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

Percentage Accurate: 95.8% → 99.8%

Time: 9.0s

Alternatives: 8

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: 95.8% 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

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \frac{z}{\frac{-1}{x}}\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

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) -5e+219)
   (* y (/ z (/ -1.0 x)))
   (if (<= (* y z) 2e+222) (* x (- 1.0 (* y z))) (* (- 0.0 z) (* y x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+219) {
		tmp = y * (z / (-1.0 / x));
	} else if ((y * z) <= 2e+222) {
		tmp = x * (1.0 - (y * z));
	} 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) <= (-5d+219)) then
        tmp = y * (z / ((-1.0d0) / x))
    else if ((y * z) <= 2d+222) then
        tmp = x * (1.0d0 - (y * z))
    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) <= -5e+219) {
		tmp = y * (z / (-1.0 / x));
	} else if ((y * z) <= 2e+222) {
		tmp = x * (1.0 - (y * z));
	} 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) <= -5e+219:
		tmp = y * (z / (-1.0 / x))
	elif (y * z) <= 2e+222:
		tmp = x * (1.0 - (y * z))
	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) <= -5e+219)
		tmp = Float64(y * Float64(z / Float64(-1.0 / x)));
	elseif (Float64(y * z) <= 2e+222)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(Float64(0.0 - 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) <= -5e+219)
		tmp = y * (z / (-1.0 / x));
	elseif ((y * z) <= 2e+222)
		tmp = x * (1.0 - (y * z));
	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], -5e+219], N[(y * N[(z / N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 2e+222], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.0 - z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5e219

   1. Initial program 77.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(x \cdot z\right)\right)}\right) \]

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 99.9%

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

   5. Simplified 99.9%

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

      1. sub0-neg N/A

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

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

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.9%

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

   7. Applied egg-rr 99.9%

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

      1. *-commutative N/A

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

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

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

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

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

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

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

      5. remove-double-div N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(z \cdot \frac{1}{\frac{1}{x}}\right)\right), y\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{z}{\frac{1}{x}}\right)\right), y\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{\mathsf{neg}\left(\frac{1}{x}\right)}\right), y\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)\right), y\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{\mathsf{neg}\left(1\right)}{x}\right)\right), y\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\frac{-1}{x}\right)\right), y\right) \]

      11. /-lowering-/.f64 99.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \mathsf{/.f64}\left(-1, x\right)\right), y\right) \]

   9. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{-1}{x}} \cdot y} \]

   if -5e219 < (*.f64 y z) < 2.0000000000000001e222

   1. Initial program 99.8%

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

   if 2.0000000000000001e222 < (*.f64 y z)

   1. Initial program 74.2%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(x \cdot z\right)\right)}\right) \]

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 99.8%

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

   5. Simplified 99.8%

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

      1. sub0-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \frac{z}{\frac{-1}{x}}\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, y \cdot x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.55e+113) (fma (- 0.0 z) (* y x) x) (- x (* x (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e+113) {
		tmp = fma((0.0 - z), (y * x), x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.55e+113)
		tmp = fma(Float64(0.0 - z), Float64(y * x), x);
	else
		tmp = Float64(x - Float64(x * Float64(y * z)));
	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[y, -2.55e+113], N[(N[(0.0 - z), $MachinePrecision] * N[(y * x), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999997e113

   1. Initial program 92.1%

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

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

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

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

      7. associate-*l* N/A

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

      8. fma-define N/A

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

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

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

      10. neg-sub0 N/A

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

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

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

      12. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   if -2.54999999999999997e113 < y

   1. Initial program 95.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 95.2%

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

   4. Applied egg-rr 95.2%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(0 - z, y \cdot x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(0 - z\right) \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(y \cdot \left(0 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 z) (* y x))))
   (if (<= (* y z) -500.0)
     t_0
     (if (<= (* y z) 1.0)
       x
       (if (<= (* y z) 2e+222) (* x (* y (- 0.0 z))) 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 * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 1.0) {
		tmp = x;
	} else if ((y * z) <= 2e+222) {
		tmp = x * (y * (0.0 - 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 - z) * (y * x)
    if ((y * z) <= (-500.0d0)) then
        tmp = t_0
    else if ((y * z) <= 1.0d0) then
        tmp = x
    else if ((y * z) <= 2d+222) then
        tmp = x * (y * (0.0d0 - 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 - z) * (y * x);
	double tmp;
	if ((y * z) <= -500.0) {
		tmp = t_0;
	} else if ((y * z) <= 1.0) {
		tmp = x;
	} else if ((y * z) <= 2e+222) {
		tmp = x * (y * (0.0 - z));
	} 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 * z) <= -500.0:
		tmp = t_0
	elif (y * z) <= 1.0:
		tmp = x
	elif (y * z) <= 2e+222:
		tmp = x * (y * (0.0 - z))
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(0.0 - z) * Float64(y * x))
	tmp = 0.0
	if (Float64(y * z) <= -500.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 1.0)
		tmp = x;
	elseif (Float64(y * z) <= 2e+222)
		tmp = Float64(x * Float64(y * Float64(0.0 - 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 - z) * (y * x);
	tmp = 0.0;
	if ((y * z) <= -500.0)
		tmp = t_0;
	elseif ((y * z) <= 1.0)
		tmp = x;
	elseif ((y * z) <= 2e+222)
		tmp = x * (y * (0.0 - 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[(N[(0.0 - z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -500.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 1.0], x, If[LessEqual[N[(y * z), $MachinePrecision], 2e+222], N[(x * N[(y * N[(0.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -500 or 2.0000000000000001e222 < (*.f64 y z)

   1. Initial program 84.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(x \cdot z\right)\right)}\right) \]

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 91.0%

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

   5. Simplified 91.0%

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

      1. sub0-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 92.8%

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

   7. Applied egg-rr 92.8%

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

   if -500 < (*.f64 y z) < 1

   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 97.9%

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

   if 1 < (*.f64 y z) < 2.0000000000000001e222

   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(x \cdot z\right)\right)}\right) \]

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 89.1%

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

   5. Simplified 89.1%

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

      1. sub0-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 79.0%

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

   7. Applied egg-rr 79.0%

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

      1. associate-*r* N/A

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 95.5%

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

   9. Applied egg-rr 95.5%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -500:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(y \cdot \left(0 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(0 - z\right) \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+231}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 z) (* y x))))
   (if (<= (* y z) -5e+231)
     t_0
     (if (<= (* y z) 2e+222) (* 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 - z) * (y * x);
	double tmp;
	if ((y * z) <= -5e+231) {
		tmp = t_0;
	} else if ((y * z) <= 2e+222) {
		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 - z) * (y * x)
    if ((y * z) <= (-5d+231)) then
        tmp = t_0
    else if ((y * z) <= 2d+222) 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 - z) * (y * x);
	double tmp;
	if ((y * z) <= -5e+231) {
		tmp = t_0;
	} else if ((y * z) <= 2e+222) {
		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 - z) * (y * x)
	tmp = 0
	if (y * z) <= -5e+231:
		tmp = t_0
	elif (y * z) <= 2e+222:
		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(Float64(0.0 - z) * Float64(y * x))
	tmp = 0.0
	if (Float64(y * z) <= -5e+231)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e+222)
		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 - z) * (y * x);
	tmp = 0.0;
	if ((y * z) <= -5e+231)
		tmp = t_0;
	elseif ((y * z) <= 2e+222)
		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[(N[(0.0 - z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5e+231], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e+222], 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) < -5.00000000000000028e231 or 2.0000000000000001e222 < (*.f64 y z)

   1. Initial program 75.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(x \cdot z\right)\right)}\right) \]

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 99.8%

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

   5. Simplified 99.8%

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

      1. sub0-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -5.00000000000000028e231 < (*.f64 y z) < 2.0000000000000001e222

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+231}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(0 - z\right) \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -6.3 \cdot 10^{+63}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 -6.3e+63) t_0 (if (<= y 6.8e-105) 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 <= -6.3e+63) {
		tmp = t_0;
	} else if (y <= 6.8e-105) {
		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 <= (-6.3d+63)) then
        tmp = t_0
    else if (y <= 6.8d-105) 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 <= -6.3e+63) {
		tmp = t_0;
	} else if (y <= 6.8e-105) {
		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 <= -6.3e+63:
		tmp = t_0
	elif y <= 6.8e-105:
		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(0.0 - z) * Float64(y * x))
	tmp = 0.0
	if (y <= -6.3e+63)
		tmp = t_0;
	elseif (y <= 6.8e-105)
		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 <= -6.3e+63)
		tmp = t_0;
	elseif (y <= 6.8e-105)
		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[(0.0 - z), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.3e+63], t$95$0, If[LessEqual[y, 6.8e-105], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2999999999999998e63 or 6.79999999999999984e-105 < y

   1. Initial program 89.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(x \cdot z\right)\right)}\right) \]

      7. mul-1-neg N/A

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

      8. neg-sub0 N/A

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

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

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

      10. *-lowering-*.f64 68.8%

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

   5. Simplified 68.8%

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

      1. sub0-neg N/A

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

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

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

      3. *-commutative N/A

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

      4. associate-*l* N/A

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

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

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. *-lowering-*.f64 69.7%

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

   7. Applied egg-rr 69.7%

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

   if -6.2999999999999998e63 < y < 6.79999999999999984e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 69.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+63}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+113}:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.55e+113) (- x (* z (* y x))) (- x (* x (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.55e+113) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x - (x * (y * z));
	}
	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 <= (-2.55d+113)) then
        tmp = x - (z * (y * x))
    else
        tmp = x - (x * (y * z))
    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 <= -2.55e+113) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -2.55e+113:
		tmp = x - (z * (y * x))
	else:
		tmp = x - (x * (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.55e+113)
		tmp = Float64(x - Float64(z * Float64(y * x)));
	else
		tmp = Float64(x - Float64(x * Float64(y * z)));
	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 <= -2.55e+113)
		tmp = x - (z * (y * x));
	else
		tmp = x - (x * (y * z));
	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[y, -2.55e+113], N[(x - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999997e113

   1. Initial program 92.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 92.1%

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

   4. Applied egg-rr 92.1%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -2.54999999999999997e113 < y

   1. Initial program 95.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 95.2%

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

   4. Applied egg-rr 95.2%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+113}:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e+113) (- x (* z (* y x))) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e+113) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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 <= (-2.9d+113)) then
        tmp = x - (z * (y * x))
    else
        tmp = x * (1.0d0 - (y * z))
    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 <= -2.9e+113) {
		tmp = x - (z * (y * x));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -2.9e+113:
		tmp = x - (z * (y * x))
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e+113)
		tmp = Float64(x - Float64(z * Float64(y * x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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 <= -2.9e+113)
		tmp = x - (z * (y * x));
	else
		tmp = x * (1.0 - (y * z));
	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[y, -2.9e+113], N[(x - N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999984e113

   1. Initial program 92.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 92.1%

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

   4. Applied egg-rr 92.1%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

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

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

      5. *-lowering-*.f64 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -2.89999999999999984e113 < y

   1. Initial program 95.1%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;x - z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% 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 94.7%

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

3. Taylor expanded in y around 0

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

5. Simplified 49.5%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))