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

Percentage Accurate: 95.8% → 97.8%

Time: 5.7s

Alternatives: 7

Speedup: 0.6×

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: 95.8% 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: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x_m - \left(x_m \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x_m - x_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 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 (<= x_m 2e-26) (- x_m (* (* x_m y) z)) (- x_m (* x_m (* y 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 tmp;
	if (x_m <= 2e-26) {
		tmp = x_m - ((x_m * y) * z);
	} else {
		tmp = x_m - (x_m * (y * 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) :: tmp
    if (x_m <= 2d-26) then
        tmp = x_m - ((x_m * y) * z)
    else
        tmp = x_m - (x_m * (y * 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 tmp;
	if (x_m <= 2e-26) {
		tmp = x_m - ((x_m * y) * z);
	} else {
		tmp = x_m - (x_m * (y * 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):
	tmp = 0
	if x_m <= 2e-26:
		tmp = x_m - ((x_m * y) * z)
	else:
		tmp = x_m - (x_m * (y * 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)
	tmp = 0.0
	if (x_m <= 2e-26)
		tmp = Float64(x_m - Float64(Float64(x_m * y) * z));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y * 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)
	tmp = 0.0;
	if (x_m <= 2e-26)
		tmp = x_m - ((x_m * y) * z);
	else
		tmp = x_m - (x_m * (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]
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[x$95$m, 2e-26], N[(x$95$m - N[(N[(x$95$m * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.0000000000000001e-26

   1. Initial program 95.8%

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

      1. sub-neg 95.8%

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

      2. distribute-rgt-in 95.8%

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

      3. *-un-lft-identity 95.8%

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

      4. distribute-rgt-neg-in 95.8%

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

   4. Applied egg-rr 95.8%

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

   5. Taylor expanded in y around 0 95.8%

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

      1. neg-mul-1 95.8%

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

      2. associate-*r* 94.9%

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

   7. Simplified 94.9%

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

   if 2.0000000000000001e-26 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. associate-*r* 88.7%

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

      4. *-commutative 88.7%

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

      5. distribute-lft-neg-in 88.7%

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

      6. add-sqr-sqrt 36.3%

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

      7. sqrt-unprod 60.7%

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

      8. sqr-neg 60.7%

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

      9. sqrt-unprod 33.1%

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

      10. add-sqr-sqrt 50.7%

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

      11. *-commutative 50.7%

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

      12. distribute-lft-neg-in 50.7%

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

      13. cancel-sign-sub-inv 50.7%

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

      14. associate-*l* 55.0%

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

      15. *-commutative 55.0%

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

      16. add-sqr-sqrt 34.8%

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

      17. sqrt-unprod 75.1%

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

      18. distribute-rgt-neg-out 75.1%

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

      19. distribute-rgt-neg-out 75.1%

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

      20. sqr-neg 75.1%

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

      21. sqrt-prod 58.2%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-26}:\\ \;\;\;\;x - \left(x \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;x_m \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+62} \lor \neg \left(y \leq 2 \cdot 10^{-153}\right):\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 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 -7.5e+168)
    (* x_m (* y (- z)))
    (if (or (<= y -1.9e+62) (not (<= y 2e-153))) (* y (* x_m (- 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 <= -7.5e+168) {
		tmp = x_m * (y * -z);
	} else if ((y <= -1.9e+62) || !(y <= 2e-153)) {
		tmp = y * (x_m * -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 <= (-7.5d+168)) then
        tmp = x_m * (y * -z)
    else if ((y <= (-1.9d+62)) .or. (.not. (y <= 2d-153))) then
        tmp = y * (x_m * -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 <= -7.5e+168) {
		tmp = x_m * (y * -z);
	} else if ((y <= -1.9e+62) || !(y <= 2e-153)) {
		tmp = y * (x_m * -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 <= -7.5e+168:
		tmp = x_m * (y * -z)
	elif (y <= -1.9e+62) or not (y <= 2e-153):
		tmp = y * (x_m * -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 (y <= -7.5e+168)
		tmp = Float64(x_m * Float64(y * Float64(-z)));
	elseif ((y <= -1.9e+62) || !(y <= 2e-153))
		tmp = Float64(y * Float64(x_m * Float64(-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 <= -7.5e+168)
		tmp = x_m * (y * -z);
	elseif ((y <= -1.9e+62) || ~((y <= 2e-153)))
		tmp = y * (x_m * -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[y, -7.5e+168], N[(x$95$m * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.9e+62], N[Not[LessEqual[y, 2e-153]], $MachinePrecision]], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], x$95$m]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999999e168

   1. Initial program 96.9%

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

   3. Taylor expanded in y around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. distribute-rgt-neg-in 69.5%

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

      3. distribute-rgt-neg-out 69.5%

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

   5. Simplified 69.5%

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

   if -7.4999999999999999e168 < y < -1.89999999999999992e62 or 2.00000000000000008e-153 < y

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-*r* 71.7%

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

      3. distribute-rgt-neg-in 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-*r* 69.1%

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

      6. distribute-rgt-neg-out 69.1%

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

   5. Simplified 69.1%

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

   if -1.89999999999999992e62 < y < 2.00000000000000008e-153

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+62} \lor \neg \left(y \leq 2 \cdot 10^{-153}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+60} \lor \neg \left(y \leq 2 \cdot 10^{-153}\right):\\ \;\;\;\;x_m \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 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 -4e+60) (not (<= y 2e-153))) (* x_m (* y (- 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 <= -4e+60) || !(y <= 2e-153)) {
		tmp = x_m * (y * -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 <= (-4d+60)) .or. (.not. (y <= 2d-153))) then
        tmp = x_m * (y * -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 <= -4e+60) || !(y <= 2e-153)) {
		tmp = x_m * (y * -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 <= -4e+60) or not (y <= 2e-153):
		tmp = x_m * (y * -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 ((y <= -4e+60) || !(y <= 2e-153))
		tmp = Float64(x_m * Float64(y * Float64(-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 <= -4e+60) || ~((y <= 2e-153)))
		tmp = x_m * (y * -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[Or[LessEqual[y, -4e+60], N[Not[LessEqual[y, 2e-153]], $MachinePrecision]], N[(x$95$m * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999998e60 or 2.00000000000000008e-153 < y

   1. Initial program 94.5%

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

   3. Taylor expanded in y around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. distribute-rgt-neg-in 67.2%

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

      3. distribute-rgt-neg-out 67.2%

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

   5. Simplified 67.2%

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

   if -3.9999999999999998e60 < y < 2.00000000000000008e-153

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.2%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+60} \lor \neg \left(y \leq 2 \cdot 10^{-153}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+62}:\\ \;\;\;\;\left(x_m \cdot y\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-153}:\\ \;\;\;\;x_m\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 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 -2.35e+62)
    (* (* x_m y) (- z))
    (if (<= y 2e-153) x_m (* 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 tmp;
	if (y <= -2.35e+62) {
		tmp = (x_m * y) * -z;
	} else if (y <= 2e-153) {
		tmp = x_m;
	} 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) :: tmp
    if (y <= (-2.35d+62)) then
        tmp = (x_m * y) * -z
    else if (y <= 2d-153) then
        tmp = x_m
    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 tmp;
	if (y <= -2.35e+62) {
		tmp = (x_m * y) * -z;
	} else if (y <= 2e-153) {
		tmp = x_m;
	} 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):
	tmp = 0
	if y <= -2.35e+62:
		tmp = (x_m * y) * -z
	elif y <= 2e-153:
		tmp = x_m
	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)
	tmp = 0.0
	if (y <= -2.35e+62)
		tmp = Float64(Float64(x_m * y) * Float64(-z));
	elseif (y <= 2e-153)
		tmp = x_m;
	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)
	tmp = 0.0;
	if (y <= -2.35e+62)
		tmp = (x_m * y) * -z;
	elseif (y <= 2e-153)
		tmp = x_m;
	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_] := N[(x$95$s * If[LessEqual[y, -2.35e+62], N[(N[(x$95$m * y), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 2e-153], x$95$m, N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.3500000000000001e62

   1. Initial program 95.9%

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

      1. sub-neg 95.9%

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

      2. distribute-rgt-in 96.0%

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

      3. *-un-lft-identity 96.0%

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

      4. distribute-rgt-neg-in 96.0%

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

   4. Applied egg-rr 96.0%

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

      1. distribute-rgt-neg-out 96.0%

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

      2. distribute-lft-neg-out 96.0%

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

      3. associate-*r* 92.8%

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

      4. *-commutative 92.8%

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

      5. distribute-lft-neg-in 92.8%

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

      6. add-sqr-sqrt 49.9%

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

      7. sqrt-unprod 53.7%

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

      8. sqr-neg 53.7%

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

      9. sqrt-unprod 15.7%

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

      10. add-sqr-sqrt 22.9%

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

      11. *-commutative 22.9%

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

      12. distribute-lft-neg-in 22.9%

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

      13. cancel-sign-sub-inv 22.9%

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

      14. associate-*l* 22.7%

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

      15. *-commutative 22.7%

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

      16. add-sqr-sqrt 8.3%

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

      17. sqrt-unprod 47.4%

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

      18. distribute-rgt-neg-out 47.4%

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

      19. distribute-rgt-neg-out 47.4%

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

      20. sqr-neg 47.4%

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

      21. sqrt-prod 43.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in y around inf 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*r* 70.6%

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

      3. mul-1-neg 70.6%

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

      4. distribute-rgt-neg-out 70.6%

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

      5. *-commutative 70.6%

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

      6. associate-*r* 70.4%

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

      7. *-commutative 70.4%

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

   9. Simplified 70.4%

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

   if -2.3500000000000001e62 < y < 2.00000000000000008e-153

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.2%

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

   if 2.00000000000000008e-153 < y

   1. Initial program 93.8%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. mul-1-neg 65.4%

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

      2. associate-*r* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. *-commutative 70.5%

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

      5. associate-*r* 67.3%

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

      6. distribute-rgt-neg-out 67.3%

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

   5. Simplified 67.3%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+62}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-153}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 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) -5e+155) (* y (* x_m (- z))) (* x_m (- 1.0 (* y 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 tmp;
	if ((y * z) <= -5e+155) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m * (1.0 - (y * 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) :: tmp
    if ((y * z) <= (-5d+155)) then
        tmp = y * (x_m * -z)
    else
        tmp = x_m * (1.0d0 - (y * 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 tmp;
	if ((y * z) <= -5e+155) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m * (1.0 - (y * 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):
	tmp = 0
	if (y * z) <= -5e+155:
		tmp = y * (x_m * -z)
	else:
		tmp = x_m * (1.0 - (y * 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)
	tmp = 0.0
	if (Float64(y * z) <= -5e+155)
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	else
		tmp = Float64(x_m * Float64(1.0 - Float64(y * 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)
	tmp = 0.0;
	if ((y * z) <= -5e+155)
		tmp = y * (x_m * -z);
	else
		tmp = x_m * (1.0 - (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]
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], -5e+155], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], N[(x$95$m * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.9999999999999999e155

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      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-*r* 99.9%

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

      6. distribute-rgt-neg-out 99.9%

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

   5. Simplified 99.9%

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

   if -4.9999999999999999e155 < (*.f64 y z)

   1. Initial program 98.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m - x_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 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) -5e+155) (* y (* x_m (- z))) (- x_m (* x_m (* y 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 tmp;
	if ((y * z) <= -5e+155) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m - (x_m * (y * 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) :: tmp
    if ((y * z) <= (-5d+155)) then
        tmp = y * (x_m * -z)
    else
        tmp = x_m - (x_m * (y * 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 tmp;
	if ((y * z) <= -5e+155) {
		tmp = y * (x_m * -z);
	} else {
		tmp = x_m - (x_m * (y * 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):
	tmp = 0
	if (y * z) <= -5e+155:
		tmp = y * (x_m * -z)
	else:
		tmp = x_m - (x_m * (y * 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)
	tmp = 0.0
	if (Float64(y * z) <= -5e+155)
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	else
		tmp = Float64(x_m - Float64(x_m * Float64(y * 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)
	tmp = 0.0;
	if ((y * z) <= -5e+155)
		tmp = y * (x_m * -z);
	else
		tmp = x_m - (x_m * (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]
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], -5e+155], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], N[(x$95$m - N[(x$95$m * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.9999999999999999e155

   1. Initial program 84.6%

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

   3. Taylor expanded in y around inf 84.6%

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

      1. mul-1-neg 84.6%

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

      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-*r* 99.9%

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

      6. distribute-rgt-neg-out 99.9%

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

   5. Simplified 99.9%

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

   if -4.9999999999999999e155 < (*.f64 y z)

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. distribute-rgt-in 98.6%

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

      3. *-un-lft-identity 98.6%

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

      4. distribute-rgt-neg-in 98.6%

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

   4. Applied egg-rr 98.6%

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

      1. distribute-rgt-neg-out 98.6%

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

      2. distribute-lft-neg-out 98.6%

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

      3. associate-*r* 92.4%

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

      4. *-commutative 92.4%

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

      5. distribute-lft-neg-in 92.4%

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

      6. add-sqr-sqrt 47.0%

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

      7. sqrt-unprod 62.3%

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

      8. sqr-neg 62.3%

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

      9. sqrt-unprod 32.4%

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

      10. add-sqr-sqrt 54.3%

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

      11. *-commutative 54.3%

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

      12. distribute-lft-neg-in 54.3%

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

      13. cancel-sign-sub-inv 54.3%

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

      14. associate-*l* 56.0%

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

      15. *-commutative 56.0%

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

      16. add-sqr-sqrt 35.6%

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

      17. sqrt-unprod 80.1%

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

      18. distribute-rgt-neg-out 80.1%

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

      19. distribute-rgt-neg-out 80.1%

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

      20. sqr-neg 80.1%

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

      21. sqrt-prod 63.9%

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

   6. Applied egg-rr 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.4% 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 1 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 96.9%

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

3. Taylor expanded in y around 0 50.7%

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

4. Final simplification 50.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))