Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 96.0% → 97.5%

Time: 8.6s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;z \leq 5 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t_0}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (<= z 5e-143) (/ x (/ z t_0)) (/ (* x t_0) z))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if (z <= 5e-143) {
		tmp = x / (z / t_0);
	} else {
		tmp = (x * t_0) / 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (z <= 5d-143) then
        tmp = x / (z / t_0)
    else
        tmp = (x * t_0) / z
    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 (z <= 5e-143) {
		tmp = x / (z / t_0);
	} else {
		tmp = (x * t_0) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if z <= 5e-143:
		tmp = x / (z / t_0)
	else:
		tmp = (x * t_0) / z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (z <= 5e-143)
		tmp = Float64(x / Float64(z / t_0));
	else
		tmp = Float64(Float64(x * t_0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (z <= 5e-143)
		tmp = x / (z / t_0);
	else
		tmp = (x * t_0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, 5e-143], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 5.0000000000000002e-143

   1. Initial program 95.2%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   if 5.0000000000000002e-143 < z

   1. Initial program 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-285}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (<= t_0 -1e-285) (* (/ (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 <= -1e-285) {
		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 <= (-1d-285)) 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 <= -1e-285) {
		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 <= -1e-285:
		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 <= -1e-285)
		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 <= -1e-285)
		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, -1e-285], 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) < -1.00000000000000007e-285

   1. Initial program 97.6%

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

      1. associate-*r/ 97.8%

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

      2. associate-/l/ 89.5%

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

      3. *-commutative 89.5%

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

      4. times-frac 97.6%

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

   3. Simplified 97.6%

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

   if -1.00000000000000007e-285 < (/.f64 (sin.f64 y) y)

   1. Initial program 96.9%

      \[\frac{x \cdot \frac{\sin y}{y}}{z} \]
   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 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \leq -1 \cdot 10^{-285}:\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array} \]

Alternative 3: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.48 \lor \neg \left(y \leq 6.5 \cdot 10^{-24}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.48) (not (<= y 6.5e-24)))
   (* (sin y) (/ x (* z y)))
   (/ x (/ z (+ 1.0 (* -0.16666666666666666 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.48) || !(y <= 6.5e-24)) {
		tmp = sin(y) * (x / (z * y));
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (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 <= (-0.48d0)) .or. (.not. (y <= 6.5d-24))) then
        tmp = sin(y) * (x / (z * y))
    else
        tmp = x / (z / (1.0d0 + ((-0.16666666666666666d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.48) || !(y <= 6.5e-24)) {
		tmp = Math.sin(y) * (x / (z * y));
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.48) or not (y <= 6.5e-24):
		tmp = math.sin(y) * (x / (z * y))
	else:
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.48) || !(y <= 6.5e-24))
		tmp = Float64(sin(y) * Float64(x / Float64(z * y)));
	else
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.48) || ~((y <= 6.5e-24)))
		tmp = sin(y) * (x / (z * y));
	else
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.48], N[Not[LessEqual[y, 6.5e-24]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.47999999999999998 or 6.5e-24 < y

   1. Initial program 93.7%

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

      1. associate-*l/ 93.2%

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

      2. times-frac 93.3%

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

      3. *-commutative 93.3%

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

      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%

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

   if -0.47999999999999998 < y < 6.5e-24

   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%

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

      1. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.48 \lor \neg \left(y \leq 6.5 \cdot 10^{-24}\right):\\ \;\;\;\;\sin y \cdot \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \]

Alternative 4: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.48 \lor \neg \left(y \leq 7.8 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.48) (not (<= y 7.8e-19)))
   (* (/ (sin y) z) (/ x y))
   (/ x (/ z (+ 1.0 (* -0.16666666666666666 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.48) || !(y <= 7.8e-19)) {
		tmp = (sin(y) / z) * (x / y);
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (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 <= (-0.48d0)) .or. (.not. (y <= 7.8d-19))) then
        tmp = (sin(y) / z) * (x / y)
    else
        tmp = x / (z / (1.0d0 + ((-0.16666666666666666d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.48) || !(y <= 7.8e-19)) {
		tmp = (Math.sin(y) / z) * (x / y);
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.48) or not (y <= 7.8e-19):
		tmp = (math.sin(y) / z) * (x / y)
	else:
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.48) || !(y <= 7.8e-19))
		tmp = Float64(Float64(sin(y) / z) * Float64(x / y));
	else
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.48) || ~((y <= 7.8e-19)))
		tmp = (sin(y) / z) * (x / y);
	else
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.48], N[Not[LessEqual[y, 7.8e-19]], $MachinePrecision]], N[(N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.47999999999999998 or 7.7999999999999999e-19 < y

   1. Initial program 93.6%

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

      1. associate-*r/ 93.7%

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

      2. associate-/l/ 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. times-frac 93.7%

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

   3. Simplified 93.7%

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

   if -0.47999999999999998 < y < 7.7999999999999999e-19

   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%

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

      1. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.48 \lor \neg \left(y \leq 7.8 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\sin y}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \]

Alternative 5: 66.1% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+32} \lor \neg \left(y \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{z}{y} + \left(z \cdot y\right) \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+32) (not (<= y 5e-8)))
   (/ (/ x y) (+ (/ z y) (* (* z y) 0.16666666666666666)))
   (/ x (/ z (+ 1.0 (* -0.16666666666666666 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+32) || !(y <= 5e-8)) {
		tmp = (x / y) / ((z / y) + ((z * y) * 0.16666666666666666));
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (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 <= (-4.8d+32)) .or. (.not. (y <= 5d-8))) then
        tmp = (x / y) / ((z / y) + ((z * y) * 0.16666666666666666d0))
    else
        tmp = x / (z / (1.0d0 + ((-0.16666666666666666d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+32) || !(y <= 5e-8)) {
		tmp = (x / y) / ((z / y) + ((z * y) * 0.16666666666666666));
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+32) or not (y <= 5e-8):
		tmp = (x / y) / ((z / y) + ((z * y) * 0.16666666666666666))
	else:
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+32) || !(y <= 5e-8))
		tmp = Float64(Float64(x / y) / Float64(Float64(z / y) + Float64(Float64(z * y) * 0.16666666666666666)));
	else
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e+32) || ~((y <= 5e-8)))
		tmp = (x / y) / ((z / y) + ((z * y) * 0.16666666666666666));
	else
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+32], N[Not[LessEqual[y, 5e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] / N[(N[(z / y), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.79999999999999983e32 or 4.9999999999999998e-8 < y

   1. Initial program 93.2%

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

      1. associate-/l* 92.8%

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

      2. associate-/r/ 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around 0 29.2%

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

      1. expm1-log1p-u 15.5%

         \[\leadsto \frac{x}{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)\right)} + \frac{z}{y}\right) \cdot y} \]

      2. expm1-udef 15.4%

         \[\leadsto \frac{x}{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)} - 1\right)} + \frac{z}{y}\right) \cdot y} \]

      3. *-commutative 15.4%

         \[\leadsto \frac{x}{\left(\left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot 0.16666666666666666}\right)} - 1\right) + \frac{z}{y}\right) \cdot y} \]

   6. Applied egg-rr 15.4%

      \[\leadsto \frac{x}{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(\left(y \cdot z\right) \cdot 0.16666666666666666\right)} - 1\right)} + \frac{z}{y}\right) \cdot y} \]
   7. Step-by-step derivation

      1. expm1-def 15.5%

         \[\leadsto \frac{x}{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y \cdot z\right) \cdot 0.16666666666666666\right)\right)} + \frac{z}{y}\right) \cdot y} \]

      2. expm1-log1p 29.2%

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

      3. *-commutative 29.2%

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

      4. associate-*l* 29.2%

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

      5. *-commutative 29.2%

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

   8. Simplified 29.2%

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

   9. Taylor expanded in x around 0 29.2%

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

       1. associate-/r* 29.3%

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

       2. *-commutative 29.3%

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

       3. *-commutative 29.3%

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

   11. Simplified 29.3%

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

   if -4.79999999999999983e32 < y < 4.9999999999999998e-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 98.0%

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

      1. unpow2 98.0%

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

   6. Simplified 98.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+32} \lor \neg \left(y \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{z}{y} + \left(z \cdot y\right) \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \]

Alternative 6: 66.0% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+32} \lor \neg \left(y \leq 32000000\right):\\ \;\;\;\;\frac{6}{z} \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e+32) (not (<= y 32000000.0)))
   (* (/ 6.0 z) (/ x (* y y)))
   (/ x (/ z (+ 1.0 (* -0.16666666666666666 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+32) || !(y <= 32000000.0)) {
		tmp = (6.0 / z) * (x / (y * y));
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (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 <= (-4.3d+32)) .or. (.not. (y <= 32000000.0d0))) then
        tmp = (6.0d0 / z) * (x / (y * y))
    else
        tmp = x / (z / (1.0d0 + ((-0.16666666666666666d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+32) || !(y <= 32000000.0)) {
		tmp = (6.0 / z) * (x / (y * y));
	} else {
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e+32) or not (y <= 32000000.0):
		tmp = (6.0 / z) * (x / (y * y))
	else:
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e+32) || !(y <= 32000000.0))
		tmp = Float64(Float64(6.0 / z) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.3e+32) || ~((y <= 32000000.0)))
		tmp = (6.0 / z) * (x / (y * y));
	else
		tmp = x / (z / (1.0 + (-0.16666666666666666 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e+32], N[Not[LessEqual[y, 32000000.0]], $MachinePrecision]], N[(N[(6.0 / z), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2999999999999997e32 or 3.2e7 < y

   1. Initial program 93.1%

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

      1. associate-/l* 92.7%

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

      2. associate-/r/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 27.9%

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

      1. expm1-log1p-u 14.9%

         \[\leadsto \frac{x}{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)\right)} + \frac{z}{y}\right) \cdot y} \]

      2. expm1-udef 14.8%

         \[\leadsto \frac{x}{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)} - 1\right)} + \frac{z}{y}\right) \cdot y} \]

      3. *-commutative 14.8%

         \[\leadsto \frac{x}{\left(\left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot 0.16666666666666666}\right)} - 1\right) + \frac{z}{y}\right) \cdot y} \]

   6. Applied egg-rr 14.8%

      \[\leadsto \frac{x}{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(\left(y \cdot z\right) \cdot 0.16666666666666666\right)} - 1\right)} + \frac{z}{y}\right) \cdot y} \]
   7. Step-by-step derivation

      1. expm1-def 14.9%

         \[\leadsto \frac{x}{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y \cdot z\right) \cdot 0.16666666666666666\right)\right)} + \frac{z}{y}\right) \cdot y} \]

      2. expm1-log1p 27.9%

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

      3. *-commutative 27.9%

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

      4. associate-*l* 27.9%

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

      5. *-commutative 27.9%

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

   8. Simplified 27.9%

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

   9. Taylor expanded in y around inf 27.9%

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

       1. associate-*r/ 27.9%

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

       2. *-commutative 27.9%

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

       3. times-frac 28.0%

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

       4. unpow2 28.0%

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

   11. Simplified 28.0%

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

   if -4.2999999999999997e32 < y < 3.2e7

   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 98.1%

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

      1. unpow2 98.1%

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

   6. Simplified 98.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+32} \lor \neg \left(y \leq 32000000\right):\\ \;\;\;\;\frac{6}{z} \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}}\\ \end{array} \]

Alternative 7: 65.9% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.45) (not (<= y 2.5))) (* 6.0 (/ x (* z (* y y)))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.45) || !(y <= 2.5)) {
		tmp = 6.0 * (x / (z * (y * 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 <= (-2.45d0)) .or. (.not. (y <= 2.5d0))) then
        tmp = 6.0d0 * (x / (z * (y * 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 <= -2.45) || !(y <= 2.5)) {
		tmp = 6.0 * (x / (z * (y * y)));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.45) or not (y <= 2.5):
		tmp = 6.0 * (x / (z * (y * y)))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.45) || !(y <= 2.5))
		tmp = Float64(6.0 * Float64(x / Float64(z * Float64(y * y))));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.45) || ~((y <= 2.5)))
		tmp = 6.0 * (x / (z * (y * y)));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.45], N[Not[LessEqual[y, 2.5]], $MachinePrecision]], N[(6.0 * N[(x / N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000002 or 2.5 < y

   1. Initial program 93.3%

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

      1. associate-/l* 92.9%

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

      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 27.2%

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

   5. Taylor expanded in y around inf 27.2%

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

      1. unpow2 27.2%

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

      2. *-commutative 27.2%

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

   7. Simplified 27.2%

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

   if -2.4500000000000002 < y < 2.5

   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 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;6 \cdot \frac{x}{z \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 8: 66.0% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;\frac{6}{z} \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.45) (not (<= y 2.5))) (* (/ 6.0 z) (/ x (* y y))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.45) || !(y <= 2.5)) {
		tmp = (6.0 / z) * (x / (y * 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 <= (-2.45d0)) .or. (.not. (y <= 2.5d0))) then
        tmp = (6.0d0 / z) * (x / (y * 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 <= -2.45) || !(y <= 2.5)) {
		tmp = (6.0 / z) * (x / (y * y));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.45) or not (y <= 2.5):
		tmp = (6.0 / z) * (x / (y * y))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.45) || !(y <= 2.5))
		tmp = Float64(Float64(6.0 / z) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.45) || ~((y <= 2.5)))
		tmp = (6.0 / z) * (x / (y * y));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.45], N[Not[LessEqual[y, 2.5]], $MachinePrecision]], N[(N[(6.0 / z), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000002 or 2.5 < y

   1. Initial program 93.3%

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

      1. associate-/l* 92.9%

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

      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 27.2%

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

      1. expm1-log1p-u 14.6%

         \[\leadsto \frac{x}{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)\right)} + \frac{z}{y}\right) \cdot y} \]

      2. expm1-udef 14.5%

         \[\leadsto \frac{x}{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(0.16666666666666666 \cdot \left(y \cdot z\right)\right)} - 1\right)} + \frac{z}{y}\right) \cdot y} \]

      3. *-commutative 14.5%

         \[\leadsto \frac{x}{\left(\left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right) \cdot 0.16666666666666666}\right)} - 1\right) + \frac{z}{y}\right) \cdot y} \]

   6. Applied egg-rr 14.5%

      \[\leadsto \frac{x}{\left(\color{blue}{\left(e^{\mathsf{log1p}\left(\left(y \cdot z\right) \cdot 0.16666666666666666\right)} - 1\right)} + \frac{z}{y}\right) \cdot y} \]
   7. Step-by-step derivation

      1. expm1-def 14.6%

         \[\leadsto \frac{x}{\left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y \cdot z\right) \cdot 0.16666666666666666\right)\right)} + \frac{z}{y}\right) \cdot y} \]

      2. expm1-log1p 27.2%

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

      3. *-commutative 27.2%

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

      4. associate-*l* 27.2%

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

      5. *-commutative 27.2%

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

   8. Simplified 27.2%

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

   9. Taylor expanded in y around inf 27.2%

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

       1. associate-*r/ 27.2%

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

       2. *-commutative 27.2%

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

       3. times-frac 27.3%

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

       4. unpow2 27.3%

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

   11. Simplified 27.3%

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

   if -2.4500000000000002 < y < 2.5

   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 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \lor \neg \left(y \leq 2.5\right):\\ \;\;\;\;\frac{6}{z} \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 9: 65.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+61} \lor \neg \left(y \leq 6.5 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e+61) (not (<= y 6.5e-24))) (* y (/ x (* z y))) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e+61) || !(y <= 6.5e-24)) {
		tmp = y * (x / (z * 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 <= (-1.15d+61)) .or. (.not. (y <= 6.5d-24))) then
        tmp = y * (x / (z * 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 <= -1.15e+61) || !(y <= 6.5e-24)) {
		tmp = y * (x / (z * y));
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e+61) or not (y <= 6.5e-24):
		tmp = y * (x / (z * y))
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e+61) || !(y <= 6.5e-24))
		tmp = Float64(y * Float64(x / Float64(z * y)));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e+61) || ~((y <= 6.5e-24)))
		tmp = y * (x / (z * y));
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e+61], N[Not[LessEqual[y, 6.5e-24]], $MachinePrecision]], N[(y * N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e61 or 6.5e-24 < y

   1. Initial program 93.1%

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

      1. associate-*l/ 92.6%

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

      2. times-frac 92.7%

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

      3. *-commutative 92.7%

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

      4. associate-*r/ 92.7%

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

      5. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around 0 33.0%

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

   if -1.15e61 < y < 6.5e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+61} \lor \neg \left(y \leq 6.5 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 10: 58.1% 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 97.0%

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

2. Taylor expanded in y around 0 61.0%

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

3. Final simplification 61.0%

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

Developer target: 99.5% 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 2023185 
(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))