Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.1% → 96.5%
Time: 4.9s
Alternatives: 8
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]
(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))
double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

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

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

def code(x, y, z):
	return (x * (y + z)) / z

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

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

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

\begin{array}{l}

\\
\frac{x \cdot \left(y + z\right)}{z}
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 8 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 84.1% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{x \cdot \left(y + z\right)}{z} \end{array} \]
(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))
double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

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

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

def code(x, y, z):
	return (x * (y + z)) / z

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

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

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

\begin{array}{l}

\\
\frac{x \cdot \left(y + z\right)}{z}
\end{array}

Alternative 1: 96.5% accurate, 0.1× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x_m \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x_m + \frac{x_m \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x_m, \frac{y}{z}, x_m\right)\\ \end{array} \end{array} \]
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 (+ y z)) z) 5e+281)
    (+ x_m (/ (* x_m y) z))
    (fma x_m (/ y z) x_m))))
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 * (y + z)) / z) <= 5e+281) {
		tmp = x_m + ((x_m * y) / z);
	} else {
		tmp = fma(x_m, (y / z), x_m);
	}
	return x_s * tmp;
}

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (Float64(Float64(x_m * Float64(y + z)) / z) <= 5e+281)
		tmp = Float64(x_m + Float64(Float64(x_m * y) / z));
	else
		tmp = fma(x_m, Float64(y / z), x_m);
	end
	return Float64(x_s * tmp)
end

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[N[(N[(x$95$m * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 5e+281], N[(x$95$m + N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(y / z), $MachinePrecision] + x$95$m), $MachinePrecision]]), $MachinePrecision]

\begin{array}{l}
x_m = \left|x\right|
\\
x_s = \mathsf{copysign}\left(1, x\right)

\\
x_s \cdot \begin{array}{l}
\mathbf{if}\;\frac{x_m \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+281}:\\
\;\;\;\;x_m + \frac{x_m \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(x_m, \frac{y}{z}, x_m\right)\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 2: 70.5% accurate, 0.8× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-8} \lor \neg \left(y \leq 3.6 \cdot 10^{+76}\right):\\ \;\;\;\;x_m \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]
x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= y -7.8e-8) (not (<= y 3.6e+76))) (* x_m (/ y z)) x_m)))
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 <= -7.8e-8) || !(y <= 3.6e+76)) {
		tmp = x_m * (y / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

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 <= (-7.8d-8)) .or. (.not. (y <= 3.6d+76))) then
        tmp = x_m * (y / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

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 <= -7.8e-8) || !(y <= 3.6e+76)) {
		tmp = x_m * (y / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -7.8e-8) or not (y <= 3.6e+76):
		tmp = x_m * (y / z)
	else:
		tmp = x_m
	return x_s * tmp

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -7.8e-8) || !(y <= 3.6e+76))
		tmp = Float64(x_m * Float64(y / z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

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 <= -7.8e-8) || ~((y <= 3.6e+76)))
		tmp = x_m * (y / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

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[Or[LessEqual[y, -7.8e-8], N[Not[LessEqual[y, 3.6e+76]], $MachinePrecision]], N[(x$95$m * N[(y / z), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

\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 -7.8 \cdot 10^{-8} \lor \neg \left(y \leq 3.6 \cdot 10^{+76}\right):\\
\;\;\;\;x_m \cdot \frac{y}{z}\\

\mathbf{else}:\\
\;\;\;\;x_m\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 3: 72.8% accurate, 0.8× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-8} \lor \neg \left(y \leq 4.7 \cdot 10^{+76}\right):\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]
x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (or (<= y -4.8e-8) (not (<= y 4.7e+76))) (* y (/ x_m z)) x_m)))
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 <= -4.8e-8) || !(y <= 4.7e+76)) {
		tmp = y * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

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 <= (-4.8d-8)) .or. (.not. (y <= 4.7d+76))) then
        tmp = y * (x_m / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

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 <= -4.8e-8) || !(y <= 4.7e+76)) {
		tmp = y * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if (y <= -4.8e-8) or not (y <= 4.7e+76):
		tmp = y * (x_m / z)
	else:
		tmp = x_m
	return x_s * tmp

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((y <= -4.8e-8) || !(y <= 4.7e+76))
		tmp = Float64(y * Float64(x_m / z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

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 <= -4.8e-8) || ~((y <= 4.7e+76)))
		tmp = y * (x_m / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

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[Or[LessEqual[y, -4.8e-8], N[Not[LessEqual[y, 4.7e+76]], $MachinePrecision]], N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

\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 -4.8 \cdot 10^{-8} \lor \neg \left(y \leq 4.7 \cdot 10^{+76}\right):\\
\;\;\;\;y \cdot \frac{x_m}{z}\\

\mathbf{else}:\\
\;\;\;\;x_m\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 4: 72.9% accurate, 0.8× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-8}:\\ \;\;\;\;\frac{x_m \cdot y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+74}:\\ \;\;\;\;x_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x_m}{z}\\ \end{array} \end{array} \]
x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= y -7e-8) (/ (* x_m y) z) (if (<= y 7.2e+74) x_m (* y (/ x_m z))))))
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 <= -7e-8) {
		tmp = (x_m * y) / z;
	} else if (y <= 7.2e+74) {
		tmp = x_m;
	} else {
		tmp = y * (x_m / z);
	}
	return x_s * tmp;
}

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 <= (-7d-8)) then
        tmp = (x_m * y) / z
    else if (y <= 7.2d+74) then
        tmp = x_m
    else
        tmp = y * (x_m / z)
    end if
    code = x_s * tmp
end function

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 <= -7e-8) {
		tmp = (x_m * y) / z;
	} else if (y <= 7.2e+74) {
		tmp = x_m;
	} else {
		tmp = y * (x_m / z);
	}
	return x_s * tmp;
}

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if y <= -7e-8:
		tmp = (x_m * y) / z
	elif y <= 7.2e+74:
		tmp = x_m
	else:
		tmp = y * (x_m / z)
	return x_s * tmp

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (y <= -7e-8)
		tmp = Float64(Float64(x_m * y) / z);
	elseif (y <= 7.2e+74)
		tmp = x_m;
	else
		tmp = Float64(y * Float64(x_m / z));
	end
	return Float64(x_s * tmp)
end

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 <= -7e-8)
		tmp = (x_m * y) / z;
	elseif (y <= 7.2e+74)
		tmp = x_m;
	else
		tmp = y * (x_m / z);
	end
	tmp_2 = x_s * tmp;
end

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, -7e-8], N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.2e+74], x$95$m, N[(y * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

\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 \cdot 10^{-8}:\\
\;\;\;\;\frac{x_m \cdot y}{z}\\

\mathbf{elif}\;y \leq 7.2 \cdot 10^{+74}:\\
\;\;\;\;x_m\\

\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x_m}{z}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 5: 87.9% accurate, 0.8× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 6.4 \cdot 10^{+174}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x_m}{z}\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]
x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= z 6.4e+174) (* (+ y z) (/ x_m z)) x_m)))
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 (z <= 6.4e+174) {
		tmp = (y + z) * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

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 (z <= 6.4d+174) then
        tmp = (y + z) * (x_m / z)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

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 (z <= 6.4e+174) {
		tmp = (y + z) * (x_m / z);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z):
	tmp = 0
	if z <= 6.4e+174:
		tmp = (y + z) * (x_m / z)
	else:
		tmp = x_m
	return x_s * tmp

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (z <= 6.4e+174)
		tmp = Float64(Float64(y + z) * Float64(x_m / z));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

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 (z <= 6.4e+174)
		tmp = (y + z) * (x_m / z);
	else
		tmp = x_m;
	end
	tmp_2 = x_s * tmp;
end

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[z, 6.4e+174], N[(N[(y + z), $MachinePrecision] * N[(x$95$m / z), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

\begin{array}{l}
x_m = \left|x\right|
\\
x_s = \mathsf{copysign}\left(1, x\right)

\\
x_s \cdot \begin{array}{l}
\mathbf{if}\;z \leq 6.4 \cdot 10^{+174}:\\
\;\;\;\;\left(y + z\right) \cdot \frac{x_m}{z}\\

\mathbf{else}:\\
\;\;\;\;x_m\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 6: 97.8% accurate, 0.8× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 2 \cdot 10^{+36}:\\ \;\;\;\;x_m + \frac{x_m \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{\frac{z}{y + z}}\\ \end{array} \end{array} \]
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 2e+36) (+ x_m (/ (* x_m y) z)) (/ x_m (/ z (+ y z))))))
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 <= 2e+36) {
		tmp = x_m + ((x_m * y) / z);
	} else {
		tmp = x_m / (z / (y + z));
	}
	return x_s * tmp;
}

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 <= 2d+36) then
        tmp = x_m + ((x_m * y) / z)
    else
        tmp = x_m / (z / (y + z))
    end if
    code = x_s * tmp
end function

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 <= 2e+36) {
		tmp = x_m + ((x_m * y) / z);
	} else {
		tmp = x_m / (z / (y + z));
	}
	return x_s * tmp;
}

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 <= 2e+36:
		tmp = x_m + ((x_m * y) / z)
	else:
		tmp = x_m / (z / (y + z))
	return x_s * tmp

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (x_m <= 2e+36)
		tmp = Float64(x_m + Float64(Float64(x_m * y) / z));
	else
		tmp = Float64(x_m / Float64(z / Float64(y + z)));
	end
	return Float64(x_s * tmp)
end

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 <= 2e+36)
		tmp = x_m + ((x_m * y) / z);
	else
		tmp = x_m / (z / (y + z));
	end
	tmp_2 = x_s * tmp;
end

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, 2e+36], N[(x$95$m + N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

\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 2 \cdot 10^{+36}:\\
\;\;\;\;x_m + \frac{x_m \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x_m}{\frac{z}{y + z}}\\


\end{array}
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 7: 93.8% accurate, 1.0× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(x_m + \frac{x_m \cdot y}{z}\right) \end{array} \]
x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s (+ x_m (/ (* x_m y) z))))
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 + ((x_m * y) / z));
}

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 + ((x_m * y) / z))
end function

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 + ((x_m * y) / z));
}

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 + ((x_m * y) / z))

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

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 + ((x_m * y) / z));
end

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[(x$95$m + N[(N[(x$95$m * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\begin{array}{l}
x_m = \left|x\right|
\\
x_s = \mathsf{copysign}\left(1, x\right)

\\
x_s \cdot \left(x_m + \frac{x_m \cdot y}{z}\right)
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Alternative 8: 50.2% accurate, 7.0× speedup?

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot x_m \end{array} \]
x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))
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;
}

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
end function

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;
}

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

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

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;
end

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 * x$95$m), $MachinePrecision]

\begin{array}{l}
x_m = \left|x\right|
\\
x_s = \mathsf{copysign}\left(1, x\right)

\\
x_s \cdot x_m
\end{array}
Derivation
    &prev;&pcontext;&pcontext2;&ctx;
  1. Add Preprocessing

Developer target: 96.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{x}{\frac{z}{y + z}} \end{array} \]
(FPCore (x y z) :precision binary64 (/ x (/ z (+ y z))))
double code(double x, double y, double z) {
	return x / (z / (y + z));
}

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 / (y + z))
end function

public static double code(double x, double y, double z) {
	return x / (z / (y + z));
}

def code(x, y, z):
	return x / (z / (y + z))

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

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

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

\begin{array}{l}

\\
\frac{x}{\frac{z}{y + z}}
\end{array}

Reproduce

?
herbie shell --seed 2023350 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))