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

Percentage Accurate: 96.0% → 99.2%

Time: 10.6s

Alternatives: 7

Speedup: 0.4×

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: 96.0% 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

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+218}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(-z\right), x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-1}{y \cdot x}}\\ \end{array} \end{array} \]

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) -2e+218)
   (- (* y (* z x)))
   (if (<= (* y z) 2e+99) (fma (* y (- z)) x x) (/ z (/ -1.0 (* y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2e+218) {
		tmp = -(y * (z * x));
	} else if ((y * z) <= 2e+99) {
		tmp = fma((y * -z), x, x);
	} else {
		tmp = z / (-1.0 / (y * x));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -2e+218)
		tmp = Float64(-Float64(y * Float64(z * x)));
	elseif (Float64(y * z) <= 2e+99)
		tmp = fma(Float64(y * Float64(-z)), x, x);
	else
		tmp = Float64(z / Float64(-1.0 / Float64(y * x)));
	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[N[(y * z), $MachinePrecision], -2e+218], (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], 2e+99], N[(N[(y * (-z)), $MachinePrecision] * x + x), $MachinePrecision], N[(z / N[(-1.0 / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2.00000000000000017e218

   1. Initial program 79.1%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -2.00000000000000017e218 < (*.f64 y z) < 1.9999999999999999e99

   1. Initial program 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if 1.9999999999999999e99 < (*.f64 y z)

   1. Initial program 84.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 95.0

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

   4. Applied rewrites 95.0%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-rgt-identity N/A

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

      8. rgt-mult-inverse N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-rgt-identity N/A

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

      19. associate-*r/ N/A

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

      20. rgt-mult-inverse N/A

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

      21. *-rgt-identity 95.0

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

   7. Applied rewrites 95.0%

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

   9. Applied rewrites 95.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+218}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(-z\right), x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-1}{y \cdot x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+114}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-z, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 -2e+114)
     (- (* z (* y x)))
     (if (<= t_0 5e+306) (* x (fma (- z) y 1.0)) (- (* y (* z x)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -2e+114) {
		tmp = -(z * (y * x));
	} else if (t_0 <= 5e+306) {
		tmp = x * fma(-z, y, 1.0);
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= -2e+114)
		tmp = Float64(-Float64(z * Float64(y * x)));
	elseif (t_0 <= 5e+306)
		tmp = Float64(x * fma(Float64(-z), y, 1.0));
	else
		tmp = Float64(-Float64(y * Float64(z * x)));
	end
	return 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[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+114], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t$95$0, 5e+306], N[(x * N[((-z) * y + 1.0), $MachinePrecision]), $MachinePrecision], (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z))) < -2e114

   1. Initial program 90.0%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 89.5

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-rgt-identity N/A

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

      8. rgt-mult-inverse N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-rgt-identity N/A

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

      19. associate-*r/ N/A

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

      20. rgt-mult-inverse N/A

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

      21. *-rgt-identity 67.0

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

   7. Applied rewrites 67.0%

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

   if -2e114 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z))) < 4.99999999999999993e306

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

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

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   if 4.99999999999999993e306 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z)))

   1. Initial program 74.1%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq -2 \cdot 10^{+114}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - y \cdot z\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-z, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-31}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 -1e-31)
     (- (* z (* y x)))
     (if (<= t_0 5e+306) t_0 (- (* y (* z x)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -1e-31) {
		tmp = -(z * (y * x));
	} else if (t_0 <= 5e+306) {
		tmp = t_0;
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - (y * z))
    if (t_0 <= (-1d-31)) then
        tmp = -(z * (y * x))
    else if (t_0 <= 5d+306) then
        tmp = t_0
    else
        tmp = -(y * (z * x))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -1e-31) {
		tmp = -(z * (y * x));
	} else if (t_0 <= 5e+306) {
		tmp = t_0;
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= -1e-31:
		tmp = -(z * (y * x))
	elif t_0 <= 5e+306:
		tmp = t_0
	else:
		tmp = -(y * (z * x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= -1e-31)
		tmp = Float64(-Float64(z * Float64(y * x)));
	elseif (t_0 <= 5e+306)
		tmp = t_0;
	else
		tmp = Float64(-Float64(y * Float64(z * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= -1e-31)
		tmp = -(z * (y * x));
	elseif (t_0 <= 5e+306)
		tmp = t_0;
	else
		tmp = -(y * (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-31], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[t$95$0, 5e+306], t$95$0, (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z))) < -1e-31

   1. Initial program 92.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 92.4

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

   4. Applied rewrites 92.4%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-rgt-identity N/A

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

      8. rgt-mult-inverse N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-rgt-identity N/A

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

      19. associate-*r/ N/A

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

      20. rgt-mult-inverse N/A

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

      21. *-rgt-identity 56.2

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

   7. Applied rewrites 56.2%

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

   if -1e-31 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z))) < 4.99999999999999993e306

   1. Initial program 99.7%

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

   if 4.99999999999999993e306 < (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y z)))

   1. Initial program 74.1%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq -1 \cdot 10^{-31}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - y \cdot z\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+218}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(-z\right), x, x\right)\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -2e+218)
   (- (* y (* z x)))
   (if (<= (* y z) 2e+99) (fma (* y (- z)) x x) (- (* z (* y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -2e+218) {
		tmp = -(y * (z * x));
	} else if ((y * z) <= 2e+99) {
		tmp = fma((y * -z), x, x);
	} else {
		tmp = -(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) <= -2e+218)
		tmp = Float64(-Float64(y * Float64(z * x)));
	elseif (Float64(y * z) <= 2e+99)
		tmp = fma(Float64(y * Float64(-z)), x, x);
	else
		tmp = Float64(-Float64(z * Float64(y * x)));
	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[N[(y * z), $MachinePrecision], -2e+218], (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], 2e+99], N[(N[(y * (-z)), $MachinePrecision] * x + x), $MachinePrecision], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2.00000000000000017e218

   1. Initial program 79.1%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -2.00000000000000017e218 < (*.f64 y z) < 1.9999999999999999e99

   1. Initial program 99.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-rgt-in N/A

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

      6. *-lft-identity N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if 1.9999999999999999e99 < (*.f64 y z)

   1. Initial program 84.1%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 95.0

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

   4. Applied rewrites 95.0%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-rgt-identity N/A

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

      8. rgt-mult-inverse N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-rgt-identity N/A

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

      19. associate-*r/ N/A

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

      20. rgt-mult-inverse N/A

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

      21. *-rgt-identity 95.0

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

   7. Applied rewrites 95.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2 \cdot 10^{+218}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \left(-z\right), x, x\right)\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000000:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -20000000000.0)
   (- (* y (* z x)))
   (if (<= (* y z) 1.0) (* x 1.0) (- (* z (* y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -20000000000.0) {
		tmp = -(y * (z * x));
	} else if ((y * z) <= 1.0) {
		tmp = x * 1.0;
	} else {
		tmp = -(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) <= (-20000000000.0d0)) then
        tmp = -(y * (z * x))
    else if ((y * z) <= 1.0d0) then
        tmp = x * 1.0d0
    else
        tmp = -(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) <= -20000000000.0) {
		tmp = -(y * (z * x));
	} else if ((y * z) <= 1.0) {
		tmp = x * 1.0;
	} else {
		tmp = -(z * (y * x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -20000000000.0:
		tmp = -(y * (z * x))
	elif (y * z) <= 1.0:
		tmp = x * 1.0
	else:
		tmp = -(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) <= -20000000000.0)
		tmp = Float64(-Float64(y * Float64(z * x)));
	elseif (Float64(y * z) <= 1.0)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(-Float64(z * Float64(y * x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -20000000000.0)
		tmp = -(y * (z * x));
	elseif ((y * z) <= 1.0)
		tmp = x * 1.0;
	else
		tmp = -(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], -20000000000.0], (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(y * z), $MachinePrecision], 1.0], N[(x * 1.0), $MachinePrecision], (-N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2e10

   1. Initial program 87.9%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 93.5

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

   5. Applied rewrites 93.5%

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

   if -2e10 < (*.f64 y z) < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 96.4%

      \[\leadsto x \cdot \color{blue}{1} \]

   if 1 < (*.f64 y z)

   1. Initial program 87.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. distribute-lft-in N/A

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

      6. lift-*.f64 N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-rgt-identity N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 88.7

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

   4. Applied rewrites 88.7%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. *-rgt-identity N/A

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

      8. rgt-mult-inverse N/A

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

      9. associate-*r/ N/A

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

      10. *-rgt-identity N/A

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

      11. associate-/l* N/A

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

      12. associate-*l/ N/A

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

      13. lower-*.f64 N/A

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

      14. mul-1-neg N/A

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

      15. lower-neg.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. *-rgt-identity N/A

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

      19. associate-*r/ N/A

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

      20. rgt-mult-inverse N/A

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

      21. *-rgt-identity 88.8

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

   7. Applied rewrites 88.8%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000000:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \cdot z \leq -20000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y (* z x)))))
   (if (<= (* y z) -20000000000.0) t_0 (if (<= (* y z) 1.0) (* x 1.0) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -(y * (z * x));
	double tmp;
	if ((y * z) <= -20000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 1.0) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(y * (z * x))
    if ((y * z) <= (-20000000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 1.0d0) then
        tmp = x * 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -(y * (z * x));
	double tmp;
	if ((y * z) <= -20000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 1.0) {
		tmp = x * 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -(y * (z * x))
	tmp = 0
	if (y * z) <= -20000000000.0:
		tmp = t_0
	elif (y * z) <= 1.0:
		tmp = x * 1.0
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(y * Float64(z * x)))
	tmp = 0.0
	if (Float64(y * z) <= -20000000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 1.0)
		tmp = Float64(x * 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -(y * (z * x));
	tmp = 0.0;
	if ((y * z) <= -20000000000.0)
		tmp = t_0;
	elseif ((y * z) <= 1.0)
		tmp = x * 1.0;
	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[(z * x), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -20000000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 1.0], N[(x * 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e10 or 1 < (*.f64 y z)

   1. Initial program 87.6%

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

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if -2e10 < (*.f64 y z) < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 96.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -20000000000:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \cdot z \leq 1:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \cdot 1 \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* x 1.0))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x * 1.0;
}

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 * 1.0d0
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x * 1.0

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(x * 1.0)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x * 1.0;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(x * 1.0), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in y around 0

   \[\leadsto x \cdot \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 52.1%

   \[\leadsto x \cdot \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024233 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))