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

Percentage Accurate: 96.0% → 99.8%

Time: 6.8s

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: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+198}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) (- INFINITY)) (not (<= (* y z) 2e+198)))
   (* z (* y (- x)))
   (* x (- 1.0 (* y z)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -((double) INFINITY)) || !((y * z) <= 2e+198)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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) <= 2e+198)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -math.inf) or not ((y * z) <= 2e+198):
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	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) <= 2e+198))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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) <= 2e+198)))
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	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], 2e+198]], $MachinePrecision]], N[(z * N[(y * (-x)), $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) < -inf.0 or 2.00000000000000004e198 < (*.f64 y z)

   1. Initial program 71.8%

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

   2. Taylor expanded in y around inf 71.8%

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

      1. associate-*r* 71.8%

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

      2. associate-*r* 99.9%

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

      3. mul-1-neg 99.9%

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

      4. *-commutative 99.9%

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

      5. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   if -inf.0 < (*.f64 y z) < 2.00000000000000004e198

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+198}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 2: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{if}\;y \cdot z \leq -5000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \cdot z \leq 0.05:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z (- x)))))
   (if (<= (* y z) -5000000.0)
     t_0
     (if (<= (* y z) 0.05) x (if (<= (* y z) 2e+177) (* (* y z) (- x)) t_0)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = y * (z * -x);
	double tmp;
	if ((y * z) <= -5000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.05) {
		tmp = x;
	} else if ((y * z) <= 2e+177) {
		tmp = (y * z) * -x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = y * (z * -x)
    if ((y * z) <= (-5000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.05d0) then
        tmp = x
    else if ((y * z) <= 2d+177) then
        tmp = (y * z) * -x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = y * (z * -x);
	double tmp;
	if ((y * z) <= -5000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.05) {
		tmp = x;
	} else if ((y * z) <= 2e+177) {
		tmp = (y * z) * -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = y * (z * -x)
	tmp = 0
	if (y * z) <= -5000000.0:
		tmp = t_0
	elif (y * z) <= 0.05:
		tmp = x
	elif (y * z) <= 2e+177:
		tmp = (y * z) * -x
	else:
		tmp = t_0
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(z * Float64(-x)))
	tmp = 0.0
	if (Float64(y * z) <= -5000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.05)
		tmp = x;
	elseif (Float64(y * z) <= 2e+177)
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (z * -x);
	tmp = 0.0;
	if ((y * z) <= -5000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.05)
		tmp = x;
	elseif ((y * z) <= 2e+177)
		tmp = (y * z) * -x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.05], x, If[LessEqual[N[(y * z), $MachinePrecision], 2e+177], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5e6 or 2e177 < (*.f64 y z)

   1. Initial program 86.2%

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

      1. sub-neg 86.2%

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

      2. distribute-rgt-in 86.2%

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

      3. *-un-lft-identity 86.2%

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

      4. *-commutative 86.2%

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

      5. +-commutative 86.2%

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

      6. distribute-rgt-neg-in 86.2%

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

   3. Applied egg-rr 86.2%

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

      1. +-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-out 86.2%

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

      4. cancel-sign-sub-inv 86.2%

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

      5. *-commutative 86.2%

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

   5. Applied egg-rr 86.2%

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

   6. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-*r* 93.0%

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

      3. mul-1-neg 93.0%

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

      4. distribute-rgt-neg-in 93.0%

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

      5. *-commutative 93.0%

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

   8. Simplified 93.0%

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

   if -5e6 < (*.f64 y z) < 0.050000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.7%

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

   if 0.050000000000000003 < (*.f64 y z) < 2e177

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 92.1%

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

      1. mul-1-neg 92.1%

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

      2. distribute-rgt-neg-in 92.1%

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

      3. distribute-rgt-neg-out 92.1%

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

   4. Simplified 92.1%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.05:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+177}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 3: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000 \lor \neg \left(y \cdot z \leq 0.05\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -5000000.0) (not (<= (* y z) 0.05))) (* (* y z) (- x)) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -5000000.0) || !((y * z) <= 0.05)) {
		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 (((y * z) <= (-5000000.0d0)) .or. (.not. ((y * z) <= 0.05d0))) 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 (((y * z) <= -5000000.0) || !((y * z) <= 0.05)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -5000000.0) or not ((y * z) <= 0.05):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -5000000.0) || !(Float64(y * z) <= 0.05))
		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 (((y * z) <= -5000000.0) || ~(((y * z) <= 0.05)))
		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[N[(y * z), $MachinePrecision], -5000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.05]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5e6 or 0.050000000000000003 < (*.f64 y z)

   1. Initial program 90.0%

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

   2. Taylor expanded in y around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. distribute-rgt-neg-in 86.7%

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

      3. distribute-rgt-neg-out 86.7%

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

   4. Simplified 86.7%

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

   if -5e6 < (*.f64 y z) < 0.050000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000 \lor \neg \left(y \cdot z \leq 0.05\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5000000.0)
   (* y (* z (- x)))
   (if (<= (* y z) 0.05) x (* z (* y (- x))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5000000.0) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 0.05) {
		tmp = x;
	} else {
		tmp = z * (y * -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 ((y * z) <= (-5000000.0d0)) then
        tmp = y * (z * -x)
    else if ((y * z) <= 0.05d0) then
        tmp = x
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5000000.0) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 0.05) {
		tmp = x;
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -5000000.0:
		tmp = y * (z * -x)
	elif (y * z) <= 0.05:
		tmp = x
	else:
		tmp = z * (y * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5000000.0)
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (Float64(y * z) <= 0.05)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * Float64(-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) <= -5000000.0)
		tmp = y * (z * -x);
	elseif ((y * z) <= 0.05)
		tmp = x;
	else
		tmp = z * (y * -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], -5000000.0], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.05], x, N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5e6

   1. Initial program 89.3%

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

      1. sub-neg 89.3%

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

      2. distribute-rgt-in 89.3%

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

      3. *-un-lft-identity 89.3%

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

      4. *-commutative 89.3%

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

      5. +-commutative 89.3%

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

      6. distribute-rgt-neg-in 89.3%

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

   3. Applied egg-rr 89.3%

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

      1. +-commutative 89.3%

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

      2. *-commutative 89.3%

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

      3. distribute-rgt-neg-out 89.3%

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

      4. cancel-sign-sub-inv 89.3%

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

      5. *-commutative 89.3%

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

   5. Applied egg-rr 89.3%

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

   6. Taylor expanded in y around inf 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*r* 89.4%

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

      3. mul-1-neg 89.4%

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

      4. distribute-rgt-neg-in 89.4%

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

      5. *-commutative 89.4%

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

   8. Simplified 89.4%

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

   if -5e6 < (*.f64 y z) < 0.050000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.7%

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

   if 0.050000000000000003 < (*.f64 y z)

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 86.6%

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

      1. associate-*r* 86.6%

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

      2. associate-*r* 89.5%

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

      3. mul-1-neg 89.5%

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

      4. *-commutative 89.5%

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

      5. *-commutative 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.05:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 5: 49.7% 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 95.5%

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

2. Taylor expanded in y around 0 54.4%

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

3. Final simplification 54.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))