Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.1% → 96.3%

Time: 8.2s

Alternatives: 12

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: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-184}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (<= t_0 5e-184) (* (/ (sin y) z) (/ x y)) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if (t_0 <= 5e-184) {
		tmp = (sin(y) / z) * (x / y);
	} 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) :: tmp
    t_0 = sin(y) / y
    if (t_0 <= 5d-184) then
        tmp = (sin(y) / z) * (x / y)
    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 tmp;
	if (t_0 <= 5e-184) {
		tmp = (Math.sin(y) / z) * (x / y);
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if t_0 <= 5e-184:
		tmp = (math.sin(y) / z) * (x / y)
	else:
		tmp = x / (z / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (t_0 <= 5e-184)
		tmp = Float64(Float64(sin(y) / z) * Float64(x / y));
	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;
	tmp = 0.0;
	if (t_0 <= 5e-184)
		tmp = (sin(y) / z) * (x / y);
	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]}, If[LessEqual[t$95$0, 5e-184], N[(N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (sin.f64 y) y) < 5.00000000000000003e-184

   1. Initial program 96.6%

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

      1. associate-*r/ 96.6%

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

      2. associate-/l/ 91.3%

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

      3. *-commutative 91.3%

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

      4. times-frac 96.6%

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

   3. Simplified 96.6%

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

   if 5.00000000000000003e-184 < (/.f64 (sin.f64 y) y)

   1. Initial program 98.7%

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

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \leq 5 \cdot 10^{-184}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array} \]

Alternative 2: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0004 \lor \neg \left(y \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0004) (not (<= y 5e-5)))
   (* (sin y) (/ x (* y z)))
   (/ (* x (+ 1.0 (* -0.16666666666666666 (* y y)))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0004) || !(y <= 5e-5)) {
		tmp = sin(y) * (x / (y * z));
	} else {
		tmp = (x * (1.0 + (-0.16666666666666666 * (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 <= (-0.0004d0)) .or. (.not. (y <= 5d-5))) then
        tmp = sin(y) * (x / (y * z))
    else
        tmp = (x * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0004) || !(y <= 5e-5)) {
		tmp = Math.sin(y) * (x / (y * z));
	} else {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0004) or not (y <= 5e-5):
		tmp = math.sin(y) * (x / (y * z))
	else:
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0004) || !(y <= 5e-5))
		tmp = Float64(sin(y) * Float64(x / Float64(y * z)));
	else
		tmp = Float64(Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0004) || ~((y <= 5e-5)))
		tmp = sin(y) * (x / (y * z));
	else
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0004], N[Not[LessEqual[y, 5e-5]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000019e-4 or 5.00000000000000024e-5 < y

   1. Initial program 96.2%

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

      1. associate-*l/ 87.6%

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

      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 -4.00000000000000019e-4 < y < 5.00000000000000024e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0004 \lor \neg \left(y \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \end{array} \]

Alternative 3: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-8} \lor \neg \left(y \leq 2.45 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e-8) (not (<= y 2.45e-8))) (* (/ (sin y) z) (/ x y)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-8) || !(y <= 2.45e-8)) {
		tmp = (sin(y) / z) * (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5d-8)) .or. (.not. (y <= 2.45d-8))) then
        tmp = (sin(y) / z) * (x / y)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-8) || !(y <= 2.45e-8)) {
		tmp = (Math.sin(y) / z) * (x / y);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e-8) or not (y <= 2.45e-8):
		tmp = (math.sin(y) / z) * (x / y)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e-8) || !(y <= 2.45e-8))
		tmp = Float64(Float64(sin(y) / z) * Float64(x / y));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e-8) || ~((y <= 2.45e-8)))
		tmp = (sin(y) / z) * (x / y);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e-8], N[Not[LessEqual[y, 2.45e-8]], $MachinePrecision]], N[(N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999998e-8 or 2.4500000000000001e-8 < y

   1. Initial program 96.2%

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

      1. associate-*r/ 96.2%

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

      2. associate-/l/ 94.1%

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

      3. *-commutative 94.1%

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

      4. times-frac 96.2%

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

   3. Simplified 96.2%

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

   if -4.9999999999999998e-8 < y < 2.4500000000000001e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-8} \lor \neg \left(y \leq 2.45 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 4: 96.1% 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 97.9%

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

2. Final simplification 97.9%

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

Alternative 5: 67.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot 0.16666666666666666\right)\\ \mathbf{if}\;y \leq -12.5:\\ \;\;\;\;\frac{1}{y \cdot \frac{t_0}{x}}\\ \mathbf{elif}\;y \leq 390000000:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t_0}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z 0.16666666666666666))))
   (if (<= y -12.5)
     (/ 1.0 (* y (/ t_0 x)))
     (if (<= y 390000000.0)
       (/ x (/ z (+ 1.0 (* -0.16666666666666666 (* y y)))))
       (/ (/ x t_0) y)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * 0.16666666666666666);
	double tmp;
	if (y <= -12.5) {
		tmp = 1.0 / (y * (t_0 / x));
	} else if (y <= 390000000.0) {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	} else {
		tmp = (x / t_0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * 0.16666666666666666d0)
    if (y <= (-12.5d0)) then
        tmp = 1.0d0 / (y * (t_0 / x))
    else if (y <= 390000000.0d0) then
        tmp = x / (z / (1.0d0 + ((-0.16666666666666666d0) * (y * y))))
    else
        tmp = (x / t_0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * 0.16666666666666666);
	double tmp;
	if (y <= -12.5) {
		tmp = 1.0 / (y * (t_0 / x));
	} else if (y <= 390000000.0) {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	} else {
		tmp = (x / t_0) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * 0.16666666666666666)
	tmp = 0
	if y <= -12.5:
		tmp = 1.0 / (y * (t_0 / x))
	elif y <= 390000000.0:
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))))
	else:
		tmp = (x / t_0) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * 0.16666666666666666))
	tmp = 0.0
	if (y <= -12.5)
		tmp = Float64(1.0 / Float64(y * Float64(t_0 / x)));
	elseif (y <= 390000000.0)
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))));
	else
		tmp = Float64(Float64(x / t_0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * 0.16666666666666666);
	tmp = 0.0;
	if (y <= -12.5)
		tmp = 1.0 / (y * (t_0 / x));
	elseif (y <= 390000000.0)
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	else
		tmp = (x / t_0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -12.5], N[(1.0 / N[(y * N[(t$95$0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 390000000.0], N[(x / N[(z / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t$95$0), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -12.5

   1. Initial program 96.3%

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

      1. associate-/l* 93.0%

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

      2. associate-/r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 30.1%

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

   5. Taylor expanded in y around inf 30.1%

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

      1. associate-*r/ 30.1%

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

      2. *-commutative 30.1%

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

      3. times-frac 30.1%

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

      4. unpow2 30.1%

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

      5. associate-/r* 30.1%

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

   7. Simplified 30.1%

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

      1. associate-*r/ 30.1%

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

      2. div-inv 30.1%

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

      3. associate-*l* 30.1%

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

      4. metadata-eval 30.1%

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

      5. times-frac 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 30.2%

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

      9. *-un-lft-identity 30.2%

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

      10. *-commutative 30.2%

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

      11. associate-/r* 30.1%

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

      12. clear-num 30.1%

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

      13. *-commutative 30.1%

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

      14. *-un-lft-identity 30.1%

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

      15. times-frac 30.2%

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

      16. /-rgt-identity 30.2%

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

      17. associate-*l* 30.2%

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

   9. Applied egg-rr 30.2%

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

   if -12.5 < y < 3.9e8

   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 98.5%

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

      1. unpow2 98.5%

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

   6. Simplified 98.5%

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

   if 3.9e8 < y

   1. Initial program 96.0%

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

      1. associate-/l* 94.6%

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

      2. associate-/r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 35.7%

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

   5. Taylor expanded in y around inf 35.6%

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

      1. associate-*r/ 35.6%

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

      2. *-commutative 35.6%

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

      3. times-frac 35.5%

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

      4. unpow2 35.5%

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

      5. associate-/r* 35.6%

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

   7. Simplified 35.6%

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

      1. associate-*r/ 38.0%

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

      2. div-inv 38.0%

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

      3. associate-*l* 38.0%

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

      4. metadata-eval 38.0%

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

      5. times-frac 38.0%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 38.0%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 38.0%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 38.0%

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

      9. *-un-lft-identity 38.0%

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

      10. *-commutative 38.0%

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

      11. associate-*l* 38.0%

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

   9. Applied egg-rr 38.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12.5:\\ \;\;\;\;\frac{1}{y \cdot \frac{y \cdot \left(z \cdot 0.16666666666666666\right)}{x}}\\ \mathbf{elif}\;y \leq 390000000:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}\\ \end{array} \]

Alternative 6: 67.2% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot 0.16666666666666666\right)\\ \mathbf{if}\;y \leq -12.5:\\ \;\;\;\;\frac{1}{y \cdot \frac{t_0}{x}}\\ \mathbf{elif}\;y \leq 390000000:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t_0}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z 0.16666666666666666))))
   (if (<= y -12.5)
     (/ 1.0 (* y (/ t_0 x)))
     (if (<= y 390000000.0)
       (/ (* x (+ 1.0 (* -0.16666666666666666 (* y y)))) z)
       (/ (/ x t_0) y)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * 0.16666666666666666);
	double tmp;
	if (y <= -12.5) {
		tmp = 1.0 / (y * (t_0 / x));
	} else if (y <= 390000000.0) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = (x / t_0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * 0.16666666666666666d0)
    if (y <= (-12.5d0)) then
        tmp = 1.0d0 / (y * (t_0 / x))
    else if (y <= 390000000.0d0) then
        tmp = (x * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))) / z
    else
        tmp = (x / t_0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * 0.16666666666666666);
	double tmp;
	if (y <= -12.5) {
		tmp = 1.0 / (y * (t_0 / x));
	} else if (y <= 390000000.0) {
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	} else {
		tmp = (x / t_0) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * 0.16666666666666666)
	tmp = 0
	if y <= -12.5:
		tmp = 1.0 / (y * (t_0 / x))
	elif y <= 390000000.0:
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z
	else:
		tmp = (x / t_0) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * 0.16666666666666666))
	tmp = 0.0
	if (y <= -12.5)
		tmp = Float64(1.0 / Float64(y * Float64(t_0 / x)));
	elseif (y <= 390000000.0)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))) / z);
	else
		tmp = Float64(Float64(x / t_0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * 0.16666666666666666);
	tmp = 0.0;
	if (y <= -12.5)
		tmp = 1.0 / (y * (t_0 / x));
	elseif (y <= 390000000.0)
		tmp = (x * (1.0 + (-0.16666666666666666 * (y * y)))) / z;
	else
		tmp = (x / t_0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -12.5], N[(1.0 / N[(y * N[(t$95$0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 390000000.0], N[(N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t$95$0), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -12.5

   1. Initial program 96.3%

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

      1. associate-/l* 93.0%

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

      2. associate-/r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 30.1%

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

   5. Taylor expanded in y around inf 30.1%

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

      1. associate-*r/ 30.1%

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

      2. *-commutative 30.1%

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

      3. times-frac 30.1%

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

      4. unpow2 30.1%

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

      5. associate-/r* 30.1%

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

   7. Simplified 30.1%

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

      1. associate-*r/ 30.1%

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

      2. div-inv 30.1%

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

      3. associate-*l* 30.1%

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

      4. metadata-eval 30.1%

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

      5. times-frac 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 30.2%

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

      9. *-un-lft-identity 30.2%

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

      10. *-commutative 30.2%

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

      11. associate-/r* 30.1%

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

      12. clear-num 30.1%

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

      13. *-commutative 30.1%

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

      14. *-un-lft-identity 30.1%

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

      15. times-frac 30.2%

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

      16. /-rgt-identity 30.2%

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

      17. associate-*l* 30.2%

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

   9. Applied egg-rr 30.2%

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

   if -12.5 < y < 3.9e8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

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

      1. unpow2 98.5%

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

   4. Simplified 98.5%

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

   if 3.9e8 < y

   1. Initial program 96.0%

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

      1. associate-/l* 94.6%

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

      2. associate-/r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around 0 35.7%

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

   5. Taylor expanded in y around inf 35.6%

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

      1. associate-*r/ 35.6%

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

      2. *-commutative 35.6%

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

      3. times-frac 35.5%

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

      4. unpow2 35.5%

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

      5. associate-/r* 35.6%

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

   7. Simplified 35.6%

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

      1. associate-*r/ 38.0%

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

      2. div-inv 38.0%

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

      3. associate-*l* 38.0%

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

      4. metadata-eval 38.0%

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

      5. times-frac 38.0%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 38.0%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 38.0%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 38.0%

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

      9. *-un-lft-identity 38.0%

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

      10. *-commutative 38.0%

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

      11. associate-*l* 38.0%

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

   9. Applied egg-rr 38.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12.5:\\ \;\;\;\;\frac{1}{y \cdot \frac{y \cdot \left(z \cdot 0.16666666666666666\right)}{x}}\\ \mathbf{elif}\;y \leq 390000000:\\ \;\;\;\;\frac{x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}\\ \end{array} \]

Alternative 7: 67.2% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \lor \neg \left(y \leq 2.4\right):\\ \;\;\;\;\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4) (not (<= y 2.4)))
   (/ (/ x (* y (* z 0.16666666666666666))) y)
   (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4) || !(y <= 2.4)) {
		tmp = (x / (y * (z * 0.16666666666666666))) / y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.4d0)) .or. (.not. (y <= 2.4d0))) then
        tmp = (x / (y * (z * 0.16666666666666666d0))) / y
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4) || !(y <= 2.4)) {
		tmp = (x / (y * (z * 0.16666666666666666))) / y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4) or not (y <= 2.4):
		tmp = (x / (y * (z * 0.16666666666666666))) / y
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4) || !(y <= 2.4))
		tmp = Float64(Float64(x / Float64(y * Float64(z * 0.16666666666666666))) / y);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4) || ~((y <= 2.4)))
		tmp = (x / (y * (z * 0.16666666666666666))) / y;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4], N[Not[LessEqual[y, 2.4]], $MachinePrecision]], N[(N[(x / N[(y * N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999991 or 2.39999999999999991 < y

   1. Initial program 96.2%

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

      1. associate-/l* 94.1%

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

      2. associate-/r/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 32.7%

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

   5. Taylor expanded in y around inf 32.7%

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

      1. associate-*r/ 32.7%

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

      2. *-commutative 32.7%

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

      3. times-frac 32.6%

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

      4. unpow2 32.6%

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

      5. associate-/r* 32.7%

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

   7. Simplified 32.7%

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

      1. associate-*r/ 34.0%

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

      2. div-inv 34.0%

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

      3. associate-*l* 34.0%

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

      4. metadata-eval 34.0%

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

      5. times-frac 34.1%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 34.1%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 34.1%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 34.1%

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

      9. *-un-lft-identity 34.1%

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

      10. *-commutative 34.1%

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

      11. associate-*l* 34.1%

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

   9. Applied egg-rr 34.1%

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

   if -2.39999999999999991 < y < 2.39999999999999991

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \lor \neg \left(y \leq 2.4\right):\\ \;\;\;\;\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 8: 67.1% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot 0.16666666666666666\right)\\ \mathbf{if}\;y \leq -2.4:\\ \;\;\;\;\frac{1}{y \cdot \frac{t_0}{x}}\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t_0}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z 0.16666666666666666))))
   (if (<= y -2.4)
     (/ 1.0 (* y (/ t_0 x)))
     (if (<= y 2.4) (/ x z) (/ (/ x t_0) y)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * 0.16666666666666666);
	double tmp;
	if (y <= -2.4) {
		tmp = 1.0 / (y * (t_0 / x));
	} else if (y <= 2.4) {
		tmp = x / z;
	} else {
		tmp = (x / t_0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * 0.16666666666666666d0)
    if (y <= (-2.4d0)) then
        tmp = 1.0d0 / (y * (t_0 / x))
    else if (y <= 2.4d0) then
        tmp = x / z
    else
        tmp = (x / t_0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * 0.16666666666666666);
	double tmp;
	if (y <= -2.4) {
		tmp = 1.0 / (y * (t_0 / x));
	} else if (y <= 2.4) {
		tmp = x / z;
	} else {
		tmp = (x / t_0) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * 0.16666666666666666)
	tmp = 0
	if y <= -2.4:
		tmp = 1.0 / (y * (t_0 / x))
	elif y <= 2.4:
		tmp = x / z
	else:
		tmp = (x / t_0) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * 0.16666666666666666))
	tmp = 0.0
	if (y <= -2.4)
		tmp = Float64(1.0 / Float64(y * Float64(t_0 / x)));
	elseif (y <= 2.4)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x / t_0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * 0.16666666666666666);
	tmp = 0.0;
	if (y <= -2.4)
		tmp = 1.0 / (y * (t_0 / x));
	elseif (y <= 2.4)
		tmp = x / z;
	else
		tmp = (x / t_0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4], N[(1.0 / N[(y * N[(t$95$0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4], N[(x / z), $MachinePrecision], N[(N[(x / t$95$0), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999991

   1. Initial program 96.3%

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

      1. associate-/l* 93.0%

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

      2. associate-/r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 30.1%

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

   5. Taylor expanded in y around inf 30.1%

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

      1. associate-*r/ 30.1%

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

      2. *-commutative 30.1%

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

      3. times-frac 30.1%

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

      4. unpow2 30.1%

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

      5. associate-/r* 30.1%

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

   7. Simplified 30.1%

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

      1. associate-*r/ 30.1%

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

      2. div-inv 30.1%

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

      3. associate-*l* 30.1%

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

      4. metadata-eval 30.1%

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

      5. times-frac 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 30.2%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 30.2%

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

      9. *-un-lft-identity 30.2%

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

      10. *-commutative 30.2%

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

      11. associate-/r* 30.1%

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

      12. clear-num 30.1%

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

      13. *-commutative 30.1%

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

      14. *-un-lft-identity 30.1%

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

      15. times-frac 30.2%

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

      16. /-rgt-identity 30.2%

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

      17. associate-*l* 30.2%

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

   9. Applied egg-rr 30.2%

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

   if -2.39999999999999991 < y < 2.39999999999999991

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

   if 2.39999999999999991 < y

   1. Initial program 96.1%

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

      1. associate-/l* 94.8%

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

      2. associate-/r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 34.5%

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

   5. Taylor expanded in y around inf 34.4%

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

      1. associate-*r/ 34.4%

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

      2. *-commutative 34.4%

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

      3. times-frac 34.3%

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

      4. unpow2 34.3%

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

      5. associate-/r* 34.4%

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

   7. Simplified 34.4%

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

      1. associate-*r/ 36.7%

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

      2. div-inv 36.7%

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

      3. associate-*l* 36.7%

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

      4. metadata-eval 36.7%

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

      5. times-frac 36.8%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \color{blue}{\frac{1 \cdot x}{z \cdot y}}}{y} \]

      6. *-un-lft-identity 36.8%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{\color{blue}{x}}{z \cdot y}}{y} \]

      7. *-commutative 36.8%

         \[\leadsto \frac{\frac{1}{0.16666666666666666} \cdot \frac{x}{\color{blue}{y \cdot z}}}{y} \]

      8. times-frac 36.8%

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

      9. *-un-lft-identity 36.8%

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

      10. *-commutative 36.8%

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

      11. associate-*l* 36.8%

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

   9. Applied egg-rr 36.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4:\\ \;\;\;\;\frac{1}{y \cdot \frac{y \cdot \left(z \cdot 0.16666666666666666\right)}{x}}\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot \left(z \cdot 0.16666666666666666\right)}}{y}\\ \end{array} \]

Alternative 9: 66.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+54} \lor \neg \left(y \leq 10^{+39}\right):\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+54) (not (<= y 1e+39))) (* y (/ x (* y z))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+54) || !(y <= 1e+39)) {
		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 <= (-1d+54)) .or. (.not. (y <= 1d+39))) 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 <= -1e+54) || !(y <= 1e+39)) {
		tmp = y * (x / (y * z));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+54) or not (y <= 1e+39):
		tmp = y * (x / (y * z))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+54) || !(y <= 1e+39))
		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 <= -1e+54) || ~((y <= 1e+39)))
		tmp = y * (x / (y * z));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+54], N[Not[LessEqual[y, 1e+39]], $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 < -1.0000000000000001e54 or 9.9999999999999994e38 < y

   1. Initial program 96.5%

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

      1. associate-*l/ 85.5%

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

      2. times-frac 93.1%

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

      3. *-commutative 93.1%

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

      4. associate-*r/ 93.1%

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

      5. *-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. Taylor expanded in y around 0 36.6%

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

   if -1.0000000000000001e54 < y < 9.9999999999999994e38

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 87.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+54} \lor \neg \left(y \leq 10^{+39}\right):\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 10: 66.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 0.022:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4)
   (* 6.0 (/ x (* z (* y y))))
   (if (<= y 0.022) (/ x z) (* y (/ x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 0.022) {
		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 <= (-2.4d0)) then
        tmp = 6.0d0 * (x / (z * (y * y)))
    else if (y <= 0.022d0) 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 <= -2.4) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else if (y <= 0.022) {
		tmp = x / z;
	} else {
		tmp = y * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4:
		tmp = 6.0 * (x / (z * (y * y)))
	elif y <= 0.022:
		tmp = x / z
	else:
		tmp = y * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4)
		tmp = Float64(6.0 * Float64(x / Float64(z * Float64(y * y))));
	elseif (y <= 0.022)
		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 <= -2.4)
		tmp = 6.0 * (x / (z * (y * y)));
	elseif (y <= 0.022)
		tmp = x / z;
	else
		tmp = y * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4], N[(6.0 * N[(x / N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.022], N[(x / z), $MachinePrecision], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999991

   1. Initial program 96.3%

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

      1. associate-/l* 93.0%

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

      2. associate-/r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 30.1%

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

   5. Taylor expanded in y around inf 30.1%

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

      1. *-commutative 30.1%

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

      2. unpow2 30.1%

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

   7. Simplified 30.1%

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

   if -2.39999999999999991 < y < 0.021999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

   if 0.021999999999999999 < y

   1. Initial program 96.1%

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

      1. associate-*l/ 86.0%

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

      2. times-frac 94.7%

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

      3. *-commutative 94.7%

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

      4. associate-*r/ 94.7%

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

      5. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 36.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4:\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 0.022:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 11: 66.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y \cdot z}\\ \mathbf{elif}\;y \leq 0.0034:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4)
   (* 6.0 (/ (/ x y) (* y z)))
   (if (<= y 0.0034) (/ x z) (* y (/ x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4) {
		tmp = 6.0 * ((x / y) / (y * z));
	} else if (y <= 0.0034) {
		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 <= (-2.4d0)) then
        tmp = 6.0d0 * ((x / y) / (y * z))
    else if (y <= 0.0034d0) 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 <= -2.4) {
		tmp = 6.0 * ((x / y) / (y * z));
	} else if (y <= 0.0034) {
		tmp = x / z;
	} else {
		tmp = y * (x / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4:
		tmp = 6.0 * ((x / y) / (y * z))
	elif y <= 0.0034:
		tmp = x / z
	else:
		tmp = y * (x / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4)
		tmp = Float64(6.0 * Float64(Float64(x / y) / Float64(y * z)));
	elseif (y <= 0.0034)
		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 <= -2.4)
		tmp = 6.0 * ((x / y) / (y * z));
	elseif (y <= 0.0034)
		tmp = x / z;
	else
		tmp = y * (x / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4], N[(6.0 * N[(N[(x / y), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0034], N[(x / z), $MachinePrecision], N[(y * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999991

   1. Initial program 96.3%

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

      1. associate-/l* 93.0%

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

      2. associate-/r/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 30.1%

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

   5. Taylor expanded in y around inf 30.1%

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

      1. *-commutative 30.1%

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

   7. Simplified 30.1%

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

      1. associate-/r* 30.2%

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

      2. *-un-lft-identity 30.2%

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

      3. *-commutative 30.2%

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

      4. times-frac 30.2%

         \[\leadsto \frac{\color{blue}{\frac{1}{0.16666666666666666} \cdot \frac{x}{y \cdot z}}}{y} \]

      5. metadata-eval 30.2%

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

      6. *-un-lft-identity 30.2%

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

      7. *-commutative 30.2%

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

      8. times-frac 30.1%

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

      9. associate-*l* 30.1%

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

      10. div-inv 30.1%

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

      11. associate-*r/ 30.1%

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

      12. frac-times 30.2%

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

      13. *-commutative 30.2%

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

      14. *-un-lft-identity 30.2%

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

      15. times-frac 30.2%

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

      16. metadata-eval 30.2%

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

   9. Applied egg-rr 30.2%

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

   if -2.39999999999999991 < y < 0.00339999999999999981

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.5%

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

   if 0.00339999999999999981 < y

   1. Initial program 96.1%

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

      1. associate-*l/ 86.0%

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

      2. times-frac 94.7%

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

      3. *-commutative 94.7%

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

      4. associate-*r/ 94.7%

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

      5. *-commutative 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 36.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4:\\ \;\;\;\;6 \cdot \frac{\frac{x}{y}}{y \cdot z}\\ \mathbf{elif}\;y \leq 0.0034:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y \cdot z}\\ \end{array} \]

Alternative 12: 59.3% 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 97.9%

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

2. Taylor expanded in y around 0 55.9%

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

3. Final simplification 55.9%

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

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 2023195 
(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))