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

Percentage Accurate: 95.8% → 97.9%

Time: 7.4s

Alternatives: 4

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.8% 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: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+256}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{\frac{-1}{y}}\\ \end{array} \end{array} \]

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+256) (* x (- 1.0 (* y z))) (/ (* z x) (/ -1.0 y))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 1e+256) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = (z * x) / (-1.0 / y);
	}
	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+256) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = (z * x) / ((-1.0d0) / y)
    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+256) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = (z * x) / (-1.0 / y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 1e+256:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = (z * x) / (-1.0 / y)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 1e+256)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(Float64(z * x) / Float64(-1.0 / y));
	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+256)
		tmp = x * (1.0 - (y * z));
	else
		tmp = (z * x) / (-1.0 / y);
	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+256], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 1e256

   1. Initial program 99.5%

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

   if 1e256 < (*.f64 y z)

   1. Initial program 62.3%

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

   4. Applied egg-rr 0.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. clear-num N/A

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) - 1\right)}{\color{blue}{1} + y \cdot z}}\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)}{1 + y \cdot z}}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) + -1\right)}{1 + y \cdot z}}\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(-1 + z \cdot \left(y \cdot \left(y \cdot z\right)\right)\right)}{1 + y \cdot z}}\right)\right) \]

      9. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{\left(0 - -1\right) - z \cdot \left(y \cdot \left(y \cdot z\right)\right)}{\color{blue}{1} + y \cdot z}}\right)\right) \]

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

      14. flip-- N/A

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

   6. Applied egg-rr 62.3%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{-1}{y \cdot z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 62.3%

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

   9. Simplified 62.3%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   10. Step-by-step derivation

       1. associate-/r* N/A

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

       2. associate-/r/ N/A

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

       3. associate-*l/ N/A

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

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

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

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

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

       6. clear-num N/A

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

       7. metadata-eval N/A

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

       8. distribute-neg-frac N/A

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

       9. distribute-frac-neg2 N/A

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

       10. clear-num N/A

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

       11. metadata-eval N/A

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

       12. distribute-frac-neg2 N/A

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

       13. metadata-eval N/A

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

       14. distribute-neg-frac N/A

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

       15. metadata-eval N/A

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

       16. inv-pow N/A

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

       17. pow-flip N/A

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

       18. /-lowering-/.f64 N/A

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

       19. pow-flip N/A

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

       20. metadata-eval N/A

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

       21. inv-pow N/A

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

       22. metadata-eval N/A

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

       23. distribute-neg-frac N/A

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

       24. distribute-frac-neg2 N/A

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

       25. metadata-eval N/A

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

       26. frac-2neg N/A

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

       27. metadata-eval N/A

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

       28. remove-double-div N/A

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

       29. remove-double-neg 99.7%

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

   11. Applied egg-rr 99.7%

       \[\leadsto \color{blue}{\frac{x \cdot z}{\frac{-1}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+256}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{\frac{-1}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(0 - z \cdot x\right)\\ \mathbf{if}\;z \leq -1.56 \cdot 10^{-77}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 0.0 (* z x)))))
   (if (<= z -1.56e-77) t_0 (if (<= z 1.3e+43) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = y * (0.0 - (z * x));
	double tmp;
	if (z <= -1.56e-77) {
		tmp = t_0;
	} else if (z <= 1.3e+43) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (0.0d0 - (z * x))
    if (z <= (-1.56d-77)) then
        tmp = t_0
    else if (z <= 1.3d+43) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = y * (0.0 - (z * x));
	double tmp;
	if (z <= -1.56e-77) {
		tmp = t_0;
	} else if (z <= 1.3e+43) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = y * (0.0 - (z * x))
	tmp = 0
	if z <= -1.56e-77:
		tmp = t_0
	elif z <= 1.3e+43:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(0.0 - Float64(z * x)))
	tmp = 0.0
	if (z <= -1.56e-77)
		tmp = t_0;
	elseif (z <= 1.3e+43)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (0.0 - (z * x));
	tmp = 0.0;
	if (z <= -1.56e-77)
		tmp = t_0;
	elseif (z <= 1.3e+43)
		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[(y * N[(0.0 - N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.56e-77], t$95$0, If[LessEqual[z, 1.3e+43], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5600000000000001e-77 or 1.3000000000000001e43 < z

   1. Initial program 93.7%

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

   4. Applied egg-rr 52.8%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. clear-num N/A

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) - 1\right)}{\color{blue}{1} + y \cdot z}}\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)}{1 + y \cdot z}}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) + -1\right)}{1 + y \cdot z}}\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(-1 + z \cdot \left(y \cdot \left(y \cdot z\right)\right)\right)}{1 + y \cdot z}}\right)\right) \]

      9. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{\left(0 - -1\right) - z \cdot \left(y \cdot \left(y \cdot z\right)\right)}{\color{blue}{1} + y \cdot z}}\right)\right) \]

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

      14. flip-- N/A

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{-1}{y \cdot z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 67.3%

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

   9. Simplified 67.3%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   10. Step-by-step derivation

       1. frac-2neg N/A

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

       2. distribute-frac-neg N/A

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

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

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

       4. distribute-frac-neg2 N/A

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

       5. neg-mul-1 N/A

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

       6. clear-num N/A

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

       7. div-inv N/A

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

       8. associate-/r* N/A

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

       9. associate-/l/ N/A

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

       10. associate-/r/ N/A

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

       11. frac-2neg N/A

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

       12. metadata-eval N/A

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

       13. distribute-neg-frac N/A

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

       14. metadata-eval N/A

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

       15. inv-pow N/A

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

       16. pow-flip N/A

           \[\leadsto \mathsf{neg.f64}\left(\left({y}^{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(x \cdot z\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(\left(x \cdot z\right) \cdot {y}^{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right) \]

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

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

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

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

       20. pow-flip N/A

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

       21. metadata-eval N/A

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

       22. inv-pow N/A

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

       23. metadata-eval N/A

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

       24. distribute-neg-frac N/A

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

       25. distribute-frac-neg2 N/A

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

       26. metadata-eval N/A

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

       27. frac-2neg N/A

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

   11. Applied egg-rr 71.4%

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

   if -1.5600000000000001e-77 < z < 1.3000000000000001e43

   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 80.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+237}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \end{array} \]

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+237) (* 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+237) {
		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+237) 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+237) {
		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+237:
		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+237)
		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+237)
		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+237], 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 2 regimes

2. if (*.f64 y z) < 9.9999999999999994e236

   1. Initial program 99.5%

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

   if 9.9999999999999994e236 < (*.f64 y z)

   1. Initial program 71.0%

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

   4. Applied egg-rr 12.4%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. clear-num N/A

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

      5. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) - 1\right)}{\color{blue}{1} + y \cdot z}}\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)}{1 + y \cdot z}}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(z \cdot \left(y \cdot \left(y \cdot z\right)\right) + -1\right)}{1 + y \cdot z}}\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{0 - \left(-1 + z \cdot \left(y \cdot \left(y \cdot z\right)\right)\right)}{1 + y \cdot z}}\right)\right) \]

      9. associate--r+ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\frac{\left(0 - -1\right) - z \cdot \left(y \cdot \left(y \cdot z\right)\right)}{\color{blue}{1} + y \cdot z}}\right)\right) \]

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. associate-*r* N/A

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

      13. *-commutative N/A

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

      14. flip-- N/A

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

   6. Applied egg-rr 71.0%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{-1}{y \cdot z}\right)}\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 71.0%

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

   9. Simplified 71.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   10. Step-by-step derivation

       1. frac-2neg N/A

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

       2. distribute-frac-neg N/A

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

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

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

       4. distribute-frac-neg2 N/A

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

       5. neg-mul-1 N/A

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

       6. clear-num N/A

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

       7. div-inv N/A

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

       8. associate-/r* N/A

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

       9. associate-/l/ N/A

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

       10. associate-/r/ N/A

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

       11. frac-2neg N/A

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

       12. metadata-eval N/A

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

       13. distribute-neg-frac N/A

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

       14. metadata-eval N/A

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

       15. inv-pow N/A

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

       16. pow-flip N/A

           \[\leadsto \mathsf{neg.f64}\left(\left({y}^{\left(\mathsf{neg}\left(-1\right)\right)} \cdot \left(x \cdot z\right)\right)\right) \]

       17. *-commutative N/A

           \[\leadsto \mathsf{neg.f64}\left(\left(\left(x \cdot z\right) \cdot {y}^{\left(\mathsf{neg}\left(-1\right)\right)}\right)\right) \]

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

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

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

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

       20. pow-flip N/A

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

       21. metadata-eval N/A

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

       22. inv-pow N/A

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

       23. metadata-eval N/A

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

       24. distribute-neg-frac N/A

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

       25. distribute-frac-neg2 N/A

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

       26. metadata-eval N/A

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

       27. frac-2neg N/A

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

   11. Applied egg-rr 99.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+237}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0 - z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% 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 96.6%

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

3. Taylor expanded in y around 0

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

5. Simplified 53.3%

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

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))