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

Percentage Accurate: 95.9% → 97.0%

Time: 10.3s

Alternatives: 6

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: 95.9% 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: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -1 \cdot 10^{+75}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-1}{\mathsf{fma}\left(y, z, -1\right)}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 (* y z)) -1e+75)
   (- (* z (* y x)))
   (/ x (/ -1.0 (fma y z -1.0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - (y * z)) <= -1e+75) {
		tmp = -(z * (y * x));
	} else {
		tmp = x / (-1.0 / fma(y, z, -1.0));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - Float64(y * z)) <= -1e+75)
		tmp = Float64(-Float64(z * Float64(y * x)));
	else
		tmp = Float64(x / Float64(-1.0 / fma(y, z, -1.0)));
	end
	return 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[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], -1e+75], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), N[(x / N[(-1.0 / N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -9.99999999999999927e74

   1. Initial program 87.0%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 96.1

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

   5. Simplified 96.1%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-lowering-neg.f64 96.1

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

   7. Applied egg-rr 96.1%

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

   if -9.99999999999999927e74 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 98.9%

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

      1. flip-- N/A

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

      2. metadata-eval N/A

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

      3. div-sub N/A

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

      4. swap-sqr N/A

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

      5. associate-/l* N/A

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

      6. cancel-sign-sub-inv N/A

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

      7. +-lowering-+.f64 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. *-lowering-*.f64 N/A

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

      12. neg-lowering-neg.f64 N/A

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

      13. *-lowering-*.f64 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. *-lowering-*.f64 N/A

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

      16. +-commutative N/A

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

      17. accelerator-lowering-fma.f64 75.8

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

   4. Applied egg-rr 75.8%

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

      1. flip3-+ N/A

         \[\leadsto x \cdot \color{blue}{\frac{{\left(\frac{1}{y \cdot z + 1}\right)}^{3} + {\left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right)}^{3}}{\frac{1}{y \cdot z + 1} \cdot \frac{1}{y \cdot z + 1} + \left(\left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right) \cdot \left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right) - \frac{1}{y \cdot z + 1} \cdot \left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right)\right)}} \]

      2. clear-num N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{\frac{1}{y \cdot z + 1} \cdot \frac{1}{y \cdot z + 1} + \left(\left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right) \cdot \left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right) - \frac{1}{y \cdot z + 1} \cdot \left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right)\right)}{{\left(\frac{1}{y \cdot z + 1}\right)}^{3} + {\left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right)}^{3}}}} \]

      3. un-div-inv N/A

         \[\leadsto \color{blue}{\frac{x}{\frac{\frac{1}{y \cdot z + 1} \cdot \frac{1}{y \cdot z + 1} + \left(\left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right) \cdot \left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right) - \frac{1}{y \cdot z + 1} \cdot \left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right)\right)}{{\left(\frac{1}{y \cdot z + 1}\right)}^{3} + {\left(\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \frac{z \cdot z}{y \cdot z + 1}\right)}^{3}}}} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{-1}{\mathsf{fma}\left(y, z, -1\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -1 \cdot 10^{+75}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-1}{\mathsf{fma}\left(y, z, -1\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -\left(y \cdot z\right) \cdot x\\ \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+121}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (* y z) x))))
   (if (<= (* y z) -500.0)
     t_0
     (if (<= (* y z) 2e-5) x (if (<= (* y z) 5e+121) t_0 (- (* y (* z x))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -((y * z) * x);
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x;
	} else if ((y * z) <= 5e+121) {
		tmp = t_0;
	} else {
		tmp = -(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) :: t_0
    real(8) :: tmp
    t_0 = -((y * z) * x)
    if ((y * z) <= (-500.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-5) then
        tmp = x
    else if ((y * z) <= 5d+121) then
        tmp = t_0
    else
        tmp = -(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 t_0 = -((y * z) * x);
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x;
	} else if ((y * z) <= 5e+121) {
		tmp = t_0;
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -((y * z) * x)
	tmp = 0
	if (y * z) <= -500.0:
		tmp = t_0
	elif (y * z) <= 2e-5:
		tmp = x
	elif (y * z) <= 5e+121:
		tmp = t_0
	else:
		tmp = -(y * (z * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(Float64(y * z) * x))
	tmp = 0.0
	if (Float64(y * z) <= -500.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-5)
		tmp = x;
	elseif (Float64(y * z) <= 5e+121)
		tmp = t_0;
	else
		tmp = Float64(-Float64(y * Float64(z * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -((y * z) * x);
	tmp = 0.0;
	if ((y * z) <= -500.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-5)
		tmp = x;
	elseif ((y * z) <= 5e+121)
		tmp = t_0;
	else
		tmp = -(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_] := Block[{t$95$0 = (-N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -500.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-5], x, If[LessEqual[N[(y * z), $MachinePrecision], 5e+121], t$95$0, (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -500 or 2.00000000000000016e-5 < (*.f64 y z) < 5.00000000000000007e121

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 94.2

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

   5. Simplified 94.2%

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

   if -500 < (*.f64 y z) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 98.6%

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

   if 5.00000000000000007e121 < (*.f64 y z)

   1. Initial program 84.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 99.8

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

   5. Simplified 99.8%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+121}:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* z (* y x)))))
   (if (<= (* y z) -500.0) t_0 (if (<= (* y z) 2e-5) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -(z * (y * x));
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = -(z * (y * x))
    if ((y * z) <= (-500.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-5) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -(z * (y * x));
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -(z * (y * x))
	tmp = 0
	if (y * z) <= -500.0:
		tmp = t_0
	elif (y * z) <= 2e-5:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(z * Float64(y * x)))
	tmp = 0.0
	if (Float64(y * z) <= -500.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-5)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -(z * (y * x));
	tmp = 0.0;
	if ((y * z) <= -500.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-5)
		tmp = x;
	else
		tmp = t_0;
	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_] := Block[{t$95$0 = (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -500.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-5], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -500 or 2.00000000000000016e-5 < (*.f64 y z)

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 89.8

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

   5. Simplified 89.8%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-lowering-neg.f64 93.7

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

   7. Applied egg-rr 93.7%

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

   if -500 < (*.f64 y z) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 98.6%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -\left(y \cdot z\right) \cdot x\\ \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (* y z) x))))
   (if (<= (* y z) -500.0) t_0 (if (<= (* y z) 2e-5) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -((y * z) * x);
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = -((y * z) * x)
    if ((y * z) <= (-500.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-5) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -((y * z) * x);
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -((y * z) * x)
	tmp = 0
	if (y * z) <= -500.0:
		tmp = t_0
	elif (y * z) <= 2e-5:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(Float64(y * z) * x))
	tmp = 0.0
	if (Float64(y * z) <= -500.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-5)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -((y * z) * x);
	tmp = 0.0;
	if ((y * z) <= -500.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-5)
		tmp = x;
	else
		tmp = t_0;
	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_] := Block[{t$95$0 = (-N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -500.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-5], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -500 or 2.00000000000000016e-5 < (*.f64 y z)

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 90.8

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

   5. Simplified 90.8%

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

   if -500 < (*.f64 y z) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 98.6%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+94}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= t_0 -5e+94) (- (* z (* y x))) (* t_0 x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -5e+94) {
		tmp = -(z * (y * x));
	} else {
		tmp = t_0 * 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if (t_0 <= (-5d+94)) then
        tmp = -(z * (y * x))
    else
        tmp = t_0 * x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -5e+94) {
		tmp = -(z * (y * x));
	} else {
		tmp = t_0 * x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if t_0 <= -5e+94:
		tmp = -(z * (y * x))
	else:
		tmp = t_0 * x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= -5e+94)
		tmp = Float64(-Float64(z * Float64(y * x)));
	else
		tmp = Float64(t_0 * x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= -5e+94)
		tmp = -(z * (y * x));
	else
		tmp = t_0 * 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_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+94], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), N[(t$95$0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -5.0000000000000001e94

   1. Initial program 86.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. *-lowering-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. neg-lowering-neg.f64 95.9

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

   5. Simplified 95.9%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-lowering-*.f64 N/A

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

      5. neg-lowering-neg.f64 95.9

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

   7. Applied egg-rr 95.9%

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

   if -5.0000000000000001e94 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 98.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -5 \cdot 10^{+94}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 14.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 53.7%

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))