Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Percentage Accurate: 96.0% → 99.1%

Time: 7.1s

Alternatives: 6

Speedup: 0.2×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ \begin{array}{l} t_0 := x\_m \cdot \left(1 - y \cdot z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+206}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\_m\right)\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+307}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x\_m \cdot \left(-z\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (- 1.0 (* y z)))))
   (*
    x_s
    (if (<= t_0 -2e+206)
      (* z (* y (- x_m)))
      (if (<= t_0 1e+307) t_0 (* y (* x_m (- z))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -2e+206) {
		tmp = z * (y * -x_m);
	} else if (t_0 <= 1e+307) {
		tmp = t_0;
	} else {
		tmp = y * (x_m * -z);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
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 = x_m * (1.0d0 - (y * z))
    if (t_0 <= (-2d+206)) then
        tmp = z * (y * -x_m)
    else if (t_0 <= 1d+307) then
        tmp = t_0
    else
        tmp = y * (x_m * -z)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -2e+206) {
		tmp = z * (y * -x_m);
	} else if (t_0 <= 1e+307) {
		tmp = t_0;
	} else {
		tmp = y * (x_m * -z);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	t_0 = x_m * (1.0 - (y * z))
	tmp = 0
	if t_0 <= -2e+206:
		tmp = z * (y * -x_m)
	elif t_0 <= 1e+307:
		tmp = t_0
	else:
		tmp = y * (x_m * -z)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= -2e+206)
		tmp = Float64(z * Float64(y * Float64(-x_m)));
	elseif (t_0 <= 1e+307)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = x_m * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= -2e+206)
		tmp = z * (y * -x_m);
	elseif (t_0 <= 1e+307)
		tmp = t_0;
	else
		tmp = y * (x_m * -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]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$0, -2e+206], N[(z * N[(y * (-x$95$m)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+307], t$95$0, N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z))) < -2.0000000000000001e206

   1. Initial program 87.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 57.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.0%

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

      2. associate-*r* 67.8%

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

   5. Simplified 67.8%

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

   if -2.0000000000000001e206 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z))) < 9.99999999999999986e306

   1. Initial program 99.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   if 9.99999999999999986e306 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z)))

   1. Initial program 77.3%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 77.3%

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

      2. associate-*r* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq -2 \cdot 10^{+206}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \cdot \left(1 - y \cdot z\right) \leq 10^{+307}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ \begin{array}{l} t_0 := x\_m \cdot \left(y \cdot \left(-z\right)\right)\\ t_1 := z \cdot \left(y \cdot \left(-x\_m\right)\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \cdot z \leq 10^{+165}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (let* ((t_0 (* x_m (* y (- z)))) (t_1 (* z (* y (- x_m)))))
   (*
    x_s
    (if (<= (* y z) (- INFINITY))
      t_1
      (if (<= (* y z) -50.0)
        t_0
        (if (<= (* y z) 2e-8) x_m (if (<= (* y z) 1e+165) t_0 t_1)))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (y * -z);
	double t_1 = z * (y * -x_m);
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = t_1;
	} else if ((y * z) <= -50.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-8) {
		tmp = x_m;
	} else if ((y * z) <= 1e+165) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double t_0 = x_m * (y * -z);
	double t_1 = z * (y * -x_m);
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if ((y * z) <= -50.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-8) {
		tmp = x_m;
	} else if ((y * z) <= 1e+165) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	t_0 = x_m * (y * -z)
	t_1 = z * (y * -x_m)
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = t_1
	elif (y * z) <= -50.0:
		tmp = t_0
	elif (y * z) <= 2e-8:
		tmp = x_m
	elif (y * z) <= 1e+165:
		tmp = t_0
	else:
		tmp = t_1
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	t_0 = Float64(x_m * Float64(y * Float64(-z)))
	t_1 = Float64(z * Float64(y * Float64(-x_m)))
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = t_1;
	elseif (Float64(y * z) <= -50.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-8)
		tmp = x_m;
	elseif (Float64(y * z) <= 1e+165)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	t_0 = x_m * (y * -z);
	t_1 = z * (y * -x_m);
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = t_1;
	elseif ((y * z) <= -50.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-8)
		tmp = x_m;
	elseif ((y * z) <= 1e+165)
		tmp = t_0;
	else
		tmp = t_1;
	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]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := Block[{t$95$0 = N[(x$95$m * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * (-x$95$m)), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -50.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-8], x$95$m, If[LessEqual[N[(y * z), $MachinePrecision], 1e+165], t$95$0, t$95$1]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -inf.0 or 9.99999999999999899e164 < (*.f64 y z)

   1. Initial program 78.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.1%

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

      2. associate-*r* 97.8%

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

   5. Simplified 97.8%

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

   if -inf.0 < (*.f64 y z) < -50 or 2e-8 < (*.f64 y z) < 9.99999999999999899e164

   1. Initial program 99.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-- 85.8%

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

      2. associate-*r/ 80.2%

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

      3. metadata-eval 80.2%

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

      4. pow2 80.2%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

      5. +-commutative 80.2%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{y \cdot z + 1}} \]

      6. fma-define 80.2%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{\mathsf{fma}\left(y, z, 1\right)}} \]

   4. Applied egg-rr 80.2%

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

      1. *-commutative 80.2%

         \[\leadsto \frac{\color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot x}}{\mathsf{fma}\left(y, z, 1\right)} \]

      2. associate-/l* 81.9%

         \[\leadsto \color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot \frac{x}{\mathsf{fma}\left(y, z, 1\right)}} \]

   6. Simplified 81.9%

      \[\leadsto \color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot \frac{x}{\mathsf{fma}\left(y, z, 1\right)}} \]

   7. Taylor expanded in z around inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. +-commutative 84.9%

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

      3. unsub-neg 84.9%

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

   9. Simplified 84.9%

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

   10. Taylor expanded in z around inf 96.0%

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 96.0%

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

       2. *-commutative 96.0%

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

       3. distribute-rgt-neg-in 96.0%

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

       4. *-commutative 96.0%

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

       5. distribute-rgt-neg-in 96.0%

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

   12. Simplified 96.0%

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

   if -50 < (*.f64 y z) < 2e-8

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.1%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq -50:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 10^{+165}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500000:\\ \;\;\;\;y \cdot \left(x\_m \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x\_m\\ \mathbf{elif}\;y \cdot z \leq 10^{+165}:\\ \;\;\;\;x\_m \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\_m\right)\right)\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (<= (* y z) -500000.0)
    (* y (* x_m (- z)))
    (if (<= (* y z) 2e-8)
      x_m
      (if (<= (* y z) 1e+165) (* x_m (* y (- z))) (* z (* y (- x_m))))))))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y * z) <= -500000.0) {
		tmp = y * (x_m * -z);
	} else if ((y * z) <= 2e-8) {
		tmp = x_m;
	} else if ((y * z) <= 1e+165) {
		tmp = x_m * (y * -z);
	} else {
		tmp = z * (y * -x_m);
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
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 * z) <= (-500000.0d0)) then
        tmp = y * (x_m * -z)
    else if ((y * z) <= 2d-8) then
        tmp = x_m
    else if ((y * z) <= 1d+165) then
        tmp = x_m * (y * -z)
    else
        tmp = z * (y * -x_m)
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y * z) <= -500000.0) {
		tmp = y * (x_m * -z);
	} else if ((y * z) <= 2e-8) {
		tmp = x_m;
	} else if ((y * z) <= 1e+165) {
		tmp = x_m * (y * -z);
	} else {
		tmp = z * (y * -x_m);
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if (y * z) <= -500000.0:
		tmp = y * (x_m * -z)
	elif (y * z) <= 2e-8:
		tmp = x_m
	elif (y * z) <= 1e+165:
		tmp = x_m * (y * -z)
	else:
		tmp = z * (y * -x_m)
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -500000.0)
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	elseif (Float64(y * z) <= 2e-8)
		tmp = x_m;
	elseif (Float64(y * z) <= 1e+165)
		tmp = Float64(x_m * Float64(y * Float64(-z)));
	else
		tmp = Float64(z * Float64(y * Float64(-x_m)));
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y * z) <= -500000.0)
		tmp = y * (x_m * -z);
	elseif ((y * z) <= 2e-8)
		tmp = x_m;
	elseif ((y * z) <= 1e+165)
		tmp = x_m * (y * -z);
	else
		tmp = z * (y * -x_m);
	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]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[N[(y * z), $MachinePrecision], -500000.0], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 2e-8], x$95$m, If[LessEqual[N[(y * z), $MachinePrecision], 1e+165], N[(x$95$m * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x$95$m)), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if (*.f64 y z) < -5e5

   1. Initial program 89.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 87.7%

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

      2. associate-*r* 92.0%

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

      3. distribute-rgt-neg-in 92.0%

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

      4. *-commutative 92.0%

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

      5. associate-*l* 90.3%

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

   5. Simplified 90.3%

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

   if -5e5 < (*.f64 y z) < 2e-8

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.4%

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

   if 2e-8 < (*.f64 y z) < 9.99999999999999899e164

   1. Initial program 99.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-- 92.6%

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

      2. associate-*r/ 90.0%

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

      3. metadata-eval 90.0%

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

      4. pow2 90.0%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

      5. +-commutative 90.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{y \cdot z + 1}} \]

      6. fma-define 90.0%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{\mathsf{fma}\left(y, z, 1\right)}} \]

   4. Applied egg-rr 90.0%

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

      1. *-commutative 90.0%

         \[\leadsto \frac{\color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot x}}{\mathsf{fma}\left(y, z, 1\right)} \]

      2. associate-/l* 85.2%

         \[\leadsto \color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot \frac{x}{\mathsf{fma}\left(y, z, 1\right)}} \]

   6. Simplified 85.2%

      \[\leadsto \color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot \frac{x}{\mathsf{fma}\left(y, z, 1\right)}} \]

   7. Taylor expanded in z around inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. +-commutative 81.0%

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

      3. unsub-neg 81.0%

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

   9. Simplified 81.0%

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

   10. Taylor expanded in z around inf 96.4%

       \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 96.4%

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

       2. *-commutative 96.4%

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

       3. distribute-rgt-neg-in 96.4%

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

       4. *-commutative 96.4%

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

       5. distribute-rgt-neg-in 96.4%

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

   12. Simplified 96.4%

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

   if 9.99999999999999899e164 < (*.f64 y z)

   1. Initial program 85.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 85.9%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 85.9%

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

      2. associate-*r* 97.0%

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

   5. Simplified 97.0%

      \[\leadsto \color{blue}{-\left(x \cdot y\right) \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500000:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 10^{+165}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -50 \lor \neg \left(y \cdot z \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (*
  x_s
  (if (or (<= (* y z) -50.0) (not (<= (* y z) 2e-8)))
    (* z (* y (- x_m)))
    x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -50.0) || !((y * z) <= 2e-8)) {
		tmp = z * (y * -x_m);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
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 * z) <= (-50.0d0)) .or. (.not. ((y * z) <= 2d-8))) then
        tmp = z * (y * -x_m)
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if (((y * z) <= -50.0) || !((y * z) <= 2e-8)) {
		tmp = z * (y * -x_m);
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if ((y * z) <= -50.0) or not ((y * z) <= 2e-8):
		tmp = z * (y * -x_m)
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -50.0) || !(Float64(y * z) <= 2e-8))
		tmp = Float64(z * Float64(y * Float64(-x_m)));
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if (((y * z) <= -50.0) || ~(((y * z) <= 2e-8)))
		tmp = z * (y * -x_m);
	else
		tmp = x_m;
	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]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[Or[LessEqual[N[(y * z), $MachinePrecision], -50.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e-8]], $MachinePrecision]], N[(z * N[(y * (-x$95$m)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -50 or 2e-8 < (*.f64 y z)

   1. Initial program 91.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 89.5%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 89.5%

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

      2. associate-*r* 90.2%

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

   5. Simplified 90.2%

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

   if -50 < (*.f64 y z) < 2e-8

   1. Initial program 100.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.1%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -50 \lor \neg \left(y \cdot z \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+73}:\\ \;\;\;\;\frac{x\_m \cdot z}{z}\\ \mathbf{else}:\\ \;\;\;\;x\_m\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z)
 :precision binary64
 (* x_s (if (<= (* y z) -2e+73) (/ (* x_m z) z) x_m)))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y * z) <= -2e+73) {
		tmp = (x_m * z) / z;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
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 * z) <= (-2d+73)) then
        tmp = (x_m * z) / z
    else
        tmp = x_m
    end if
    code = x_s * tmp
end function

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	double tmp;
	if ((y * z) <= -2e+73) {
		tmp = (x_m * z) / z;
	} else {
		tmp = x_m;
	}
	return x_s * tmp;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	tmp = 0
	if (y * z) <= -2e+73:
		tmp = (x_m * z) / z
	else:
		tmp = x_m
	return x_s * tmp

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -2e+73)
		tmp = Float64(Float64(x_m * z) / z);
	else
		tmp = x_m;
	end
	return Float64(x_s * tmp)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp_2 = code(x_s, x_m, y, z)
	tmp = 0.0;
	if ((y * z) <= -2e+73)
		tmp = (x_m * z) / z;
	else
		tmp = x_m;
	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]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * If[LessEqual[N[(y * z), $MachinePrecision], -2e+73], N[(N[(x$95$m * z), $MachinePrecision] / z), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.99999999999999997e73

   1. Initial program 86.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-- 48.2%

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

      2. associate-*r/ 41.9%

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

      3. metadata-eval 41.9%

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

      4. pow2 41.9%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

      5. +-commutative 41.9%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{y \cdot z + 1}} \]

      6. fma-define 41.9%

         \[\leadsto \frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{\color{blue}{\mathsf{fma}\left(y, z, 1\right)}} \]

   4. Applied egg-rr 41.9%

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

      1. *-commutative 41.9%

         \[\leadsto \frac{\color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot x}}{\mathsf{fma}\left(y, z, 1\right)} \]

      2. associate-/l* 47.6%

         \[\leadsto \color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot \frac{x}{\mathsf{fma}\left(y, z, 1\right)}} \]

   6. Simplified 47.6%

      \[\leadsto \color{blue}{\left(1 - {\left(y \cdot z\right)}^{2}\right) \cdot \frac{x}{\mathsf{fma}\left(y, z, 1\right)}} \]

   7. Taylor expanded in z around inf 95.4%

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

      1. mul-1-neg 95.4%

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

      2. +-commutative 95.4%

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

      3. unsub-neg 95.4%

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

   9. Simplified 95.4%

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

   10. Taylor expanded in z around 0 4.4%

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

       1. *-commutative 4.4%

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

       2. associate-*l/ 19.7%

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

   12. Applied egg-rr 19.7%

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

   if -1.99999999999999997e73 < (*.f64 y z)

   1. Initial program 97.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 58.4%

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

Alternative 6: 50.9% accurate, 7.0× speedup

Math

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

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
(FPCore (x_s x_m y z) :precision binary64 (* x_s x_m))

C

x\_m = fabs(x);
x\_s = copysign(1.0, x);
assert(x_m < y && y < z);
double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Fortran

x\_m = abs(x)
x\_s = copysign(1.0d0, x)
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
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

Java

x\_m = Math.abs(x);
x\_s = Math.copySign(1.0, x);
assert x_m < y && y < z;
public static double code(double x_s, double x_m, double y, double z) {
	return x_s * x_m;
}

Python

x\_m = math.fabs(x)
x\_s = math.copysign(1.0, x)
[x_m, y, z] = sort([x_m, y, z])
def code(x_s, x_m, y, z):
	return x_s * x_m

Julia

x\_m = abs(x)
x\_s = copysign(1.0, x)
x_m, y, z = sort([x_m, y, z])
function code(x_s, x_m, y, z)
	return Float64(x_s * x_m)
end

MATLAB

x\_m = abs(x);
x\_s = sign(x) * abs(1.0);
x_m, y, z = num2cell(sort([x_m, y, z])){:}
function tmp = code(x_s, x_m, y, z)
	tmp = x_s * x_m;
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]
NOTE: x_m, y, and z should be sorted in increasing order before calling this function.
code[x$95$s_, x$95$m_, y_, z_] := N[(x$95$s * x$95$m), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 49.2%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))