Linear.Quaternion:$ctanh from linear-1.19.1.3

Percentage Accurate: 95.9% → 99.5%

Time: 5.8s

Alternatives: 8

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: 95.9% 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: 99.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 8.8 \cdot 10^{-69}:\\ \;\;\;\;\left(\frac{1}{y} \cdot \sin y\right) \cdot \frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot \frac{\sin y}{y}}{z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= x_m 8.8e-69)
    (* (* (/ 1.0 y) (sin y)) (/ x_m z))
    (/ (* x_m (/ (sin y) y)) z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8.8e-69) {
		tmp = ((1.0 / y) * sin(y)) * (x_m / z);
	} else {
		tmp = (x_m * (sin(y) / y)) / z;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x_m <= 8.8d-69) then
        tmp = ((1.0d0 / y) * sin(y)) * (x_m / z)
    else
        tmp = (x_m * (sin(y) / y)) / z
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (x_m <= 8.8e-69) {
		tmp = ((1.0 / y) * Math.sin(y)) * (x_m / z);
	} else {
		tmp = (x_m * (Math.sin(y) / y)) / z;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if x_m <= 8.8e-69:
		tmp = ((1.0 / y) * math.sin(y)) * (x_m / z)
	else:
		tmp = (x_m * (math.sin(y) / y)) / z
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 8.8e-69)
		tmp = Float64(Float64(Float64(1.0 / y) * sin(y)) * Float64(x_m / z));
	else
		tmp = Float64(Float64(x_m * Float64(sin(y) / y)) / z);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (x_m <= 8.8e-69)
		tmp = ((1.0 / y) * sin(y)) * (x_m / z);
	else
		tmp = (x_m * (sin(y) / y)) / z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[x$95$m, 8.8e-69], N[(N[(N[(1.0 / y), $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 8.8000000000000001e-69

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

      1. clear-num 97.2%

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

      2. associate-/r/ 97.2%

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

   6. Applied egg-rr 97.2%

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

   if 8.8000000000000001e-69 < x

   1. Initial program 99.7%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{-69}:\\ \;\;\;\;\left(\frac{1}{y} \cdot \sin y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-8}:\\ \;\;\;\;\frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;x\_m \cdot \frac{\sin y}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= y 1.85e-8) (/ x_m z) (* x_m (/ (sin y) (* y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= 1.85e-8) {
		tmp = x_m / z;
	} else {
		tmp = x_m * (sin(y) / (y * z));
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.85d-8) then
        tmp = x_m / z
    else
        tmp = x_m * (sin(y) / (y * z))
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= 1.85e-8) {
		tmp = x_m / z;
	} else {
		tmp = x_m * (Math.sin(y) / (y * z));
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= 1.85e-8:
		tmp = x_m / z
	else:
		tmp = x_m * (math.sin(y) / (y * z))
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= 1.85e-8)
		tmp = Float64(x_m / z);
	else
		tmp = Float64(x_m * Float64(sin(y) / Float64(y * z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= 1.85e-8)
		tmp = x_m / z;
	else
		tmp = x_m * (sin(y) / (y * z));
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, 1.85e-8], N[(x$95$m / z), $MachinePrecision], N[(x$95$m * N[(N[Sin[y], $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 1.85e-8

   1. Initial program 98.0%

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

      1. associate-*r/ 98.8%

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

      2. associate-/l/ 88.9%

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

      3. *-commutative 88.9%

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

   3. Simplified 88.9%

      \[\leadsto \color{blue}{x \cdot \frac{\sin y}{y \cdot z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.4%

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

   if 1.85e-8 < y

   1. Initial program 93.0%

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

      1. associate-*r/ 91.3%

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

      2. associate-/l/ 91.3%

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

      3. *-commutative 91.3%

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

   3. Simplified 91.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\sin y}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 2.35 \cdot 10^{-40}:\\ \;\;\;\;\frac{x\_m}{\frac{z}{t\_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{z} \cdot t\_0\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (* x_s (if (<= z 2.35e-40) (/ x_m (/ z t_0)) (* (/ x_m z) t_0)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if (z <= 2.35e-40) {
		tmp = x_m / (z / t_0);
	} else {
		tmp = (x_m / z) * t_0;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (z <= 2.35d-40) then
        tmp = x_m / (z / t_0)
    else
        tmp = (x_m / z) * t_0
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = Math.sin(y) / y;
	double tmp;
	if (z <= 2.35e-40) {
		tmp = x_m / (z / t_0);
	} else {
		tmp = (x_m / z) * t_0;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if z <= 2.35e-40:
		tmp = x_m / (z / t_0)
	else:
		tmp = (x_m / z) * t_0
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (z <= 2.35e-40)
		tmp = Float64(x_m / Float64(z / t_0));
	else
		tmp = Float64(Float64(x_m / z) * t_0);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (z <= 2.35e-40)
		tmp = x_m / (z / t_0);
	else
		tmp = (x_m / z) * t_0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, 2.35e-40], N[(x$95$m / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * t$95$0), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.35e-40

   1. Initial program 95.7%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\frac{\sin y}{y}}}} \]
   4. Add Preprocessing

   if 2.35e-40 < z

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.35 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\sin y}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_0 := \frac{\sin y}{y}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 7.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{x\_m}{z} \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot t\_0}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (/ (sin y) y)))
   (* x_s (if (<= x_m 7.4e-54) (* (/ x_m z) t_0) (/ (* x_m t_0) z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = sin(y) / y;
	double tmp;
	if (x_m <= 7.4e-54) {
		tmp = (x_m / z) * t_0;
	} else {
		tmp = (x_m * t_0) / z;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin(y) / y
    if (x_m <= 7.4d-54) then
        tmp = (x_m / z) * t_0
    else
        tmp = (x_m * t_0) / z
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = Math.sin(y) / y;
	double tmp;
	if (x_m <= 7.4e-54) {
		tmp = (x_m / z) * t_0;
	} else {
		tmp = (x_m * t_0) / z;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	t_0 = math.sin(y) / y
	tmp = 0
	if x_m <= 7.4e-54:
		tmp = (x_m / z) * t_0
	else:
		tmp = (x_m * t_0) / z
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	t_0 = Float64(sin(y) / y)
	tmp = 0.0
	if (x_m <= 7.4e-54)
		tmp = Float64(Float64(x_m / z) * t_0);
	else
		tmp = Float64(Float64(x_m * t_0) / z);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = sin(y) / y;
	tmp = 0.0;
	if (x_m <= 7.4e-54)
		tmp = (x_m / z) * t_0;
	else
		tmp = (x_m * t_0) / z;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]}, N[(x$95$s * If[LessEqual[x$95$m, 7.4e-54], N[(N[(x$95$m / z), $MachinePrecision] * t$95$0), $MachinePrecision], N[(N[(x$95$m * t$95$0), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.4000000000000006e-54

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 97.2%

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   if 7.4000000000000006e-54 < x

   1. Initial program 99.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.4 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(\frac{x\_m}{z} \cdot \frac{\sin y}{y}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (* (/ x_m z) (/ (sin y) y))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * ((x_m / z) * (sin(y) / y));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * ((x_m / z) * (sin(y) / y))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * ((x_m / z) * (Math.sin(y) / y));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * ((x_m / z) * (math.sin(y) / y))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * Float64(Float64(x_m / z) * Float64(sin(y) / y)))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * ((x_m / z) * (sin(y) / y));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * N[(N[(x$95$m / z), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

   1. *-commutative 96.9%

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

   2. associate-*r/ 97.3%

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

3. Simplified 97.3%

   \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot \frac{x}{z}} \]
4. Add Preprocessing

5. Final simplification 97.3%

   \[\leadsto \frac{x}{z} \cdot \frac{\sin y}{y} \]
6. Add Preprocessing

Alternative 6: 62.3% accurate, 8.9× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{x\_m}{z}\right) + -1\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= y 7.5e+44) (/ x_m z) (+ (+ 1.0 (/ x_m z)) -1.0))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= 7.5e+44) {
		tmp = x_m / z;
	} else {
		tmp = (1.0 + (x_m / z)) + -1.0;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 7.5d+44) then
        tmp = x_m / z
    else
        tmp = (1.0d0 + (x_m / z)) + (-1.0d0)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= 7.5e+44) {
		tmp = x_m / z;
	} else {
		tmp = (1.0 + (x_m / z)) + -1.0;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= 7.5e+44:
		tmp = x_m / z
	else:
		tmp = (1.0 + (x_m / z)) + -1.0
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= 7.5e+44)
		tmp = Float64(x_m / z);
	else
		tmp = Float64(Float64(1.0 + Float64(x_m / z)) + -1.0);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= 7.5e+44)
		tmp = x_m / z;
	else
		tmp = (1.0 + (x_m / z)) + -1.0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, 7.5e+44], N[(x$95$m / z), $MachinePrecision], N[(N[(1.0 + N[(x$95$m / z), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 7.50000000000000027e44

   1. Initial program 98.1%

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

      1. associate-*r/ 98.9%

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

      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. Add Preprocessing

   5. Taylor expanded in y around 0 70.0%

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

   if 7.50000000000000027e44 < y

   1. Initial program 90.5%

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

      1. associate-*r/ 88.2%

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

      2. associate-/l/ 87.9%

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

      3. *-commutative 87.9%

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

   3. Simplified 87.9%

      \[\leadsto \color{blue}{x \cdot \frac{\sin y}{y \cdot z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 13.6%

      \[\leadsto x \cdot \color{blue}{\frac{1}{z}} \]
   6. Step-by-step derivation

      1. div-inv 13.6%

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

      2. clear-num 13.6%

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

   7. Applied egg-rr 13.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 12.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{z}{x}}\right)\right)} \]

      2. expm1-udef 31.2%

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

      3. log1p-udef 31.2%

         \[\leadsto e^{\color{blue}{\log \left(1 + \frac{1}{\frac{z}{x}}\right)}} - 1 \]

      4. rem-exp-log 32.0%

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

      5. clear-num 32.0%

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

   9. Applied egg-rr 32.0%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{x}{z}\right) + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 13.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= y 4.2e+69) (/ x_m z) 0.0)))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= 4.2e+69) {
		tmp = x_m / z;
	} else {
		tmp = 0.0;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 4.2d+69) then
        tmp = x_m / z
    else
        tmp = 0.0d0
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (y <= 4.2e+69) {
		tmp = x_m / z;
	} else {
		tmp = 0.0;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= 4.2e+69:
		tmp = x_m / z
	else:
		tmp = 0.0
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= 4.2e+69)
		tmp = Float64(x_m / z);
	else
		tmp = 0.0;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (y <= 4.2e+69)
		tmp = x_m / z;
	else
		tmp = 0.0;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[y, 4.2e+69], N[(x$95$m / z), $MachinePrecision], 0.0]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 4.2000000000000003e69

   1. Initial program 98.1%

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

      1. associate-*r/ 98.9%

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

      2. associate-/l/ 89.8%

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

      3. *-commutative 89.8%

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

   3. Simplified 89.8%

      \[\leadsto \color{blue}{x \cdot \frac{\sin y}{y \cdot z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.7%

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

   if 4.2000000000000003e69 < y

   1. Initial program 90.2%

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

      1. associate-*r/ 87.9%

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

      2. associate-/l/ 87.6%

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

      3. *-commutative 87.6%

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

   3. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \frac{\sin y}{y \cdot z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 13.7%

      \[\leadsto x \cdot \color{blue}{\frac{1}{z}} \]
   6. Step-by-step derivation

      1. div-inv 13.7%

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

      2. clear-num 13.7%

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

   7. Applied egg-rr 13.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 13.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{z}{x}}\right)\right)} \]

      2. expm1-udef 32.0%

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

      3. log1p-udef 32.0%

         \[\leadsto e^{\color{blue}{\log \left(1 + \frac{1}{\frac{z}{x}}\right)}} - 1 \]

      4. rem-exp-log 32.6%

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

      5. clear-num 32.6%

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

   9. Applied egg-rr 32.6%

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

   10. Taylor expanded in x around 0 33.1%

       \[\leadsto \color{blue}{1} - 1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 23.0% accurate, 107.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot 0 \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s 0.0))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z) {
	return x_s * 0.0;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x_s * 0.0d0
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * 0.0;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	return x_s * 0.0

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	return Float64(x_s * 0.0)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * 0.0;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * 0.0), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

   1. associate-*r/ 97.2%

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

   2. associate-/l/ 89.4%

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

   3. *-commutative 89.4%

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

3. Simplified 89.4%

   \[\leadsto \color{blue}{x \cdot \frac{\sin y}{y \cdot z}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 60.7%

   \[\leadsto x \cdot \color{blue}{\frac{1}{z}} \]
6. Step-by-step derivation

   1. div-inv 60.9%

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

   2. clear-num 60.5%

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

7. Applied egg-rr 60.5%

   \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \]
8. Step-by-step derivation

   1. expm1-log1p-u 43.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1}{\frac{z}{x}}\right)\right)} \]

   2. expm1-udef 34.6%

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

   3. log1p-udef 34.6%

      \[\leadsto e^{\color{blue}{\log \left(1 + \frac{1}{\frac{z}{x}}\right)}} - 1 \]

   4. rem-exp-log 51.9%

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

   5. clear-num 52.0%

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

9. Applied egg-rr 52.0%

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

10. Taylor expanded in x around 0 23.9%

    \[\leadsto \color{blue}{1} - 1 \]

11. Final simplification 23.9%

    \[\leadsto 0 \]
12. Add Preprocessing

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 2024026 
(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))