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

Percentage Accurate: 95.7% → 99.2%

Time: 8.3s

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: 95.7% 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

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{x}}{z}}\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

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) -1e+147)
   (/ y (/ (/ -1.0 x) z))
   (if (<= (* y z) 5e+117) (* 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) <= -1e+147) {
		tmp = y / ((-1.0 / x) / z);
	} else if ((y * z) <= 5e+117) {
		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) <= (-1d+147)) then
        tmp = y / (((-1.0d0) / x) / z)
    else if ((y * z) <= 5d+117) 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) <= -1e+147) {
		tmp = y / ((-1.0 / x) / z);
	} else if ((y * z) <= 5e+117) {
		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) <= -1e+147:
		tmp = y / ((-1.0 / x) / z)
	elif (y * z) <= 5e+117:
		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) <= -1e+147)
		tmp = Float64(y / Float64(Float64(-1.0 / x) / z));
	elseif (Float64(y * z) <= 5e+117)
		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) <= -1e+147)
		tmp = y / ((-1.0 / x) / z);
	elseif ((y * z) <= 5e+117)
		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], -1e+147], N[(y / N[(N[(-1.0 / x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+117], 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) < -9.9999999999999998e146

   1. Initial program 86.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 94.4%

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

   5. Simplified 94.4%

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

      1. sub0-neg N/A

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

      2. 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 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. *-commutative N/A

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

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

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

      3. associate-*r* N/A

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

      4. remove-double-div N/A

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

      5. metadata-eval N/A

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

      6. frac-2neg N/A

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

      7. div-inv N/A

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

      8. clear-num N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

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

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

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

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

      13. /-lowering-/.f64 97.1%

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

   9. Applied egg-rr 97.1%

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

   if -9.9999999999999998e146 < (*.f64 y z) < 4.99999999999999983e117

   1. Initial program 99.9%

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

   if 4.99999999999999983e117 < (*.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 98.0%

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

   5. Simplified 98.0%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 98.0%

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

   7. Applied egg-rr 98.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{\frac{\frac{-1}{x}}{z}}\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0 - \left(y \cdot z\right) \cdot x\\ t_1 := z \cdot \left(0 - y \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+269}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (- 0.0 (* (* y z) x))) (t_1 (* z (- 0.0 (* y x)))))
   (if (<= (* y z) -1e+194)
     t_1
     (if (<= (* y z) -50.0)
       t_0
       (if (<= (* y z) 4e-13) x (if (<= (* y z) 2e+269) t_0 t_1))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.0 - ((y * z) * x);
	double t_1 = z * (0.0 - (y * x));
	double tmp;
	if ((y * z) <= -1e+194) {
		tmp = t_1;
	} else if ((y * z) <= -50.0) {
		tmp = t_0;
	} else if ((y * z) <= 4e-13) {
		tmp = x;
	} else if ((y * z) <= 2e+269) {
		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 = 0.0d0 - ((y * z) * x)
    t_1 = z * (0.0d0 - (y * x))
    if ((y * z) <= (-1d+194)) then
        tmp = t_1
    else if ((y * z) <= (-50.0d0)) then
        tmp = t_0
    else if ((y * z) <= 4d-13) then
        tmp = x
    else if ((y * z) <= 2d+269) 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 = 0.0 - ((y * z) * x);
	double t_1 = z * (0.0 - (y * x));
	double tmp;
	if ((y * z) <= -1e+194) {
		tmp = t_1;
	} else if ((y * z) <= -50.0) {
		tmp = t_0;
	} else if ((y * z) <= 4e-13) {
		tmp = x;
	} else if ((y * z) <= 2e+269) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 0.0 - ((y * z) * x)
	t_1 = z * (0.0 - (y * x))
	tmp = 0
	if (y * z) <= -1e+194:
		tmp = t_1
	elif (y * z) <= -50.0:
		tmp = t_0
	elif (y * z) <= 4e-13:
		tmp = x
	elif (y * z) <= 2e+269:
		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(0.0 - Float64(Float64(y * z) * x))
	t_1 = Float64(z * Float64(0.0 - Float64(y * x)))
	tmp = 0.0
	if (Float64(y * z) <= -1e+194)
		tmp = t_1;
	elseif (Float64(y * z) <= -50.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 4e-13)
		tmp = x;
	elseif (Float64(y * z) <= 2e+269)
		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 = 0.0 - ((y * z) * x);
	t_1 = z * (0.0 - (y * x));
	tmp = 0.0;
	if ((y * z) <= -1e+194)
		tmp = t_1;
	elseif ((y * z) <= -50.0)
		tmp = t_0;
	elseif ((y * z) <= 4e-13)
		tmp = x;
	elseif ((y * z) <= 2e+269)
		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[(0.0 - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(0.0 - N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -1e+194], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -50.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 4e-13], x, If[LessEqual[N[(y * z), $MachinePrecision], 2e+269], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -9.99999999999999945e193 or 2.0000000000000001e269 < (*.f64 y z)

   1. Initial program 78.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 98.2%

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

   5. Simplified 98.2%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 -9.99999999999999945e193 < (*.f64 y z) < -50 or 4.0000000000000001e-13 < (*.f64 y z) < 2.0000000000000001e269

   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 79.4%

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

   5. Simplified 79.4%

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

   7. Applied egg-rr 95.4%

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

   if -50 < (*.f64 y z) < 4.0000000000000001e-13

   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 99.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(0 - y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -50:\\ \;\;\;\;0 - \left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+269}:\\ \;\;\;\;0 - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(0 - y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(0 - y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -50:\\ \;\;\;\;0 - \left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

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) -1e+194)
   (* z (- 0.0 (* y x)))
   (if (<= (* y z) -50.0)
     (- 0.0 (* (* y z) x))
     (if (<= (* y z) 4e-13) 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) <= -1e+194) {
		tmp = z * (0.0 - (y * x));
	} else if ((y * z) <= -50.0) {
		tmp = 0.0 - ((y * z) * x);
	} else if ((y * z) <= 4e-13) {
		tmp = 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) <= (-1d+194)) then
        tmp = z * (0.0d0 - (y * x))
    else if ((y * z) <= (-50.0d0)) then
        tmp = 0.0d0 - ((y * z) * x)
    else if ((y * z) <= 4d-13) then
        tmp = 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) <= -1e+194) {
		tmp = z * (0.0 - (y * x));
	} else if ((y * z) <= -50.0) {
		tmp = 0.0 - ((y * z) * x);
	} else if ((y * z) <= 4e-13) {
		tmp = 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) <= -1e+194:
		tmp = z * (0.0 - (y * x))
	elif (y * z) <= -50.0:
		tmp = 0.0 - ((y * z) * x)
	elif (y * z) <= 4e-13:
		tmp = 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) <= -1e+194)
		tmp = Float64(z * Float64(0.0 - Float64(y * x)));
	elseif (Float64(y * z) <= -50.0)
		tmp = Float64(0.0 - Float64(Float64(y * z) * x));
	elseif (Float64(y * z) <= 4e-13)
		tmp = 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) <= -1e+194)
		tmp = z * (0.0 - (y * x));
	elseif ((y * z) <= -50.0)
		tmp = 0.0 - ((y * z) * x);
	elseif ((y * z) <= 4e-13)
		tmp = 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], -1e+194], N[(z * N[(0.0 - N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], -50.0], N[(0.0 - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 4e-13], x, N[(y * N[(0.0 - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 y z) < -9.99999999999999945e193

   1. Initial program 84.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 96.6%

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

   5. Simplified 96.6%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -9.99999999999999945e193 < (*.f64 y z) < -50

   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 76.1%

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

   5. Simplified 76.1%

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

   7. Applied egg-rr 92.9%

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

   if -50 < (*.f64 y z) < 4.0000000000000001e-13

   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 99.3%

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

   if 4.0000000000000001e-13 < (*.f64 y z)

   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. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

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

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

      8. *-lowering-*.f64 88.4%

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

   5. Simplified 88.4%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 88.4%

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

   7. Applied egg-rr 88.4%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(0 - y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq -50:\\ \;\;\;\;0 - \left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(0 - y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

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) -1e+194)
   (* z (- 0.0 (* y x)))
   (if (<= (* y z) 5e+117) (* 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) <= -1e+194) {
		tmp = z * (0.0 - (y * x));
	} else if ((y * z) <= 5e+117) {
		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) <= (-1d+194)) then
        tmp = z * (0.0d0 - (y * x))
    else if ((y * z) <= 5d+117) 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) <= -1e+194) {
		tmp = z * (0.0 - (y * x));
	} else if ((y * z) <= 5e+117) {
		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) <= -1e+194:
		tmp = z * (0.0 - (y * x))
	elif (y * z) <= 5e+117:
		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) <= -1e+194)
		tmp = Float64(z * Float64(0.0 - Float64(y * x)));
	elseif (Float64(y * z) <= 5e+117)
		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) <= -1e+194)
		tmp = z * (0.0 - (y * x));
	elseif ((y * z) <= 5e+117)
		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], -1e+194], N[(z * N[(0.0 - N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+117], 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) < -9.99999999999999945e193

   1. Initial program 84.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 96.6%

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

   5. Simplified 96.6%

      \[\leadsto \color{blue}{0 - y \cdot \left(x \cdot z\right)} \]
   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 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -9.99999999999999945e193 < (*.f64 y z) < 4.99999999999999983e117

   1. Initial program 99.9%

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

   if 4.99999999999999983e117 < (*.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 98.0%

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

   5. Simplified 98.0%

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

      1. sub0-neg N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 98.0%

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

   7. Applied egg-rr 98.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(0 - y \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0 - \left(y \cdot z\right) \cdot x\\ \mathbf{if}\;y \cdot z \leq -50:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 0.0 (* (* y z) x))))
   (if (<= (* y z) -50.0) t_0 (if (<= (* y z) 4e-13) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.0 - ((y * z) * x);
	double tmp;
	if ((y * z) <= -50.0) {
		tmp = t_0;
	} else if ((y * z) <= 4e-13) {
		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 - ((y * z) * x)
    if ((y * z) <= (-50.0d0)) then
        tmp = t_0
    else if ((y * z) <= 4d-13) 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 - ((y * z) * x);
	double tmp;
	if ((y * z) <= -50.0) {
		tmp = t_0;
	} else if ((y * z) <= 4e-13) {
		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 - ((y * z) * x)
	tmp = 0
	if (y * z) <= -50.0:
		tmp = t_0
	elif (y * z) <= 4e-13:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(0.0 - Float64(Float64(y * z) * x))
	tmp = 0.0
	if (Float64(y * z) <= -50.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 4e-13)
		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 - ((y * z) * x);
	tmp = 0.0;
	if ((y * z) <= -50.0)
		tmp = t_0;
	elseif ((y * z) <= 4e-13)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(0.0 - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -50.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 4e-13], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -50 or 4.0000000000000001e-13 < (*.f64 y z)

   1. Initial program 90.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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 87.6%

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

   5. Simplified 87.6%

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

   7. Applied egg-rr 88.2%

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

   if -50 < (*.f64 y z) < 4.0000000000000001e-13

   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 99.3%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -50:\\ \;\;\;\;0 - \left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - \left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.3% 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 95.1%

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

3. Taylor expanded in y around 0

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

5. Simplified 49.4%

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))