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

Percentage Accurate: 96.0% → 97.9%

Time: 5.9s

Alternatives: 5

Speedup: 0.5×

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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -4e+205) (* z (* x (- y))) (- x (* (* y z) x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -4e+205) {
		tmp = z * (x * -y);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-4d+205)) then
        tmp = z * (x * -y)
    else
        tmp = x - ((y * z) * x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -4e+205) {
		tmp = z * (x * -y);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -4e+205:
		tmp = z * (x * -y)
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -4e+205)
		tmp = Float64(z * Float64(x * Float64(-y)));
	else
		tmp = Float64(x - Float64(Float64(y * z) * x));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -4e+205)
		tmp = z * (x * -y);
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -4e+205], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.00000000000000007e205

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-rgt-in 80.8%

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

      3. *-un-lft-identity 80.8%

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

      4. distribute-rgt-neg-in 80.8%

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

   4. Applied egg-rr 80.8%

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

      1. distribute-rgt-neg-out 80.8%

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

      2. distribute-lft-neg-out 80.8%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. add-sqr-sqrt 51.7%

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

      7. sqrt-unprod 48.6%

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

      8. sqr-neg 48.6%

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

      9. sqrt-unprod 0.2%

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

      10. add-sqr-sqrt 0.4%

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

      11. *-commutative 0.4%

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

      12. distribute-lft-neg-in 0.4%

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

      13. cancel-sign-sub-inv 0.4%

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

      14. associate-*l* 0.3%

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

      15. *-commutative 0.3%

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

      16. add-sqr-sqrt 0.3%

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

      17. sqrt-unprod 0.2%

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

      18. distribute-rgt-neg-out 0.2%

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

      19. distribute-rgt-neg-out 0.2%

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

   6. Applied egg-rr 80.8%

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

      1. expm1-log1p-u 31.8%

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

      2. expm1-udef 28.0%

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

      3. associate-*r* 35.0%

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

   8. Applied egg-rr 35.0%

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

      1. expm1-def 38.8%

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

      2. expm1-log1p 99.8%

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

      3. *-commutative 99.8%

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

   10. Simplified 99.8%

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

   11. Taylor expanded in z around inf 80.8%

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

       1. mul-1-neg 80.8%

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

       2. associate-*r* 99.8%

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

       3. *-commutative 99.8%

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

       4. distribute-rgt-neg-in 99.8%

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

       5. distribute-rgt-neg-in 99.8%

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

   13. Simplified 99.8%

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

   if -4.00000000000000007e205 < (*.f64 y z)

   1. Initial program 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. distribute-rgt-neg-out 98.3%

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

      2. distribute-lft-neg-out 98.3%

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

      3. associate-*r* 93.6%

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

      4. *-commutative 93.6%

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

      5. distribute-lft-neg-in 93.6%

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

      6. add-sqr-sqrt 50.2%

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

      7. sqrt-unprod 60.4%

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

      8. sqr-neg 60.4%

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

      9. sqrt-unprod 25.4%

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

      10. add-sqr-sqrt 45.8%

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

      11. *-commutative 45.8%

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

      12. distribute-lft-neg-in 45.8%

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

      13. cancel-sign-sub-inv 45.8%

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

      14. associate-*l* 47.7%

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

      15. *-commutative 47.7%

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

      16. add-sqr-sqrt 32.6%

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

      17. sqrt-unprod 70.6%

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

      18. distribute-rgt-neg-out 70.6%

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

      19. distribute-rgt-neg-out 70.6%

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

   6. Applied egg-rr 98.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-113} \lor \neg \left(z \leq 1.7 \cdot 10^{+48}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e-113) (not (<= z 1.7e+48))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-113) || !(z <= 1.7e+48)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.4d-113)) .or. (.not. (z <= 1.7d+48))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-113) || !(z <= 1.7e+48)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.4e-113) or not (z <= 1.7e+48):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e-113) || !(z <= 1.7e+48))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e-113) || ~((z <= 1.7e+48)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e-113], N[Not[LessEqual[z, 1.7e+48]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-113 or 1.7000000000000002e48 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

      2. distribute-rgt-neg-in 68.6%

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

      3. distribute-rgt-neg-out 68.6%

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

   5. Simplified 68.6%

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

   if -1.4e-113 < z < 1.7000000000000002e48

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.3%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-113} \lor \neg \left(z \leq 1.7 \cdot 10^{+48}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-114} \lor \neg \left(z \leq 6.8 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(-z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e-114) (not (<= z 6.8e+47))) (* y (- (* z x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e-114) || !(z <= 6.8e+47)) {
		tmp = y * -(z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.7d-114)) .or. (.not. (z <= 6.8d+47))) then
        tmp = y * -(z * x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e-114) || !(z <= 6.8e+47)) {
		tmp = y * -(z * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -3.7e-114) or not (z <= 6.8e+47):
		tmp = y * -(z * x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e-114) || !(z <= 6.8e+47))
		tmp = Float64(y * Float64(-Float64(z * x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e-114) || ~((z <= 6.8e+47)))
		tmp = y * -(z * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e-114], N[Not[LessEqual[z, 6.8e+47]], $MachinePrecision]], N[(y * (-N[(z * x), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999965e-114 or 6.7999999999999996e47 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in y around inf 68.6%

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

      1. mul-1-neg 68.6%

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

      2. associate-*r* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

      4. *-commutative 68.0%

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

      5. associate-*r* 71.8%

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

      6. distribute-rgt-neg-out 71.8%

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

   5. Simplified 71.8%

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

   if -3.69999999999999965e-114 < z < 6.7999999999999996e47

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-114} \lor \neg \left(z \leq 6.8 \cdot 10^{+47}\right):\\ \;\;\;\;y \cdot \left(-z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -4e+205) (* z (* x (- y))) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -4e+205) {
		tmp = z * (x * -y);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-4d+205)) then
        tmp = z * (x * -y)
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -4e+205) {
		tmp = z * (x * -y);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -4e+205:
		tmp = z * (x * -y)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -4e+205)
		tmp = Float64(z * Float64(x * Float64(-y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -4e+205)
		tmp = z * (x * -y);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -4e+205], N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -4.00000000000000007e205

   1. Initial program 80.8%

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

      1. sub-neg 80.8%

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

      2. distribute-rgt-in 80.8%

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

      3. *-un-lft-identity 80.8%

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

      4. distribute-rgt-neg-in 80.8%

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

   4. Applied egg-rr 80.8%

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

      1. distribute-rgt-neg-out 80.8%

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

      2. distribute-lft-neg-out 80.8%

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

      3. associate-*r* 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. add-sqr-sqrt 51.7%

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

      7. sqrt-unprod 48.6%

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

      8. sqr-neg 48.6%

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

      9. sqrt-unprod 0.2%

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

      10. add-sqr-sqrt 0.4%

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

      11. *-commutative 0.4%

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

      12. distribute-lft-neg-in 0.4%

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

      13. cancel-sign-sub-inv 0.4%

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

      14. associate-*l* 0.3%

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

      15. *-commutative 0.3%

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

      16. add-sqr-sqrt 0.3%

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

      17. sqrt-unprod 0.2%

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

      18. distribute-rgt-neg-out 0.2%

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

      19. distribute-rgt-neg-out 0.2%

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

   6. Applied egg-rr 80.8%

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

      1. expm1-log1p-u 31.8%

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

      2. expm1-udef 28.0%

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

      3. associate-*r* 35.0%

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

   8. Applied egg-rr 35.0%

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

      1. expm1-def 38.8%

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

      2. expm1-log1p 99.8%

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

      3. *-commutative 99.8%

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

   10. Simplified 99.8%

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

   11. Taylor expanded in z around inf 80.8%

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

       1. mul-1-neg 80.8%

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

       2. associate-*r* 99.8%

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

       3. *-commutative 99.8%

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

       4. distribute-rgt-neg-in 99.8%

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

       5. distribute-rgt-neg-in 99.8%

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

   13. Simplified 99.8%

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

   if -4.00000000000000007e205 < (*.f64 y z)

   1. Initial program 98.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -4 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in y around 0 44.6%

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

4. Final simplification 44.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024017 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))