) / (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -950000000.0], N[(N[(6.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+24], N[(x / N[(z / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / z), $MachinePrecision] * 6.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5e8

   1. Initial program 90.0%

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

      1. associate-/l* 93.3%

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

      2. associate-/r/ 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around 0 29.0%

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

   5. Taylor expanded in y around inf 29.0%

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

      1. unpow2 29.0%

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

      2. *-commutative 29.0%

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

   7. Simplified 29.0%

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

      1. *-un-lft-identity 29.0%

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

      2. times-frac 29.0%

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

      3. metadata-eval 29.0%

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

      4. associate-*r/ 29.0%

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

      5. associate-*r* 29.0%

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

      6. times-frac 29.1%

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

      7. *-commutative 29.1%

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

   9. Applied egg-rr 29.1%

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

   if -9.5e8 < y < 2.99999999999999995e24

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.4%

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

      1. unpow2 97.4%

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

   6. Simplified 97.4%

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

   if 2.99999999999999995e24 < y

   1. Initial program 92.4%

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

      1. associate-/l* 94.2%

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

      2. associate-/r/ 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around 0 24.7%

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

   5. Taylor expanded in y around inf 24.7%

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

      1. unpow2 24.7%

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

      2. *-commutative 24.7%

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

   7. Simplified 24.7%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 24.7%

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

      2. associate-/r* 29.3%

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

      3. associate-*l/ 29.3%

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

   9. Applied egg-rr 29.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -950000000:\\ \;\;\;\;\frac{6}{y \cdot z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 6}{y \cdot y}\\ \end{array} \]

Alternative 5: 66.7% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45:\\ \;\;\;\;\frac{6}{y \cdot z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.45:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 6}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.45)
   (* (/ 6.0 (* y z)) (/ x y))
   (if (<= y 2.45) (/ x z) (/ (* (/ x z) 6.0) (* y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.45) {
		tmp = (6.0 / (y * z)) * (x / y);
	} else if (y <= 2.45) {
		tmp = x / z;
	} else {
		tmp = ((x / z) * 6.0) / (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 <= (-2.45d0)) then
        tmp = (6.0d0 / (y * z)) * (x / y)
    else if (y <= 2.45d0) then
        tmp = x / z
    else
        tmp = ((x / z) * 6.0d0) / (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.45) {
		tmp = (6.0 / (y * z)) * (x / y);
	} else if (y <= 2.45) {
		tmp = x / z;
	} else {
		tmp = ((x / z) * 6.0) / (y * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.45:
		tmp = (6.0 / (y * z)) * (x / y)
	elif y <= 2.45:
		tmp = x / z
	else:
		tmp = ((x / z) * 6.0) / (y * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.45)
		tmp = Float64(Float64(6.0 / Float64(y * z)) * Float64(x / y));
	elseif (y <= 2.45)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(Float64(x / z) * 6.0) / Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.45)
		tmp = (6.0 / (y * z)) * (x / y);
	elseif (y <= 2.45)
		tmp = x / z;
	else
		tmp = ((x / z) * 6.0) / (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.45], N[(N[(6.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45], N[(x / z), $MachinePrecision], N[(N[(N[(x / z), $MachinePrecision] * 6.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000002

   1. Initial program 90.3%

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

      1. associate-/l* 93.5%

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

      2. associate-/r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 28.2%

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

   5. Taylor expanded in y around inf 28.2%

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

      1. unpow2 28.2%

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

      2. *-commutative 28.2%

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

   7. Simplified 28.2%

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

      1. *-un-lft-identity 28.2%

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

      2. times-frac 28.2%

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

      3. metadata-eval 28.2%

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

      4. associate-*r/ 28.2%

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

      5. associate-*r* 28.2%

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

      6. times-frac 28.2%

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

      7. *-commutative 28.2%

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

   9. Applied egg-rr 28.2%

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

   if -2.4500000000000002 < y < 2.4500000000000002

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.6%

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

   if 2.4500000000000002 < y

   1. Initial program 92.6%

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

      1. associate-/l* 94.3%

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

      2. associate-/r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 23.9%

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

   5. Taylor expanded in y around inf 23.9%

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

      1. unpow2 23.9%

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

      2. *-commutative 23.9%

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

   7. Simplified 23.9%

      \[\leadsto \color{blue}{6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 23.9%

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

      2. associate-/r* 28.3%

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

      3. associate-*l/ 28.3%

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

   9. Applied egg-rr 28.3%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45:\\ \;\;\;\;\frac{6}{y \cdot z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.45:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 6}{y \cdot y}\\ \end{array} \]

Alternative 6: 66.3% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+82} \lor \neg \left(y \leq 3.65 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+82) (not (<= y 3.65e-6))) (* y (/ x (* y z))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+82) || !(y <= 3.65e-6)) {
		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 <= (-1.1d+82)) .or. (.not. (y <= 3.65d-6))) 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 <= -1.1e+82) || !(y <= 3.65e-6)) {
		tmp = y * (x / (y * z));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+82) or not (y <= 3.65e-6):
		tmp = y * (x / (y * z))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+82) || !(y <= 3.65e-6))
		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 <= -1.1e+82) || ~((y <= 3.65e-6)))
		tmp = y * (x / (y * z));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+82], N[Not[LessEqual[y, 3.65e-6]], $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 < -1.1000000000000001e82 or 3.65000000000000021e-6 < y

   1. Initial program 91.3%

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

      1. associate-*l/ 93.6%

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

      2. times-frac 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-*r/ 93.3%

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

      5. *-commutative 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around 0 31.1%

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

   if -1.1000000000000001e82 < y < 3.65000000000000021e-6

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 90.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+82} \lor \neg \left(y \leq 3.65 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 7: 66.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+29)
   (* y (/ (/ x y) z))
   (if (<= y 1.12e-5) (/ x z) (* y (/ x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+29) {
		tmp = y * ((x / y) / z);
	} else if (y <= 1.12e-5) {
		tmp = x / z;
	} else {
		tmp = 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 <= (-2d+29)) then
        tmp = y * ((x / y) / z)
    else if (y <= 1.12d-5) then
        tmp = x / z
    else
        tmp = 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 <= -2e+29) {
		tmp = y * ((x / y) / z);
	} else if (y <= 1.12e-5) {
		tmp = x / z;
	} else {
		tmp = y * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+29:
		tmp = y * ((x / y) / z)
	elif y <= 1.12e-5:
		tmp = x / z
	else:
		tmp = y * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+29)
		tmp = Float64(y * Float64(Float64(x / y) / z));
	elseif (y <= 1.12e-5)
		tmp = Float64(x / z);
	else
		tmp = Float64(y * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+29)
		tmp = y * ((x / y) / z);
	elseif (y <= 1.12e-5)
		tmp = x / z;
	else
		tmp = y * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+29], N[(y * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e-5], N[(x / z), $MachinePrecision], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999983e29

   1. Initial program 89.5%

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

      1. associate-*l/ 92.8%

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

      2. times-frac 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*r/ 93.0%

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

      5. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around 0 29.6%

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

      1. expm1-log1p-u 27.1%

         \[\leadsto y \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)\right)} \]

      2. expm1-udef 27.7%

         \[\leadsto y \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)} - 1\right)} \]

      3. associate-/r* 27.7%

         \[\leadsto y \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{\frac{x}{y}}{z}}\right)} - 1\right) \]

   6. Applied egg-rr 27.7%

      \[\leadsto y \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\frac{x}{y}}{z}\right)} - 1\right)} \]
   7. Step-by-step derivation

      1. expm1-def 27.1%

         \[\leadsto y \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{x}{y}}{z}\right)\right)} \]

      2. expm1-log1p 29.6%

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

   8. Simplified 29.6%

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

   if -1.99999999999999983e29 < y < 1.11999999999999995e-5

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.3%

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

   if 1.11999999999999995e-5 < y

   1. Initial program 92.7%

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

      1. associate-*l/ 92.2%

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

      2. times-frac 94.5%

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

      3. *-commutative 94.5%

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

      4. associate-*r/ 94.6%

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

      5. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 28.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 8: 66.6% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+29)
   (/ y (* z (/ y x)))
   (if (<= y 4.9e-5) (/ x z) (* y (/ x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+29) {
		tmp = y / (z * (y / x));
	} else if (y <= 4.9e-5) {
		tmp = x / z;
	} else {
		tmp = 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 <= (-2d+29)) then
        tmp = y / (z * (y / x))
    else if (y <= 4.9d-5) then
        tmp = x / z
    else
        tmp = 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 <= -2e+29) {
		tmp = y / (z * (y / x));
	} else if (y <= 4.9e-5) {
		tmp = x / z;
	} else {
		tmp = y * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+29:
		tmp = y / (z * (y / x))
	elif y <= 4.9e-5:
		tmp = x / z
	else:
		tmp = y * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+29)
		tmp = Float64(y / Float64(z * Float64(y / x)));
	elseif (y <= 4.9e-5)
		tmp = Float64(x / z);
	else
		tmp = Float64(y * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+29)
		tmp = y / (z * (y / x));
	elseif (y <= 4.9e-5)
		tmp = x / z;
	else
		tmp = y * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+29], N[(y / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-5], N[(x / z), $MachinePrecision], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999983e29

   1. Initial program 89.5%

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

      1. associate-*r/ 89.3%

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

      2. associate-/l/ 93.0%

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

      3. *-commutative 93.0%

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

      4. times-frac 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in y around 0 20.7%

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

      1. *-commutative 20.7%

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

      2. clear-num 20.8%

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

      3. frac-times 29.7%

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

      4. *-un-lft-identity 29.7%

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

   6. Applied egg-rr 29.7%

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

   if -1.99999999999999983e29 < y < 4.9e-5

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 96.3%

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

   if 4.9e-5 < y

   1. Initial program 92.7%

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

      1. associate-*l/ 92.2%

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

      2. times-frac 94.5%

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

      3. *-commutative 94.5%

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

      4. associate-*r/ 94.6%

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

      5. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 28.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 9: 66.6% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.45)
   (* 6.0 (/ x (* z (* y y))))
   (if (<= y 2.35e-8) (/ x z) (* y (/ x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.45) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 2.35e-8) {
		tmp = x / z;
	} else {
		tmp = 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 <= (-2.45d0)) then
        tmp = 6.0d0 * (x / (z * (y * y)))
    else if (y <= 2.35d-8) then
        tmp = x / z
    else
        tmp = 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 <= -2.45) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 2.35e-8) {
		tmp = x / z;
	} else {
		tmp = y * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.45:
		tmp = 6.0 * (x / (z * (y * y)))
	elif y <= 2.35e-8:
		tmp = x / z
	else:
		tmp = y * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.45)
		tmp = Float64(6.0 * Float64(x / Float64(z * Float64(y * y))));
	elseif (y <= 2.35e-8)
		tmp = Float64(x / z);
	else
		tmp = Float64(y * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.45)
		tmp = 6.0 * (x / (z * (y * y)));
	elseif (y <= 2.35e-8)
		tmp = x / z;
	else
		tmp = y * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.45], N[(6.0 * N[(x / N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e-8], N[(x / z), $MachinePrecision], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000002

   1. Initial program 90.3%

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

      1. associate-/l* 93.5%

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

      2. associate-/r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 28.2%

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

   5. Taylor expanded in y around inf 28.2%

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

      1. unpow2 28.2%

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

      2. *-commutative 28.2%

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

   7. Simplified 28.2%

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

   if -2.4500000000000002 < y < 2.3499999999999999e-8

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   if 2.3499999999999999e-8 < y

   1. Initial program 92.8%

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

      1. associate-*l/ 92.3%

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

      2. times-frac 94.6%

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

      3. *-commutative 94.6%

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

      4. associate-*r/ 94.6%

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

      5. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 29.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 10: 66.6% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45:\\ \;\;\;\;\frac{6}{y \cdot z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.45)
   (* (/ 6.0 (* y z)) (/ x y))
   (if (<= y 4e-8) (/ x z) (* y (/ x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.45) {
		tmp = (6.0 / (y * z)) * (x / y);
	} else if (y <= 4e-8) {
		tmp = x / z;
	} else {
		tmp = 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 <= (-2.45d0)) then
        tmp = (6.0d0 / (y * z)) * (x / y)
    else if (y <= 4d-8) then
        tmp = x / z
    else
        tmp = 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 <= -2.45) {
		tmp = (6.0 / (y * z)) * (x / y);
	} else if (y <= 4e-8) {
		tmp = x / z;
	} else {
		tmp = y * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.45:
		tmp = (6.0 / (y * z)) * (x / y)
	elif y <= 4e-8:
		tmp = x / z
	else:
		tmp = y * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.45)
		tmp = Float64(Float64(6.0 / Float64(y * z)) * Float64(x / y));
	elseif (y <= 4e-8)
		tmp = Float64(x / z);
	else
		tmp = Float64(y * Float64(x / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.45)
		tmp = (6.0 / (y * z)) * (x / y);
	elseif (y <= 4e-8)
		tmp = x / z;
	else
		tmp = y * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.45], N[(N[(6.0 / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-8], N[(x / z), $MachinePrecision], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4500000000000002

   1. Initial program 90.3%

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

      1. associate-/l* 93.5%

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

      2. associate-/r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 28.2%

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

   5. Taylor expanded in y around inf 28.2%

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

      1. unpow2 28.2%

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

      2. *-commutative 28.2%

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

   7. Simplified 28.2%

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

      1. *-un-lft-identity 28.2%

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

      2. times-frac 28.2%

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

      3. metadata-eval 28.2%

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

      4. associate-*r/ 28.2%

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

      5. associate-*r* 28.2%

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

      6. times-frac 28.2%

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

      7. *-commutative 28.2%

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

   9. Applied egg-rr 28.2%

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

   if -2.4500000000000002 < y < 4.0000000000000001e-8

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   if 4.0000000000000001e-8 < y

   1. Initial program 92.8%

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

      1. associate-*l/ 92.3%

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

      2. times-frac 94.6%

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

      3. *-commutative 94.6%

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

      4. associate-*r/ 94.6%

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

      5. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 29.4%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45:\\ \;\;\;\;\frac{6}{y \cdot z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 11: 58.9% 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 95.9%

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

   1. associate-/l* 97.1%

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

3. Simplified 97.1%

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

4. Taylor expanded in y around 0 60.4%

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

5. Final simplification 60.4%

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

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 2023174 
(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))