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

Percentage Accurate: 96.3% → 93.9%

Time: 7.3s

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: 96.3% 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: 93.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500000 \lor \neg \left(y \cdot z \leq 0.2\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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) -500000.0) (not (<= (* y z) 0.2))) (* y (* x (- z))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -500000.0) || !((y * z) <= 0.2)) {
		tmp = y * (x * -z);
	} 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) <= (-500000.0d0)) .or. (.not. ((y * z) <= 0.2d0))) then
        tmp = y * (x * -z)
    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) <= -500000.0) || !((y * z) <= 0.2)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -500000.0) or not ((y * z) <= 0.2):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -500000.0) || !(Float64(y * z) <= 0.2))
		tmp = Float64(y * Float64(x * Float64(-z)));
	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) <= -500000.0) || ~(((y * z) <= 0.2)))
		tmp = y * (x * -z);
	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], -500000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.2]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5e5 or 0.20000000000000001 < (*.f64 y z)

   1. Initial program 91.7%

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

      1. remove-double-neg 91.7%

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

      2. distribute-lft-neg-out 91.7%

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

      3. neg-mul-1 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-*r* 91.7%

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

      6. distribute-lft-neg-in 91.7%

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

      7. distribute-rgt-neg-out 91.7%

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

      8. *-commutative 91.7%

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

      9. neg-mul-1 91.7%

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

      10. remove-double-neg 91.7%

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

      11. cancel-sign-sub-inv 91.7%

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

      12. +-commutative 91.7%

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

      13. distribute-lft-neg-out 91.7%

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

      14. metadata-eval 91.7%

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

      15. distribute-neg-in 91.7%

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

      16. fma-def 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around inf 91.6%

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

      1. mul-1-neg 91.6%

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

      2. distribute-rgt-neg-in 91.6%

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

      3. distribute-rgt-neg-in 91.6%

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

   6. Simplified 91.6%

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

   if -5e5 < (*.f64 y z) < 0.20000000000000001

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. *-commutative 100.0%

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

      9. neg-mul-1 100.0%

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

      10. remove-double-neg 100.0%

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

      11. cancel-sign-sub-inv 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-lft-neg-out 100.0%

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

      14. metadata-eval 100.0%

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

      15. distribute-neg-in 100.0%

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

      16. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500000 \lor \neg \left(y \cdot z \leq 0.2\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((x * (1.0 - (y * z))) <= ((double) INFINITY)) {
		tmp = x * -fma(y, z, -1.0);
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < +inf.0

   1. Initial program 95.4%

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

      1. remove-double-neg 95.4%

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

      2. distribute-lft-neg-out 95.4%

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

      3. neg-mul-1 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-*r* 95.4%

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

      6. distribute-lft-neg-in 95.4%

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

      7. distribute-rgt-neg-out 95.4%

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

      8. *-commutative 95.4%

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

      9. neg-mul-1 95.4%

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

      10. remove-double-neg 95.4%

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

      11. cancel-sign-sub-inv 95.4%

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

      12. +-commutative 95.4%

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

      13. distribute-lft-neg-out 95.4%

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

      14. metadata-eval 95.4%

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

      15. distribute-neg-in 95.4%

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

      16. fma-def 95.4%

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

   3. Simplified 95.4%

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

   if +inf.0 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 95.4%

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

      1. remove-double-neg 95.4%

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

      2. distribute-lft-neg-out 95.4%

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

      3. neg-mul-1 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-*r* 95.4%

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

      6. distribute-lft-neg-in 95.4%

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

      7. distribute-rgt-neg-out 95.4%

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

      8. *-commutative 95.4%

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

      9. neg-mul-1 95.4%

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

      10. remove-double-neg 95.4%

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

      11. cancel-sign-sub-inv 95.4%

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

      12. +-commutative 95.4%

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

      13. distribute-lft-neg-out 95.4%

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

      14. metadata-eval 95.4%

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

      15. distribute-neg-in 95.4%

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

      16. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   6. Simplified 52.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq \infty:\\ \;\;\;\;x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 3: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t_0 \leq \infty:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 INFINITY) t_0 (* y (* x (- z))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = t_0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= math.inf:
		tmp = t_0
	else:
		tmp = y * (x * -z)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = t_0;
	else
		tmp = y * (x * -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_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], t$95$0, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < +inf.0

   1. Initial program 95.4%

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

   if +inf.0 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 95.4%

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

      1. remove-double-neg 95.4%

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

      2. distribute-lft-neg-out 95.4%

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

      3. neg-mul-1 95.4%

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

      4. *-commutative 95.4%

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

      5. associate-*r* 95.4%

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

      6. distribute-lft-neg-in 95.4%

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

      7. distribute-rgt-neg-out 95.4%

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

      8. *-commutative 95.4%

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

      9. neg-mul-1 95.4%

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

      10. remove-double-neg 95.4%

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

      11. cancel-sign-sub-inv 95.4%

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

      12. +-commutative 95.4%

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

      13. distribute-lft-neg-out 95.4%

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

      14. metadata-eval 95.4%

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

      15. distribute-neg-in 95.4%

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

      16. fma-def 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. distribute-rgt-neg-in 52.5%

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

      3. distribute-rgt-neg-in 52.5%

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

   6. Simplified 52.5%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq \infty:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 4: 94.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500000 \lor \neg \left(y \cdot z \leq 0.2\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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) -500000.0) (not (<= (* y z) 0.2))) (* x (* y (- z))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -500000.0) || !((y * z) <= 0.2)) {
		tmp = x * (y * -z);
	} 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) <= (-500000.0d0)) .or. (.not. ((y * z) <= 0.2d0))) then
        tmp = x * (y * -z)
    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) <= -500000.0) || !((y * z) <= 0.2)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -500000.0) or not ((y * z) <= 0.2):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -500000.0) || !(Float64(y * z) <= 0.2))
		tmp = Float64(x * Float64(y * Float64(-z)));
	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) <= -500000.0) || ~(((y * z) <= 0.2)))
		tmp = x * (y * -z);
	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], -500000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.2]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5e5 or 0.20000000000000001 < (*.f64 y z)

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. associate-*r* 90.7%

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

      2. neg-mul-1 90.7%

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

      3. *-commutative 90.7%

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

   4. Simplified 90.7%

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

   if -5e5 < (*.f64 y z) < 0.20000000000000001

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-*r* 100.0%

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

      6. distribute-lft-neg-in 100.0%

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

      7. distribute-rgt-neg-out 100.0%

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

      8. *-commutative 100.0%

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

      9. neg-mul-1 100.0%

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

      10. remove-double-neg 100.0%

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

      11. cancel-sign-sub-inv 100.0%

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

      12. +-commutative 100.0%

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

      13. distribute-lft-neg-out 100.0%

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

      14. metadata-eval 100.0%

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

      15. distribute-neg-in 100.0%

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

      16. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500000 \lor \neg \left(y \cdot z \leq 0.2\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 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 95.4%

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

   1. remove-double-neg 95.4%

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

   2. distribute-lft-neg-out 95.4%

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

   3. neg-mul-1 95.4%

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

   4. *-commutative 95.4%

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

   5. associate-*r* 95.4%

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

   6. distribute-lft-neg-in 95.4%

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

   7. distribute-rgt-neg-out 95.4%

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

   8. *-commutative 95.4%

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

   9. neg-mul-1 95.4%

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

   10. remove-double-neg 95.4%

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

   11. cancel-sign-sub-inv 95.4%

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

   12. +-commutative 95.4%

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

   13. distribute-lft-neg-out 95.4%

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

   14. metadata-eval 95.4%

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

   15. distribute-neg-in 95.4%

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

   16. fma-def 95.4%

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

3. Simplified 95.4%

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

4. Taylor expanded in y around 0 46.3%

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

5. Final simplification 46.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))