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

Percentage Accurate: 96.1% → 99.9%

Time: 7.0s

Alternatives: 6

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: 96.1% 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: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-y\right) \cdot x\right) \cdot z\\ \end{array} \end{array} \]

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) (- INFINITY))
   (* (- y) (* x z))
   (if (<= (* y z) 5e+218) (* x (- 1.0 (* y z))) (* (* (- y) x) z))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = -y * (x * z);
	} else if ((y * z) <= 5e+218) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = (-y * x) * z;
	}
	return tmp;
}

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = -y * (x * z);
	} else if ((y * z) <= 5e+218) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = (-y * x) * z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = -y * (x * z)
	elif (y * z) <= 5e+218:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = (-y * x) * z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(Float64(-y) * Float64(x * z));
	elseif (Float64(y * z) <= 5e+218)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(Float64(Float64(-y) * x) * z);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = -y * (x * z);
	elseif ((y * z) <= 5e+218)
		tmp = x * (1.0 - (y * z));
	else
		tmp = (-y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[((-y) * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+218], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -inf.0

   1. Initial program 66.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 99.8

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

   4. Applied rewrites 99.8%

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

   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. mul-1-neg N/A

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

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

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

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

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

      13. lower-*.f64 N/A

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

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

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. associate-*r* N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. mul-1-neg N/A

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

      23. lower-neg.f64 99.8

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

   7. Applied rewrites 99.8%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 99.7%

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

   if -inf.0 < (*.f64 y z) < 4.99999999999999983e218

   1. Initial program 99.9%

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

   if 4.99999999999999983e218 < (*.f64 y z)

   1. Initial program 80.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   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. mul-1-neg N/A

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

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

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

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

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

      13. lower-*.f64 N/A

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

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

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. associate-*r* N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. mul-1-neg N/A

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

      23. lower-neg.f64 99.9

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

   7. Applied rewrites 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(\left(-y\right) \cdot x\right) \cdot z\\ \mathbf{if}\;y \cdot z \leq -2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \left(\left(-y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* (- y) x) z)))
   (if (<= (* y z) -2.0)
     t_0
     (if (<= (* y z) 2e-5)
       (* x 1.0)
       (if (<= (* y z) 5e+218) (* x (* (- y) z)) t_0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (-y * x) * z;
	double tmp;
	if ((y * z) <= -2.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x * 1.0;
	} else if ((y * z) <= 5e+218) {
		tmp = x * (-y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-y * x) * z
    if ((y * z) <= (-2.0d0)) then
        tmp = t_0
    else if ((y * z) <= 2d-5) then
        tmp = x * 1.0d0
    else if ((y * z) <= 5d+218) then
        tmp = x * (-y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = (-y * x) * z;
	double tmp;
	if ((y * z) <= -2.0) {
		tmp = t_0;
	} else if ((y * z) <= 2e-5) {
		tmp = x * 1.0;
	} else if ((y * z) <= 5e+218) {
		tmp = x * (-y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (-y * x) * z
	tmp = 0
	if (y * z) <= -2.0:
		tmp = t_0
	elif (y * z) <= 2e-5:
		tmp = x * 1.0
	elif (y * z) <= 5e+218:
		tmp = x * (-y * z)
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(Float64(-y) * x) * z)
	tmp = 0.0
	if (Float64(y * z) <= -2.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 2e-5)
		tmp = Float64(x * 1.0);
	elseif (Float64(y * z) <= 5e+218)
		tmp = Float64(x * Float64(Float64(-y) * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = (-y * x) * z;
	tmp = 0.0;
	if ((y * z) <= -2.0)
		tmp = t_0;
	elseif ((y * z) <= 2e-5)
		tmp = x * 1.0;
	elseif ((y * z) <= 5e+218)
		tmp = x * (-y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -2.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 2e-5], N[(x * 1.0), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 5e+218], N[(x * N[((-y) * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2 or 4.99999999999999983e218 < (*.f64 y z)

   1. Initial program 88.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 94.7

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

   4. Applied rewrites 94.7%

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

   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. mul-1-neg N/A

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

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

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

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

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

      13. lower-*.f64 N/A

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

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

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. associate-*r* N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. mul-1-neg N/A

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

      23. lower-neg.f64 92.5

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

   7. Applied rewrites 92.5%

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

   if -2 < (*.f64 y z) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 97.0%

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

   if 2.00000000000000016e-5 < (*.f64 y z) < 4.99999999999999983e218

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 95.3

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

   5. Applied rewrites 95.3%

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

4. Final simplification 95.2%

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

Alternative 3: 94.4% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2.0) (not (<= (* y z) 2e-5)))
   (* (* (- y) x) z)
   (* x 1.0)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2.0) || !((y * z) <= 2e-5)) {
		tmp = (-y * x) * z;
	} else {
		tmp = x * 1.0;
	}
	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) :: tmp
    if (((y * z) <= (-2.0d0)) .or. (.not. ((y * z) <= 2d-5))) then
        tmp = (-y * x) * z
    else
        tmp = x * 1.0d0
    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) <= -2.0) || !((y * z) <= 2e-5)) {
		tmp = (-y * x) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2.0) or not ((y * z) <= 2e-5):
		tmp = (-y * x) * z
	else:
		tmp = x * 1.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2.0) || !(Float64(y * z) <= 2e-5))
		tmp = Float64(Float64(Float64(-y) * x) * z);
	else
		tmp = Float64(x * 1.0);
	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) <= -2.0) || ~(((y * z) <= 2e-5)))
		tmp = (-y * x) * z;
	else
		tmp = x * 1.0;
	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_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e-5]], $MachinePrecision]], N[(N[((-y) * x), $MachinePrecision] * z), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2 or 2.00000000000000016e-5 < (*.f64 y z)

   1. Initial program 91.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 93.7

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

   4. Applied rewrites 93.7%

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

   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. mul-1-neg N/A

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

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

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

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

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

      13. lower-*.f64 N/A

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

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

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. associate-*r* N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. mul-1-neg N/A

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

      23. lower-neg.f64 91.0

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

   7. Applied rewrites 91.0%

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

   if -2 < (*.f64 y z) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 97.0%

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

4. Final simplification 94.0%

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

Alternative 4: 94.0% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -2.0) (not (<= (* y z) 2e-5)))
   (* (- y) (* x z))
   (* x 1.0)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -2.0) || !((y * z) <= 2e-5)) {
		tmp = -y * (x * z);
	} else {
		tmp = x * 1.0;
	}
	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) :: tmp
    if (((y * z) <= (-2.0d0)) .or. (.not. ((y * z) <= 2d-5))) then
        tmp = -y * (x * z)
    else
        tmp = x * 1.0d0
    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) <= -2.0) || !((y * z) <= 2e-5)) {
		tmp = -y * (x * z);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -2.0) or not ((y * z) <= 2e-5):
		tmp = -y * (x * z)
	else:
		tmp = x * 1.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -2.0) || !(Float64(y * z) <= 2e-5))
		tmp = Float64(Float64(-y) * Float64(x * z));
	else
		tmp = Float64(x * 1.0);
	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) <= -2.0) || ~(((y * z) <= 2e-5)))
		tmp = -y * (x * z);
	else
		tmp = x * 1.0;
	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_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], -2.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e-5]], $MachinePrecision]], N[((-y) * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2 or 2.00000000000000016e-5 < (*.f64 y z)

   1. Initial program 91.8%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 93.7

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

   4. Applied rewrites 93.7%

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

   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. mul-1-neg N/A

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

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

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

      3. *-lft-identity N/A

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

      4. metadata-eval N/A

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

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

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

      6. associate-*r* N/A

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

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

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

      8. mul-1-neg N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. associate-*r* N/A

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

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

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

      13. lower-*.f64 N/A

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

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

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

      15. *-commutative N/A

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

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

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

      17. metadata-eval N/A

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

      18. associate-*r* N/A

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

      19. *-lft-identity N/A

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

      20. *-commutative N/A

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

      21. lower-*.f64 N/A

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

      22. mul-1-neg N/A

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

      23. lower-neg.f64 91.0

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

   7. Applied rewrites 91.0%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 85.9%

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

   if -2 < (*.f64 y z) < 2.00000000000000016e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 97.0%

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

4. Final simplification 91.4%

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

Alternative 5: 96.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-86}:\\ \;\;\;\;\mathsf{fma}\left(x \cdot \left(-y\right), z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 2e-86) (fma (* x (- y)) z x) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-86) {
		tmp = fma((x * -y), z, x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 2e-86)
		tmp = fma(Float64(x * Float64(-y)), z, x);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[x, 2e-86], N[(N[(x * (-y)), $MachinePrecision] * z + x), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.00000000000000017e-86

   1. Initial program 94.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. lift-*.f64 N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. associate-*r* N/A

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

      8. *-rgt-identity N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lower-neg.f64 96.0

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

   4. Applied rewrites 96.0%

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

   if 2.00000000000000017e-86 < x

   1. Initial program 99.8%

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

Alternative 6: 51.0% 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 95.9%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 49.9%

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

Reproduce

herbie shell --seed 2024320 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))