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

Percentage Accurate: 96.0% → 97.5%

Time: 7.9s

Alternatives: 6

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: 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: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \leq 2 \cdot 10^{-58}:\\ \;\;\;\;x_m - y \cdot \left(x_m \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x_m - x_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

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 (<= x_m 2e-58) (- x_m (* 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 (x_m <= 2e-58) {
		tmp = x_m - (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 (x_m <= 2d-58) then
        tmp = x_m - (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 (x_m <= 2e-58) {
		tmp = x_m - (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 x_m <= 2e-58:
		tmp = x_m - (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 (x_m <= 2e-58)
		tmp = Float64(x_m - Float64(y * Float64(x_m * 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-58)
		tmp = x_m - (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[x$95$m, 2e-58], N[(x$95$m - N[(y * N[(x$95$m * z), $MachinePrecision]), $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-58

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. distribute-rgt-in 96.2%

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

      3. *-un-lft-identity 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. *-commutative 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-*r* 94.8%

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

      4. distribute-rgt-neg-in 94.8%

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

      5. distribute-lft-neg-in 94.8%

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

      6. associate-*l* 96.2%

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

      7. *-commutative 96.2%

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

      8. add-sqr-sqrt 56.1%

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

      9. sqrt-prod 71.2%

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

      10. sqr-neg 71.2%

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

      11. distribute-rgt-neg-out 71.2%

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

      12. distribute-rgt-neg-out 71.2%

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

      13. sqrt-unprod 32.2%

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

      14. add-sqr-sqrt 54.4%

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

      15. cancel-sign-sub-inv 54.4%

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

      16. add-sqr-sqrt 32.2%

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

      17. sqrt-unprod 71.2%

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

      18. distribute-rgt-neg-out 71.2%

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

      19. distribute-rgt-neg-out 71.2%

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

      20. sqr-neg 71.2%

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

   6. Applied egg-rr 96.2%

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

      1. expm1-log1p-u 77.4%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 66.1%

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

   8. Applied egg-rr 66.1%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 77.4%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-log1p 96.2%

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

      3. *-commutative 96.2%

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

      4. associate-*l* 94.8%

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

      5. *-commutative 94.8%

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

   10. Simplified 94.8%

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

   if 2.0000000000000001e-58 < 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. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 91.6%

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

      4. distribute-rgt-neg-in 91.6%

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

      5. distribute-lft-neg-in 91.6%

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

      6. associate-*l* 100.0%

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

      7. *-commutative 100.0%

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

      8. add-sqr-sqrt 58.9%

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

      9. sqrt-prod 79.9%

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

      10. sqr-neg 79.9%

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

      11. distribute-rgt-neg-out 79.9%

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

      12. distribute-rgt-neg-out 79.9%

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

      13. sqrt-unprod 38.9%

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

      14. add-sqr-sqrt 60.1%

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

      15. cancel-sign-sub-inv 60.1%

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

      16. add-sqr-sqrt 38.9%

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

      17. sqrt-unprod 79.9%

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

      18. distribute-rgt-neg-out 79.9%

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

      19. distribute-rgt-neg-out 79.9%

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

      20. sqr-neg 79.9%

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

   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 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-58}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-88} \lor \neg \left(z \leq 1.45 \cdot 10^{+43}\right) \land \left(z \leq 1.05 \cdot 10^{+72} \lor \neg \left(z \leq 2.36 \cdot 10^{+111}\right)\right):\\ \;\;\;\;x_m \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m\\ \end{array} \end{array} \]

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 (<= z -1.22e-88)
          (and (not (<= z 1.45e+43))
               (or (<= z 1.05e+72) (not (<= z 2.36e+111)))))
    (* x_m (* 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 ((z <= -1.22e-88) || (!(z <= 1.45e+43) && ((z <= 1.05e+72) || !(z <= 2.36e+111)))) {
		tmp = x_m * (z * -y);
	} 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 ((z <= (-1.22d-88)) .or. (.not. (z <= 1.45d+43)) .and. (z <= 1.05d+72) .or. (.not. (z <= 2.36d+111))) then
        tmp = x_m * (z * -y)
    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 ((z <= -1.22e-88) || (!(z <= 1.45e+43) && ((z <= 1.05e+72) || !(z <= 2.36e+111)))) {
		tmp = x_m * (z * -y);
	} 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 (z <= -1.22e-88) or (not (z <= 1.45e+43) and ((z <= 1.05e+72) or not (z <= 2.36e+111))):
		tmp = x_m * (z * -y)
	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 ((z <= -1.22e-88) || (!(z <= 1.45e+43) && ((z <= 1.05e+72) || !(z <= 2.36e+111))))
		tmp = Float64(x_m * Float64(z * Float64(-y)));
	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 ((z <= -1.22e-88) || (~((z <= 1.45e+43)) && ((z <= 1.05e+72) || ~((z <= 2.36e+111)))))
		tmp = x_m * (z * -y);
	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[z, -1.22e-88], And[N[Not[LessEqual[z, 1.45e+43]], $MachinePrecision], Or[LessEqual[z, 1.05e+72], N[Not[LessEqual[z, 2.36e+111]], $MachinePrecision]]]], N[(x$95$m * N[(z * (-y)), $MachinePrecision]), $MachinePrecision], x$95$m]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.2200000000000001e-88 or 1.4500000000000001e43 < z < 1.0500000000000001e72 or 2.3599999999999999e111 < z

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 56.6%

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

      1. mul-1-neg 56.6%

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

      2. distribute-rgt-neg-in 56.6%

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

      3. distribute-rgt-neg-out 56.6%

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

   5. Simplified 56.6%

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

   if -1.2200000000000001e-88 < z < 1.4500000000000001e43 or 1.0500000000000001e72 < z < 2.3599999999999999e111

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.0%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-88} \lor \neg \left(z \leq 1.45 \cdot 10^{+43}\right) \land \left(z \leq 1.05 \cdot 10^{+72} \lor \neg \left(z \leq 2.36 \cdot 10^{+111}\right)\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+147}:\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x_m\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x_m\right)\right)\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 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 -2.4e+147)
    (* y (* x_m (- z)))
    (if (<= y 5.1e-169) x_m (* 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 <= -2.4e+147) {
		tmp = y * (x_m * -z);
	} else if (y <= 5.1e-169) {
		tmp = x_m;
	} 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 <= (-2.4d+147)) then
        tmp = y * (x_m * -z)
    else if (y <= 5.1d-169) then
        tmp = x_m
    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 <= -2.4e+147) {
		tmp = y * (x_m * -z);
	} else if (y <= 5.1e-169) {
		tmp = x_m;
	} 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 <= -2.4e+147:
		tmp = y * (x_m * -z)
	elif y <= 5.1e-169:
		tmp = x_m
	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 (y <= -2.4e+147)
		tmp = Float64(y * Float64(x_m * Float64(-z)));
	elseif (y <= 5.1e-169)
		tmp = x_m;
	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 <= -2.4e+147)
		tmp = y * (x_m * -z);
	elseif (y <= 5.1e-169)
		tmp = x_m;
	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[y, -2.4e+147], N[(y * N[(x$95$m * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e-169], x$95$m, N[(z * N[(y * (-x$95$m)), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000002e147

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 82.9%

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

      1. mul-1-neg 82.9%

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

      2. associate-*r* 73.5%

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

      3. distribute-rgt-neg-in 73.5%

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

      4. *-commutative 73.5%

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

      5. associate-*r* 81.8%

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

      6. distribute-rgt-neg-out 81.8%

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

   5. Simplified 81.8%

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

   if -2.40000000000000002e147 < y < 5.09999999999999997e-169

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.5%

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

   if 5.09999999999999997e-169 < y

   1. Initial program 91.8%

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

      1. flip-- 75.6%

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

      2. associate-*r/ 72.2%

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

      3. metadata-eval 72.2%

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

      4. pow2 72.2%

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

      5. +-commutative 72.2%

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

      6. fma-def 72.2%

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

   4. Applied egg-rr 72.2%

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

      1. associate-/l* 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in y around inf 49.2%

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

      1. div-inv 49.3%

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

      2. frac-2neg 49.3%

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

      3. metadata-eval 49.3%

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

      4. remove-double-div 49.3%

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

      5. distribute-rgt-neg-in 49.3%

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

      6. associate-*r* 52.8%

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

      7. *-commutative 52.8%

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

      8. distribute-rgt-neg-in 52.8%

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

      9. *-commutative 52.8%

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

   9. Applied egg-rr 52.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+147}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+254}:\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

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) -1e+254) (* 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) <= -1e+254) {
		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) <= (-1d+254)) 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) <= -1e+254) {
		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) <= -1e+254:
		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) <= -1e+254)
		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) <= -1e+254)
		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], -1e+254], 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) < -9.9999999999999994e253

   1. Initial program 77.5%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      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* 99.8%

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

      6. distribute-rgt-neg-out 99.8%

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

   5. Simplified 99.8%

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

   if -9.9999999999999994e253 < (*.f64 y z)

   1. Initial program 99.1%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+254}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ [x_m, y, z] = \mathsf{sort}([x_m, y, z])\\ \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+254}:\\ \;\;\;\;y \cdot \left(x_m \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x_m - x_m \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

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) -1e+254) (* 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) <= -1e+254) {
		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) <= (-1d+254)) 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) <= -1e+254) {
		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) <= -1e+254:
		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) <= -1e+254)
		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) <= -1e+254)
		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], -1e+254], 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) < -9.9999999999999994e253

   1. Initial program 77.5%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      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* 99.8%

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

      6. distribute-rgt-neg-out 99.8%

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

   5. Simplified 99.8%

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

   if -9.9999999999999994e253 < (*.f64 y z)

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-rgt-in 99.1%

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

      3. *-un-lft-identity 99.1%

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

      4. distribute-rgt-neg-in 99.1%

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

   4. Applied egg-rr 99.1%

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

      1. *-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*r* 93.3%

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

      4. distribute-rgt-neg-in 93.3%

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

      5. distribute-lft-neg-in 93.3%

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

      6. associate-*l* 99.1%

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

      7. *-commutative 99.1%

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

      8. add-sqr-sqrt 62.0%

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

      9. sqrt-prod 80.4%

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

      10. sqr-neg 80.4%

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

      11. distribute-rgt-neg-out 80.4%

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

      12. distribute-rgt-neg-out 80.4%

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

      13. sqrt-unprod 37.3%

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

      14. add-sqr-sqrt 61.1%

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

      15. cancel-sign-sub-inv 61.1%

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

      16. add-sqr-sqrt 37.3%

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

      17. sqrt-unprod 80.4%

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

      18. distribute-rgt-neg-out 80.4%

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

      19. distribute-rgt-neg-out 80.4%

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

      20. sqr-neg 80.4%

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

   6. Applied egg-rr 99.1%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+254}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% 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 97.3%

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

3. Taylor expanded in y around 0 57.4%

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

4. Final simplification 57.4%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))