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

Percentage Accurate: 95.9% → 99.8%

Time: 8.1s

Alternatives: 5

Speedup: 0.3×

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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0 - y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+283}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (- 0.0 (* y (* z x)))))
   (if (<= (* y z) -1.4e+197)
     t_0
     (if (<= (* y z) 5e+283) (- x (* (* y z) x)) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.0 - (y * (z * x));
	double tmp;
	if ((y * z) <= -1.4e+197) {
		tmp = t_0;
	} else if ((y * z) <= 5e+283) {
		tmp = x - ((y * z) * 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 = 0.0d0 - (y * (z * x))
    if ((y * z) <= (-1.4d+197)) then
        tmp = t_0
    else if ((y * z) <= 5d+283) then
        tmp = x - ((y * z) * 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 = 0.0 - (y * (z * x));
	double tmp;
	if ((y * z) <= -1.4e+197) {
		tmp = t_0;
	} else if ((y * z) <= 5e+283) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 0.0 - (y * (z * x))
	tmp = 0
	if (y * z) <= -1.4e+197:
		tmp = t_0
	elif (y * z) <= 5e+283:
		tmp = x - ((y * z) * x)
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(0.0 - Float64(y * Float64(z * x)))
	tmp = 0.0
	if (Float64(y * z) <= -1.4e+197)
		tmp = t_0;
	elseif (Float64(y * z) <= 5e+283)
		tmp = Float64(x - Float64(Float64(y * z) * 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 = 0.0 - (y * (z * x));
	tmp = 0.0;
	if ((y * z) <= -1.4e+197)
		tmp = t_0;
	elseif ((y * z) <= 5e+283)
		tmp = x - ((y * z) * 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[(0.0 - N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -1.4e+197], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 5e+283], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.3999999999999999e197 or 5.0000000000000004e283 < (*.f64 y z)

   1. Initial program 73.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x \cdot \left(y \cdot z\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(y \cdot x\right) \cdot z\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 97.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 97.4%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(x \cdot z\right)\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(x \cdot z\right)\right), y\right) \]

      6. *-lowering-*.f64 97.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, z\right)\right), y\right) \]

   7. Applied egg-rr 97.4%

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

   if -1.3999999999999999e197 < (*.f64 y z) < 5.0000000000000004e283

   1. Initial program 99.9%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. fma-define N/A

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

      4. distribute-lft-neg-out N/A

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

      5. fmm-undef N/A

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

      6. *-lft-identity N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{x}\right)\right) \]

      9. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right)\right) \]

   4. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;0 - y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+283}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;0 - y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0 - y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+283}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (- 0.0 (* y (* z x)))))
   (if (<= (* y z) -1.4e+197)
     t_0
     (if (<= (* y z) 5e+283) (* x (- 1.0 (* y z))) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.0 - (y * (z * x));
	double tmp;
	if ((y * z) <= -1.4e+197) {
		tmp = t_0;
	} else if ((y * z) <= 5e+283) {
		tmp = x * (1.0 - (y * z));
	} 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 = 0.0d0 - (y * (z * x))
    if ((y * z) <= (-1.4d+197)) then
        tmp = t_0
    else if ((y * z) <= 5d+283) then
        tmp = x * (1.0d0 - (y * z))
    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 = 0.0 - (y * (z * x));
	double tmp;
	if ((y * z) <= -1.4e+197) {
		tmp = t_0;
	} else if ((y * z) <= 5e+283) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 0.0 - (y * (z * x))
	tmp = 0
	if (y * z) <= -1.4e+197:
		tmp = t_0
	elif (y * z) <= 5e+283:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(0.0 - Float64(y * Float64(z * x)))
	tmp = 0.0
	if (Float64(y * z) <= -1.4e+197)
		tmp = t_0;
	elseif (Float64(y * z) <= 5e+283)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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 = 0.0 - (y * (z * x));
	tmp = 0.0;
	if ((y * z) <= -1.4e+197)
		tmp = t_0;
	elseif ((y * z) <= 5e+283)
		tmp = x * (1.0 - (y * z));
	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[(0.0 - N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -1.4e+197], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 5e+283], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.3999999999999999e197 or 5.0000000000000004e283 < (*.f64 y z)

   1. Initial program 73.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x \cdot \left(y \cdot z\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(y \cdot x\right) \cdot z\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 97.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 97.4%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(x \cdot z\right)\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(x \cdot z\right)\right), y\right) \]

      6. *-lowering-*.f64 97.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, z\right)\right), y\right) \]

   7. Applied egg-rr 97.4%

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

   if -1.3999999999999999e197 < (*.f64 y z) < 5.0000000000000004e283

   1. Initial program 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1.4 \cdot 10^{+197}:\\ \;\;\;\;0 - y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+283}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;0 - y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2:\\ \;\;\;\;0 - y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -2.0)
   (- 0.0 (* y (* z x)))
   (if (<= (* y z) 0.1) x (- 0.0 (* z (* y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2.0) {
		tmp = 0.0 - (y * (z * x));
	} else if ((y * z) <= 0.1) {
		tmp = x;
	} else {
		tmp = 0.0 - (z * (y * x));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-2.0d0)) then
        tmp = 0.0d0 - (y * (z * x))
    else if ((y * z) <= 0.1d0) then
        tmp = x
    else
        tmp = 0.0d0 - (z * (y * x))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2.0) {
		tmp = 0.0 - (y * (z * x));
	} else if ((y * z) <= 0.1) {
		tmp = x;
	} else {
		tmp = 0.0 - (z * (y * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -2.0:
		tmp = 0.0 - (y * (z * x))
	elif (y * z) <= 0.1:
		tmp = x
	else:
		tmp = 0.0 - (z * (y * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -2.0)
		tmp = Float64(0.0 - Float64(y * Float64(z * x)));
	elseif (Float64(y * z) <= 0.1)
		tmp = x;
	else
		tmp = Float64(0.0 - Float64(z * Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -2.0)
		tmp = 0.0 - (y * (z * x));
	elseif ((y * z) <= 0.1)
		tmp = x;
	else
		tmp = 0.0 - (z * (y * x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -2.0], N[(0.0 - N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.1], x, N[(0.0 - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 90.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x \cdot \left(y \cdot z\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(y \cdot x\right) \cdot z\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 88.0%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-lft-neg-in N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(x \cdot z\right)\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(x \cdot z\right)\right), y\right) \]

      6. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, z\right)\right), y\right) \]

   7. Applied egg-rr 88.0%

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

   if -2 < (*.f64 y z) < 0.10000000000000001

   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 98.4%

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

   if 0.10000000000000001 < (*.f64 y z)

   1. Initial program 92.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x \cdot \left(y \cdot z\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(y \cdot x\right) \cdot z\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 88.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 88.3%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. associate-*r* N/A

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

      3. distribute-lft-neg-in N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y \cdot x\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(y \cdot x\right)\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(x \cdot y\right)\right), z\right) \]

      7. *-lowering-*.f64 90.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, y\right)\right), z\right) \]

   7. Applied egg-rr 90.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2:\\ \;\;\;\;0 - y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 0.1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0 - z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (- 0.0 (* z (* y x)))))
   (if (<= y -1.3e+117) t_0 (if (<= y 2.6e-85) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.0 - (z * (y * x));
	double tmp;
	if (y <= -1.3e+117) {
		tmp = t_0;
	} else if (y <= 2.6e-85) {
		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 = 0.0d0 - (z * (y * x))
    if (y <= (-1.3d+117)) then
        tmp = t_0
    else if (y <= 2.6d-85) 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 = 0.0 - (z * (y * x));
	double tmp;
	if (y <= -1.3e+117) {
		tmp = t_0;
	} else if (y <= 2.6e-85) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 0.0 - (z * (y * x))
	tmp = 0
	if y <= -1.3e+117:
		tmp = t_0
	elif y <= 2.6e-85:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(0.0 - Float64(z * Float64(y * x)))
	tmp = 0.0
	if (y <= -1.3e+117)
		tmp = t_0;
	elseif (y <= 2.6e-85)
		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 = 0.0 - (z * (y * x));
	tmp = 0.0;
	if (y <= -1.3e+117)
		tmp = t_0;
	elseif (y <= 2.6e-85)
		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[(0.0 - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.3e+117], t$95$0, If[LessEqual[y, 2.6e-85], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e117 or 2.60000000000000011e-85 < y

   1. Initial program 93.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{x \cdot \left(y \cdot z\right)} \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(x \cdot \left(y \cdot z\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(x \cdot y\right) \cdot \color{blue}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(y \cdot x\right) \cdot z\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(y \cdot \color{blue}{\left(x \cdot z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \color{blue}{\left(x \cdot z\right)}\right)\right) \]

      8. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. associate-*r* N/A

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

      3. distribute-lft-neg-in N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(y \cdot x\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(y \cdot x\right)\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\left(x \cdot y\right)\right), z\right) \]

      7. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(x, y\right)\right), z\right) \]

   7. Applied egg-rr 66.3%

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

   if -1.3e117 < y < 2.60000000000000011e-85

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 75.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+117}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in y around 0

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

5. Simplified 53.9%

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))