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

Percentage Accurate: 96.0% → 99.9%

Time: 6.1s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+257}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: 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)))
   (if (<= (* y z) 5e+257) (- x (* (* y z) x)) (- x (* y (* z x))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = x - (z * (y * x));
	} else if ((y * z) <= 5e+257) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = x - (y * (z * x));
	}
	return tmp;
}

Java

assert 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 if ((y * z) <= 5e+257) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = x - (y * (z * x));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = x - (z * (y * x))
	elif (y * z) <= 5e+257:
		tmp = x - ((y * z) * x)
	else:
		tmp = x - (y * (z * x))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(x - Float64(z * Float64(y * x)));
	elseif (Float64(y * z) <= 5e+257)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(x - Float64(y * Float64(z * x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = x - (z * (y * x));
	elseif ((y * z) <= 5e+257)
		tmp = x - ((y * z) * x);
	else
		tmp = x - (y * (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: 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], If[LessEqual[N[(y * z), $MachinePrecision], 5e+257], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 58.2%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 58.2%

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

      1. mul-1-neg 58.2%

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

   4. Simplified 58.2%

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

      1. expm1-log1p-u 23.7%

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

      2. expm1-udef 23.7%

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

   6. Applied egg-rr 23.7%

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

      1. expm1-def 23.7%

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

      2. expm1-log1p 58.2%

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

      3. associate-*r* 99.7%

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

   8. Simplified 99.7%

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

   if -inf.0 < (*.f64 y z) < 5.00000000000000028e257

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

   4. Simplified 99.9%

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

   if 5.00000000000000028e257 < (*.f64 y z)

   1. Initial program 57.4%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 57.4%

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

      1. mul-1-neg 57.4%

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

   4. Simplified 57.4%

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

      1. add-sqr-sqrt 37.5%

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

      2. pow2 37.5%

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

   6. Applied egg-rr 37.5%

      \[\leadsto x + \left(-\color{blue}{{\left(\sqrt{x \cdot \left(y \cdot z\right)}\right)}^{2}}\right) \]
   7. Step-by-step derivation

      1. unpow2 37.5%

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

      2. add-sqr-sqrt 57.4%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+257}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) (- INFINITY)) (not (<= (* y z) 5e+288)))
   (- x (* z (* y x)))
   (- x (* (* y z) x))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -((double) INFINITY)) || !((y * z) <= 5e+288)) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -Double.POSITIVE_INFINITY) || !((y * z) <= 5e+288)) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -math.inf) or not ((y * z) <= 5e+288):
		tmp = x - (z * (y * x))
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= Float64(-Inf)) || !(Float64(y * z) <= 5e+288))
		tmp = Float64(x - Float64(z * Float64(y * x)));
	else
		tmp = Float64(x - Float64(Float64(y * z) * x));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -Inf) || ~(((y * z) <= 5e+288)))
		tmp = x - (z * (y * x));
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(y * z), $MachinePrecision], 5e+288]], $MachinePrecision]], 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 or 5.0000000000000003e288 < (*.f64 y z)

   1. Initial program 54.3%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 54.3%

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

      1. mul-1-neg 54.3%

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

   4. Simplified 54.3%

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

      1. expm1-log1p-u 28.3%

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

      2. expm1-udef 28.3%

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

   6. Applied egg-rr 28.3%

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

      1. expm1-def 28.3%

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

      2. expm1-log1p 54.3%

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

      3. associate-*r* 99.7%

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

   8. Simplified 99.7%

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

   if -inf.0 < (*.f64 y z) < 5.0000000000000003e288

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]

Alternative 3: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-131} \lor \neg \left(z \leq 1.25 \cdot 10^{+151}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-131) (not (<= z 1.25e+151))) (* (* y z) (- x)) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-131) || !(z <= 1.25e+151)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: 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 <= (-8.5d-131)) .or. (.not. (z <= 1.25d+151))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-131) || !(z <= 1.25e+151)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-131) or not (z <= 1.25e+151):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-131) || !(z <= 1.25e+151))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-131) || ~((z <= 1.25e+151)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-131], N[Not[LessEqual[z, 1.25e+151]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000013e-131 or 1.2500000000000001e151 < z

   1. Initial program 87.4%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-in 60.4%

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

      3. distribute-rgt-neg-in 60.4%

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

   4. Simplified 60.4%

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

   if -8.50000000000000013e-131 < z < 1.2500000000000001e151

   1. Initial program 98.5%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 71.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-131} \lor \neg \left(z \leq 1.25 \cdot 10^{+151}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 96.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

assert(y < z);
double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

NOTE: 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 * (1.0d0 - (y * z))
end function

Java

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

Python

[y, z] = sort([y, z])
def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

y, z = sort([y, z])
function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

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

Derivation

1. Initial program 93.3%

   \[x \cdot \left(1 - y \cdot z\right) \]

2. Final simplification 93.3%

   \[\leadsto x \cdot \left(1 - y \cdot z\right) \]

Alternative 5: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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 - ((y * z) * x)
end function

Java

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

Python

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

Julia

y, z = sort([y, z])
function code(x, y, z)
	return Float64(x - Float64(Float64(y * z) * x))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

   \[x \cdot \left(1 - y \cdot z\right) \]

2. Taylor expanded in y around 0 93.3%

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

   1. mul-1-neg 93.3%

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

4. Simplified 93.3%

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

5. Final simplification 93.3%

   \[\leadsto x - \left(y \cdot z\right) \cdot x \]

Alternative 6: 50.8% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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 y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

   \[x \cdot \left(1 - y \cdot z\right) \]

2. Taylor expanded in y around 0 51.9%

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

3. Final simplification 51.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023336 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))