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

Percentage Accurate: 95.6% → 99.2%

Time: 8.6s

Alternatives: 6

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: 95.6% 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: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+106}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+239)
   (- 0.0 (* z (* y x)))
   (if (<= (* y z) 1e+106) (- x (* (* y z) x)) (* y (- 0.0 (* z x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+239) {
		tmp = 0.0 - (z * (y * x));
	} else if ((y * z) <= 1e+106) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (0.0 - (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) :: tmp
    if ((y * z) <= (-5d+239)) then
        tmp = 0.0d0 - (z * (y * x))
    else if ((y * z) <= 1d+106) then
        tmp = x - ((y * z) * x)
    else
        tmp = y * (0.0d0 - (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 tmp;
	if ((y * z) <= -5e+239) {
		tmp = 0.0 - (z * (y * x));
	} else if ((y * z) <= 1e+106) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (0.0 - (z * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+239:
		tmp = 0.0 - (z * (y * x))
	elif (y * z) <= 1e+106:
		tmp = x - ((y * z) * x)
	else:
		tmp = y * (0.0 - (z * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5e+239)
		tmp = Float64(0.0 - Float64(z * Float64(y * x)));
	elseif (Float64(y * z) <= 1e+106)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(y * Float64(0.0 - Float64(z * 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) <= -5e+239)
		tmp = 0.0 - (z * (y * x));
	elseif ((y * z) <= 1e+106)
		tmp = x - ((y * z) * x);
	else
		tmp = y * (0.0 - (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_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+239], N[(0.0 - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1e+106], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.0 - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000007e239

   1. Initial program 82.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 99.7%

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

   5. Simplified 99.7%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -5.00000000000000007e239 < (*.f64 y z) < 1.00000000000000009e106

   1. Initial program 99.8%

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

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

   if 1.00000000000000009e106 < (*.f64 y z)

   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. 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 97.9%

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

   5. Simplified 97.9%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 97.9%

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

   7. Applied egg-rr 97.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+106}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -20000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

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) (- 0.0 x))))
   (if (<= (* y z) -5e+239)
     (- 0.0 (* z (* y x)))
     (if (<= (* y z) -20000.0)
       t_0
       (if (<= (* y z) 2e-9)
         x
         (if (<= (* y z) 1e+106) t_0 (* y (- 0.0 (* z x)))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (y * z) * (0.0 - x);
	double tmp;
	if ((y * z) <= -5e+239) {
		tmp = 0.0 - (z * (y * x));
	} else if ((y * z) <= -20000.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-9) {
		tmp = x;
	} else if ((y * z) <= 1e+106) {
		tmp = t_0;
	} else {
		tmp = y * (0.0 - (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) * (0.0d0 - x)
    if ((y * z) <= (-5d+239)) then
        tmp = 0.0d0 - (z * (y * x))
    else if ((y * z) <= (-20000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-9) then
        tmp = x
    else if ((y * z) <= 1d+106) then
        tmp = t_0
    else
        tmp = y * (0.0d0 - (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) * (0.0 - x);
	double tmp;
	if ((y * z) <= -5e+239) {
		tmp = 0.0 - (z * (y * x));
	} else if ((y * z) <= -20000.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-9) {
		tmp = x;
	} else if ((y * z) <= 1e+106) {
		tmp = t_0;
	} else {
		tmp = y * (0.0 - (z * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (y * z) * (0.0 - x)
	tmp = 0
	if (y * z) <= -5e+239:
		tmp = 0.0 - (z * (y * x))
	elif (y * z) <= -20000.0:
		tmp = t_0
	elif (y * z) <= 2e-9:
		tmp = x
	elif (y * z) <= 1e+106:
		tmp = t_0
	else:
		tmp = y * (0.0 - (z * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(y * z) * Float64(0.0 - x))
	tmp = 0.0
	if (Float64(y * z) <= -5e+239)
		tmp = Float64(0.0 - Float64(z * Float64(y * x)));
	elseif (Float64(y * z) <= -20000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-9)
		tmp = x;
	elseif (Float64(y * z) <= 1e+106)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(0.0 - 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) * (0.0 - x);
	tmp = 0.0;
	if ((y * z) <= -5e+239)
		tmp = 0.0 - (z * (y * x));
	elseif ((y * z) <= -20000.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-9)
		tmp = x;
	elseif ((y * z) <= 1e+106)
		tmp = t_0;
	else
		tmp = y * (0.0 - (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] * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5e+239], N[(0.0 - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], -20000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-9], x, If[LessEqual[N[(y * z), $MachinePrecision], 1e+106], t$95$0, N[(y * N[(0.0 - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 y z) < -5.00000000000000007e239

   1. Initial program 82.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 99.7%

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

   5. Simplified 99.7%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -5.00000000000000007e239 < (*.f64 y z) < -2e4 or 2.00000000000000012e-9 < (*.f64 y z) < 1.00000000000000009e106

   1. Initial program 99.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 80.1%

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

   5. Simplified 80.1%

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

   7. Applied egg-rr 97.1%

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

   if -2e4 < (*.f64 y z) < 2.00000000000000012e-9

   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 98.1%

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

   if 1.00000000000000009e106 < (*.f64 y z)

   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. 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 97.9%

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

   5. Simplified 97.9%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 97.9%

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

   7. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{\left(-x \cdot z\right) \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -20000:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 10^{+106}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(y \cdot z\right) \cdot \left(0 - x\right)\\ t_1 := 0 - z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -20000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) (- 0.0 x))) (t_1 (- 0.0 (* z (* y x)))))
   (if (<= (* y z) -5e+239)
     t_1
     (if (<= (* y z) -20000.0)
       t_0
       (if (<= (* y z) 2e-9) x (if (<= (* y z) 5e+299) t_0 t_1))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (y * z) * (0.0 - x);
	double t_1 = 0.0 - (z * (y * x));
	double tmp;
	if ((y * z) <= -5e+239) {
		tmp = t_1;
	} else if ((y * z) <= -20000.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-9) {
		tmp = x;
	} else if ((y * z) <= 5e+299) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = (y * z) * (0.0d0 - x)
    t_1 = 0.0d0 - (z * (y * x))
    if ((y * z) <= (-5d+239)) then
        tmp = t_1
    else if ((y * z) <= (-20000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-9) then
        tmp = x
    else if ((y * z) <= 5d+299) then
        tmp = t_0
    else
        tmp = t_1
    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) * (0.0 - x);
	double t_1 = 0.0 - (z * (y * x));
	double tmp;
	if ((y * z) <= -5e+239) {
		tmp = t_1;
	} else if ((y * z) <= -20000.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-9) {
		tmp = x;
	} else if ((y * z) <= 5e+299) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (y * z) * (0.0 - x)
	t_1 = 0.0 - (z * (y * x))
	tmp = 0
	if (y * z) <= -5e+239:
		tmp = t_1
	elif (y * z) <= -20000.0:
		tmp = t_0
	elif (y * z) <= 2e-9:
		tmp = x
	elif (y * z) <= 5e+299:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(y * z) * Float64(0.0 - x))
	t_1 = Float64(0.0 - Float64(z * Float64(y * x)))
	tmp = 0.0
	if (Float64(y * z) <= -5e+239)
		tmp = t_1;
	elseif (Float64(y * z) <= -20000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-9)
		tmp = x;
	elseif (Float64(y * z) <= 5e+299)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (y * z) * (0.0 - x);
	t_1 = 0.0 - (z * (y * x));
	tmp = 0.0;
	if ((y * z) <= -5e+239)
		tmp = t_1;
	elseif ((y * z) <= -20000.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-9)
		tmp = x;
	elseif ((y * z) <= 5e+299)
		tmp = t_0;
	else
		tmp = t_1;
	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] * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.0 - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5e+239], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -20000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-9], x, If[LessEqual[N[(y * z), $MachinePrecision], 5e+299], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000007e239 or 5.0000000000000003e299 < (*.f64 y z)

   1. Initial program 76.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 99.8%

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -5.00000000000000007e239 < (*.f64 y z) < -2e4 or 2.00000000000000012e-9 < (*.f64 y z) < 5.0000000000000003e299

   1. Initial program 99.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. 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 84.5%

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

   5. Simplified 84.5%

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

   7. Applied egg-rr 97.8%

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

   if -2e4 < (*.f64 y z) < 2.00000000000000012e-9

   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 98.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -20000:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+239)
   (- 0.0 (* z (* y x)))
   (if (<= (* y z) 1e+106) (* x (- 1.0 (* y z))) (* y (- 0.0 (* z x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+239) {
		tmp = 0.0 - (z * (y * x));
	} else if ((y * z) <= 1e+106) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (0.0 - (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) :: tmp
    if ((y * z) <= (-5d+239)) then
        tmp = 0.0d0 - (z * (y * x))
    else if ((y * z) <= 1d+106) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (0.0d0 - (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 tmp;
	if ((y * z) <= -5e+239) {
		tmp = 0.0 - (z * (y * x));
	} else if ((y * z) <= 1e+106) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (0.0 - (z * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+239:
		tmp = 0.0 - (z * (y * x))
	elif (y * z) <= 1e+106:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (0.0 - (z * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5e+239)
		tmp = Float64(0.0 - Float64(z * Float64(y * x)));
	elseif (Float64(y * z) <= 1e+106)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(0.0 - Float64(z * 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) <= -5e+239)
		tmp = 0.0 - (z * (y * x));
	elseif ((y * z) <= 1e+106)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (0.0 - (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_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+239], N[(0.0 - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1e+106], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.0 - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5.00000000000000007e239

   1. Initial program 82.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 99.7%

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

   5. Simplified 99.7%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -5.00000000000000007e239 < (*.f64 y z) < 1.00000000000000009e106

   1. Initial program 99.8%

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

   if 1.00000000000000009e106 < (*.f64 y z)

   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. 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 97.9%

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

   5. Simplified 97.9%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 97.9%

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

   7. Applied egg-rr 97.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+239}:\\ \;\;\;\;0 - z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{if}\;y \cdot z \leq -20000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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) (- 0.0 x))))
   (if (<= (* y z) -20000.0) t_0 (if (<= (* y z) 2e-9) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (y * z) * (0.0 - x);
	double tmp;
	if ((y * z) <= -20000.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-9) {
		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) * (0.0d0 - x)
    if ((y * z) <= (-20000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-9) 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) * (0.0 - x);
	double tmp;
	if ((y * z) <= -20000.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-9) {
		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) * (0.0 - x)
	tmp = 0
	if (y * z) <= -20000.0:
		tmp = t_0
	elif (y * z) <= 2e-9:
		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(y * z) * Float64(0.0 - x))
	tmp = 0.0
	if (Float64(y * z) <= -20000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-9)
		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) * (0.0 - x);
	tmp = 0.0;
	if ((y * z) <= -20000.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-9)
		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] * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -20000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-9], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e4 or 2.00000000000000012e-9 < (*.f64 y z)

   1. Initial program 92.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 89.7%

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

   5. Simplified 89.7%

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

   7. Applied egg-rr 90.7%

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

   if -2e4 < (*.f64 y z) < 2.00000000000000012e-9

   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 98.1%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(0 - x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(0 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.9% 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 95.4%

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

3. Taylor expanded in y around 0

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

5. Simplified 44.5%

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))