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

Percentage Accurate: 96.0% → 97.7%

Time: 7.1s

Alternatives: 7

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: 97.7% accurate, 0.5× speedup

Math

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

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) (- INFINITY)) (- x (* z (* y x))) (- x (* (* y z) x))))

C

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

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = x - (z * (y * x));
	} 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) <= -math.inf:
		tmp = x - (z * (y * x))
	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) <= Float64(-Inf))
		tmp = Float64(x - Float64(z * Float64(y * x)));
	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) <= -Inf)
		tmp = x - (z * (y * x));
	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], (-Infinity)], N[(x - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.1%

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

      1. sub-neg 64.1%

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

      2. distribute-rgt-in 64.1%

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

      3. *-un-lft-identity 64.1%

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

      4. distribute-rgt-neg-in 64.1%

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

   4. Applied egg-rr 64.1%

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

      1. *-commutative 64.1%

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

      2. distribute-lft-neg-out 64.1%

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

      3. *-commutative 64.1%

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

      4. add-sqr-sqrt 31.1%

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

      5. sqrt-unprod 31.2%

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

      6. sqr-neg 31.2%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.1%

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

      9. cancel-sign-sub-inv 0.1%

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

      10. *-commutative 0.1%

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

      11. associate-*l* 0.1%

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

      12. add-sqr-sqrt 0.1%

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

      13. sqrt-unprod 31.2%

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

      14. sqr-neg 31.2%

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

      15. sqrt-unprod 38.3%

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

      16. add-sqr-sqrt 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -inf.0 < (*.f64 y z)

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      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. *-commutative 98.3%

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

      2. distribute-lft-neg-out 98.3%

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

      3. *-commutative 98.3%

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

      4. add-sqr-sqrt 49.3%

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

      5. sqrt-unprod 68.6%

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

      6. sqr-neg 68.6%

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

      7. sqrt-unprod 27.7%

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

      8. add-sqr-sqrt 55.6%

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

      9. cancel-sign-sub-inv 55.6%

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

      10. *-commutative 55.6%

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

      11. associate-*l* 51.8%

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

      12. add-sqr-sqrt 26.7%

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

      13. sqrt-unprod 65.0%

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

      14. sqr-neg 65.0%

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

      15. sqrt-unprod 45.0%

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

      16. add-sqr-sqrt 91.3%

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

   6. Applied egg-rr 91.3%

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

   7. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.4%

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

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+137} \lor \neg \left(y \leq 7.2 \cdot 10^{-171}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e+137) (not (<= y 7.2e-171))) (* (* z x) (- y)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+137) || !(y <= 7.2e-171)) {
		tmp = (z * x) * -y;
	} 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 ((y <= (-9.5d+137)) .or. (.not. (y <= 7.2d-171))) then
        tmp = (z * x) * -y
    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 ((y <= -9.5e+137) || !(y <= 7.2e-171)) {
		tmp = (z * x) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -9.5e+137) or not (y <= 7.2e-171):
		tmp = (z * x) * -y
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e+137) || !(y <= 7.2e-171))
		tmp = Float64(Float64(z * x) * Float64(-y));
	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 ((y <= -9.5e+137) || ~((y <= 7.2e-171)))
		tmp = (z * x) * -y;
	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[y, -9.5e+137], N[Not[LessEqual[y, 7.2e-171]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000031e137 or 7.20000000000000006e-171 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 65.6%

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

      4. distribute-rgt-neg-in 65.6%

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

   5. Simplified 65.6%

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

   if -9.50000000000000031e137 < y < 7.20000000000000006e-171

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 75.8%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+137} \lor \neg \left(y \leq 7.2 \cdot 10^{-171}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+138} \lor \neg \left(y \leq 7.2 \cdot 10^{-171}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+138) (not (<= y 7.2e-171))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+138) || !(y <= 7.2e-171)) {
		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 ((y <= (-1d+138)) .or. (.not. (y <= 7.2d-171))) 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 ((y <= -1e+138) || !(y <= 7.2e-171)) {
		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 (y <= -1e+138) or not (y <= 7.2e-171):
		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 ((y <= -1e+138) || !(y <= 7.2e-171))
		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 ((y <= -1e+138) || ~((y <= 7.2e-171)))
		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[y, -1e+138], N[Not[LessEqual[y, 7.2e-171]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1e138 or 7.20000000000000006e-171 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-rgt-neg-out 63.2%

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

   5. Simplified 63.2%

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

   if -1e138 < y < 7.20000000000000006e-171

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 75.8%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+138} \lor \neg \left(y \leq 7.2 \cdot 10^{-171}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+276}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

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) -5e+276) (* (* 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) <= -5e+276) {
		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) <= (-5d+276)) 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) <= -5e+276) {
		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) <= -5e+276:
		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) <= -5e+276)
		tmp = Float64(Float64(z * 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) <= -5e+276)
		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], -5e+276], N[(N[(z * x), $MachinePrecision] * (-y)), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000001e276

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

   5. Simplified 99.8%

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

   if -5.00000000000000001e276 < (*.f64 y z)

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      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. *-commutative 98.3%

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

      2. distribute-lft-neg-out 98.3%

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

      3. *-commutative 98.3%

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

      4. add-sqr-sqrt 49.1%

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

      5. sqrt-unprod 69.6%

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

      6. sqr-neg 69.6%

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

      7. sqrt-unprod 28.3%

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

      8. add-sqr-sqrt 56.7%

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

      9. cancel-sign-sub-inv 56.7%

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

      10. *-commutative 56.7%

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

      11. associate-*l* 52.8%

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

      12. add-sqr-sqrt 27.3%

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

      13. sqrt-unprod 65.9%

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

      14. sqr-neg 65.9%

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

      15. sqrt-unprod 44.7%

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

      16. add-sqr-sqrt 91.2%

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

   6. Applied egg-rr 91.2%

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

   7. Taylor expanded in z around 0 98.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+276}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+276}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

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) -5e+276) (* (* 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) <= -5e+276) {
		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) <= (-5d+276)) 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) <= -5e+276) {
		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) <= -5e+276:
		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) <= -5e+276)
		tmp = Float64(Float64(z * 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) <= -5e+276)
		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], -5e+276], N[(N[(z * x), $MachinePrecision] * (-y)), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000001e276

   1. Initial program 73.9%

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

   3. Taylor expanded in y around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

   5. Simplified 99.8%

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

   if -5.00000000000000001e276 < (*.f64 y z)

   1. Initial program 98.3%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+276}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y -7.2e+158) (/ (* y x) y) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+158) {
		tmp = (y * x) / y;
	} 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 (y <= (-7.2d+158)) then
        tmp = (y * x) / y
    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 (y <= -7.2e+158) {
		tmp = (y * x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -7.2e+158:
		tmp = (y * x) / y
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+158)
		tmp = Float64(Float64(y * x) / y);
	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 (y <= -7.2e+158)
		tmp = (y * x) / y;
	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[LessEqual[y, -7.2e+158], N[(N[(y * x), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.19999999999999976e158

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 92.9%

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

   4. Taylor expanded in z around 0 10.6%

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

      1. associate-*r/ 29.2%

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

      2. *-commutative 29.2%

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

   6. Applied egg-rr 29.2%

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

   if -7.19999999999999976e158 < y

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 60.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.3% 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 96.6%

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

3. Taylor expanded in y around 0 54.2%

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

Reproduce

herbie shell --seed 2024139 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))