Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 95.8% → 99.7%

Time: 11.6s

Alternatives: 9

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: 95.8% 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: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+64} \lor \neg \left(x \leq 7 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{x \cdot t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (or (<= x -5e+64) (not (<= x 7e-52))) (/ (* x t_0) z) (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if ((x <= -5e+64) || !(x <= 7e-52)) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if ((x <= (-5d+64)) .or. (.not. (x <= 7d-52))) then
        tmp = (x * t_0) / z
    else
        tmp = t_0 * (x / 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 ((x <= -5e+64) || !(x <= 7e-52)) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if (x <= -5e+64) or not (x <= 7e-52):
		tmp = (x * t_0) / z
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if ((x <= -5e+64) || !(x <= 7e-52))
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if ((x <= -5e+64) || ~((x <= 7e-52)))
		tmp = (x * t_0) / z;
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[x, -5e+64], N[Not[LessEqual[x, 7e-52]], $MachinePrecision]], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5e64 or 7.0000000000000001e-52 < x

   1. Initial program 99.7%

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

   if -5e64 < x < 7.0000000000000001e-52

   1. Initial program 93.4%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+64} \lor \neg \left(x \leq 7 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 2: 95.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-181}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (if (<= t_0 2e-181) (* (sin y) (/ (/ x y) z)) (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if (t_0 <= 2e-181) {
		tmp = sin(y) * ((x / y) / z);
	} else {
		tmp = t_0 * (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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (t_0 <= 2d-181) then
        tmp = sin(y) * ((x / y) / z)
    else
        tmp = t_0 * (x / 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 (t_0 <= 2e-181) {
		tmp = Math.sin(y) * ((x / y) / z);
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if t_0 <= 2e-181:
		tmp = math.sin(y) * ((x / y) / z)
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (t_0 <= 2e-181)
		tmp = Float64(sin(y) * Float64(Float64(x / y) / z));
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (t_0 <= 2e-181)
		tmp = sin(y) * ((x / y) / z);
	else
		tmp = t_0 * (x / z);
	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, 2e-181], N[(N[Sin[y], $MachinePrecision] * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (sin.f64 y) y) < 2.00000000000000009e-181

   1. Initial program 95.2%

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

      1. associate-/l* 92.0%

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

      2. associate-/l* 92.0%

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

      3. associate-/r/ 92.1%

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

      4. *-commutative 92.1%

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

      5. associate-/l/ 95.2%

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

   3. Simplified 95.2%

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

   if 2.00000000000000009e-181 < (/.f64 (sin.f64 y) y)

   1. Initial program 97.1%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \leq 2 \cdot 10^{-181}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7e-7)
   (* (/ x z) (+ 1.0 (* -0.16666666666666666 (* y y))))
   (* x (/ (sin y) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7e-7) {
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = x * (sin(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 <= 7d-7) then
        tmp = (x / z) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = x * (sin(y) / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7e-7) {
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = x * (Math.sin(y) / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 7e-7:
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = x * (math.sin(y) / (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7e-7)
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(x * Float64(sin(y) / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7e-7)
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = x * (sin(y) / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7e-7], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Sin[y], $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.99999999999999968e-7

   1. Initial program 97.4%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. unpow2 70.4%

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

   6. Simplified 70.4%

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

   if 6.99999999999999968e-7 < y

   1. Initial program 93.4%

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

      1. associate-*r/ 92.0%

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

      2. associate-/l/ 92.0%

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

      3. *-commutative 92.0%

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

   3. Simplified 92.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{y \cdot z}\\ \end{array} \]

Alternative 4: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8.2e-7)
   (* (/ x z) (+ 1.0 (* -0.16666666666666666 (* y y))))
   (* (sin y) (/ (/ x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.2e-7) {
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = sin(y) * ((x / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 8.2d-7) then
        tmp = (x / z) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = sin(y) * ((x / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.2e-7) {
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = Math.sin(y) * ((x / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.2e-7:
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = math.sin(y) * ((x / y) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.2e-7)
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(sin(y) * Float64(Float64(x / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8.2e-7)
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = sin(y) * ((x / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.2e-7], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.1999999999999998e-7

   1. Initial program 97.4%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. unpow2 70.4%

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

   6. Simplified 70.4%

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

   if 8.1999999999999998e-7 < y

   1. Initial program 93.4%

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

      1. associate-/l* 92.0%

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

      2. associate-/l* 92.0%

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

      3. associate-/r/ 91.8%

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

      4. *-commutative 91.8%

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

      5. associate-/l/ 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \]

Alternative 5: 59.2% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{y \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.4e+67)
   (* (/ x z) (+ 1.0 (* -0.16666666666666666 (* y y))))
   (* x (/ (- y) (* y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e+67) {
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = x * (-y / (y * -z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.4d+67) then
        tmp = (x / z) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = x * (-y / (y * -z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.4e+67) {
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = x * (-y / (y * -z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.4e+67:
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = x * (-y / (y * -z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.4e+67)
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(x * Float64(Float64(-y) / Float64(y * Float64(-z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.4e+67)
		tmp = (x / z) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = x * (-y / (y * -z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.4e+67], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-y) / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.3999999999999999e67

   1. Initial program 97.6%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around 0 68.7%

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

      1. unpow2 68.7%

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

   6. Simplified 68.7%

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

   if 1.3999999999999999e67 < y

   1. Initial program 91.6%

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

      1. associate-*r/ 89.7%

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

      2. associate-/l/ 89.7%

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

      3. *-commutative 89.7%

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

   3. Simplified 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-/l/ 85.8%

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

      3. associate-*l/ 85.9%

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

      4. *-commutative 85.9%

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

   5. Applied egg-rr 85.9%

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

   6. Taylor expanded in y around 0 19.2%

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

      1. associate-*r/ 19.0%

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

   8. Simplified 19.0%

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

      1. frac-2neg 19.0%

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

      2. distribute-rgt-neg-in 19.0%

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

      3. neg-mul-1 19.0%

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

      4. metadata-eval 19.0%

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

      5. times-frac 19.1%

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

      6. div-inv 19.1%

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

      7. metadata-eval 19.1%

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

      8. metadata-eval 19.1%

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

      9. metadata-eval 19.1%

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

      10. *-commutative 19.1%

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

      11. metadata-eval 19.1%

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

      12. neg-mul-1 19.1%

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

      13. frac-2neg 19.1%

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

      14. distribute-frac-neg 19.1%

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

      15. remove-double-neg 19.1%

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

   10. Applied egg-rr 19.1%

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

       1. associate-/l/ 29.9%

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

   12. Simplified 29.9%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{+67}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{y \cdot \left(-z\right)}\\ \end{array} \]

Alternative 6: 61.1% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+101}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{y \cdot \left(-z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1e+101) (/ x z) (* x (/ (- y) (* y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e+101) {
		tmp = x / z;
	} else {
		tmp = x * (-y / (y * -z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1d+101) then
        tmp = x / z
    else
        tmp = x * (-y / (y * -z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e+101) {
		tmp = x / z;
	} else {
		tmp = x * (-y / (y * -z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1e+101:
		tmp = x / z
	else:
		tmp = x * (-y / (y * -z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1e+101)
		tmp = Float64(x / z);
	else
		tmp = Float64(x * Float64(Float64(-y) / Float64(y * Float64(-z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1e+101)
		tmp = x / z;
	else
		tmp = x * (-y / (y * -z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1e+101], N[(x / z), $MachinePrecision], N[(x * N[((-y) / N[(y * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.9999999999999998e100

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0 68.5%

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

   if 9.9999999999999998e100 < y

   1. Initial program 92.3%

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

      1. associate-*r/ 92.0%

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

      2. associate-/l/ 91.9%

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

      3. *-commutative 91.9%

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

   3. Simplified 91.9%

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

      1. associate-*r/ 91.8%

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

      2. associate-/l/ 86.5%

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

      3. associate-*l/ 86.6%

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

      4. *-commutative 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in y around 0 17.6%

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

      1. associate-*r/ 17.5%

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

   8. Simplified 17.5%

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

      1. frac-2neg 17.5%

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

      2. distribute-rgt-neg-in 17.5%

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

      3. neg-mul-1 17.5%

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

      4. metadata-eval 17.5%

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

      5. times-frac 17.6%

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

      6. div-inv 17.6%

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

      7. metadata-eval 17.6%

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

      8. metadata-eval 17.6%

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

      9. metadata-eval 17.6%

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

      10. *-commutative 17.6%

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

      11. metadata-eval 17.6%

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

      12. neg-mul-1 17.6%

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

      13. frac-2neg 17.6%

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

      14. distribute-frac-neg 17.6%

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

      15. remove-double-neg 17.6%

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

   10. Applied egg-rr 17.6%

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

       1. associate-/l/ 31.6%

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

   12. Simplified 31.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+101}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-y}{y \cdot \left(-z\right)}\\ \end{array} \]

Alternative 7: 60.4% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5e+70) (/ x z) (* (/ x y) (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5e+70) {
		tmp = x / z;
	} else {
		tmp = (x / y) * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.5d+70) then
        tmp = x / z
    else
        tmp = (x / y) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.5e+70) {
		tmp = x / z;
	} else {
		tmp = (x / y) * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.5e+70:
		tmp = x / z
	else:
		tmp = (x / y) * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.5e+70)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x / y) * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.5e+70)
		tmp = x / z;
	else
		tmp = (x / y) * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.5e+70], N[(x / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5000000000000001e70

   1. Initial program 97.6%

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

   2. Taylor expanded in y around 0 70.5%

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

   if 2.5000000000000001e70 < y

   1. Initial program 91.5%

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

      1. associate-*r/ 89.5%

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

      2. associate-/l/ 89.5%

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

      3. *-commutative 89.5%

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

   3. Simplified 89.5%

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

      1. associate-*r/ 89.5%

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

      2. associate-/l/ 87.4%

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

      3. associate-*l/ 87.5%

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

      4. *-commutative 87.5%

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

   5. Applied egg-rr 87.5%

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

   6. Taylor expanded in y around 0 19.3%

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

      1. associate-*r/ 19.1%

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

   8. Simplified 19.1%

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

      1. associate-/l* 19.3%

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

      2. associate-/r/ 26.7%

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

      3. *-commutative 26.7%

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

   10. Applied egg-rr 26.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{y}{z}\\ \end{array} \]

Alternative 8: 60.5% accurate, 11.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 3.5e+104) (/ x z) (/ (* x y) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.5e+104) {
		tmp = x / z;
	} else {
		tmp = (x * y) / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 3.5d+104) then
        tmp = x / z
    else
        tmp = (x * y) / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.5e+104) {
		tmp = x / z;
	} else {
		tmp = (x * y) / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.5e+104:
		tmp = x / z
	else:
		tmp = (x * y) / (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.5e+104)
		tmp = Float64(x / z);
	else
		tmp = Float64(Float64(x * y) / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.5e+104)
		tmp = x / z;
	else
		tmp = (x * y) / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.5e+104], N[(x / z), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.5000000000000002e104

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0 68.5%

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

   if 3.5000000000000002e104 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 91.8%

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

   3. Taylor expanded in y around 0 28.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y \cdot z}\\ \end{array} \]

Alternative 9: 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 96.5%

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

2. Taylor expanded in y around 0 61.4%

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

3. Final simplification 61.4%

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

Developer target: 99.6% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y / sin(y)
    t_1 = (x * (1.0d0 / t_0)) / z
    if (z < (-4.2173720203427147d-29)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x / (z * t_0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023297 
(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))