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

Percentage Accurate: 96.2% → 98.1%

Time: 6.3s

Alternatives: 5

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% 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: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq 5 \cdot 10^{+223}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y\right) \cdot z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 (* y z)) 5e+223) (fma (* (- y) z) x x) (* (* (- x) z) y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - (y * z)) <= 5e+223) {
		tmp = fma((-y * z), x, x);
	} else {
		tmp = (-x * z) * y;
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - Float64(y * z)) <= 5e+223)
		tmp = fma(Float64(Float64(-y) * z), x, x);
	else
		tmp = Float64(Float64(Float64(-x) * z) * y);
	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[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], 5e+223], N[(N[((-y) * z), $MachinePrecision] * x + x), $MachinePrecision], N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 4.99999999999999985e223

   1. Initial program 98.3%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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-rgt-in N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 98.3

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

   4. Applied rewrites 98.3%

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

   if 4.99999999999999985e223 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 79.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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-rgt-in N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 79.5

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

   4. Applied rewrites 79.5%

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

   6. Applied rewrites 43.9%

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

   7. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-rgt-identity N/A

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

      8. *-inverses N/A

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

      9. associate-/l* N/A

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

      10. associate-*l/ N/A

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

      11. distribute-neg-frac N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

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

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

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

      17. remove-double-neg N/A

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

      18. associate-*l/ N/A

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

      19. associate-/l* N/A

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

      20. *-inverses N/A

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

      21. *-rgt-identity 99.9

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

   9. Applied rewrites 99.9%

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

Alternative 2: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -2000000 \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (or (<= t_0 -2000000.0) (not (<= t_0 2.0)))
     (* (* (- x) y) z)
     (* x 1.0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -2000000.0) || !(t_0 <= 2.0)) {
		tmp = (-x * y) * 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if ((t_0 <= (-2000000.0d0)) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = (-x * y) * 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 t_0 = 1.0 - (y * z);
	double tmp;
	if ((t_0 <= -2000000.0) || !(t_0 <= 2.0)) {
		tmp = (-x * y) * z;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if (t_0 <= -2000000.0) or not (t_0 <= 2.0):
		tmp = (-x * y) * z
	else:
		tmp = x * 1.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -2000000.0) || !(t_0 <= 2.0))
		tmp = Float64(Float64(Float64(-x) * y) * 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)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if ((t_0 <= -2000000.0) || ~((t_0 <= 2.0)))
		tmp = (-x * y) * 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_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2000000.0], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(N[((-x) * y), $MachinePrecision] * z), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -2e6 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 92.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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-rgt-in N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 92.6

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

   4. Applied rewrites 92.6%

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

   6. Applied rewrites 22.1%

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

   7. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-rgt-identity N/A

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

      8. *-inverses N/A

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

      9. associate-/l* N/A

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

      10. associate-*l/ N/A

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

      11. distribute-neg-frac N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

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

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

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

      17. remove-double-neg N/A

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

      18. associate-*l/ N/A

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

      19. associate-/l* N/A

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

      20. *-inverses N/A

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

      21. *-rgt-identity 90.1

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

   9. Applied rewrites 90.1%

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

   11. Applied rewrites 90.0%

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

   if -2e6 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   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 98.8%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -2000000 \lor \neg \left(1 - y \cdot z \leq 2\right):\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq -2000000:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot y\right) \cdot z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= t_0 -2000000.0)
     (* (* (- x) z) y)
     (if (<= t_0 2.0) (* x 1.0) (* (* (- x) y) z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -2000000.0) {
		tmp = (-x * z) * y;
	} else if (t_0 <= 2.0) {
		tmp = x * 1.0;
	} else {
		tmp = (-x * y) * z;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if (t_0 <= (-2000000.0d0)) then
        tmp = (-x * z) * y
    else if (t_0 <= 2.0d0) then
        tmp = x * 1.0d0
    else
        tmp = (-x * y) * z
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= -2000000.0) {
		tmp = (-x * z) * y;
	} else if (t_0 <= 2.0) {
		tmp = x * 1.0;
	} else {
		tmp = (-x * y) * z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if t_0 <= -2000000.0:
		tmp = (-x * z) * y
	elif t_0 <= 2.0:
		tmp = x * 1.0
	else:
		tmp = (-x * y) * z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= -2000000.0)
		tmp = Float64(Float64(Float64(-x) * z) * y);
	elseif (t_0 <= 2.0)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(Float64(Float64(-x) * y) * z);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= -2000000.0)
		tmp = (-x * z) * y;
	elseif (t_0 <= 2.0)
		tmp = x * 1.0;
	else
		tmp = (-x * y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2000000.0], N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$0, 2.0], N[(x * 1.0), $MachinePrecision], N[(N[((-x) * y), $MachinePrecision] * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -2e6

   1. Initial program 93.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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-rgt-in N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 93.0

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

   4. Applied rewrites 93.0%

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

   6. Applied rewrites 0.5%

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

   7. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-rgt-identity N/A

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

      8. *-inverses N/A

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

      9. associate-/l* N/A

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

      10. associate-*l/ N/A

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

      11. distribute-neg-frac N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

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

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

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

      17. remove-double-neg N/A

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

      18. associate-*l/ N/A

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

      19. associate-/l* N/A

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

      20. *-inverses N/A

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

      21. *-rgt-identity 90.9

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

   9. Applied rewrites 90.9%

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

   if -2e6 < (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 2

   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 98.8%

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

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

   1. Initial program 92.3%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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-rgt-in N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 92.3

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

   4. Applied rewrites 92.3%

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

   6. Applied rewrites 41.7%

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

   7. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-rgt-identity N/A

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

      8. *-inverses N/A

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

      9. associate-/l* N/A

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

      10. associate-*l/ N/A

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

      11. distribute-neg-frac N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

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

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

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

      17. remove-double-neg N/A

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

      18. associate-*l/ N/A

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

      19. associate-/l* N/A

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

      20. *-inverses N/A

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

      21. *-rgt-identity 89.3

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

   9. Applied rewrites 89.3%

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

   11. Applied rewrites 91.2%

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

Alternative 4: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-x\right) \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))))
   (if (<= t_0 5e+223) (* x t_0) (* (* (- x) z) y))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= 5e+223) {
		tmp = x * t_0;
	} else {
		tmp = (-x * z) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    if (t_0 <= 5d+223) then
        tmp = x * t_0
    else
        tmp = (-x * z) * y
    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 = 1.0 - (y * z);
	double tmp;
	if (t_0 <= 5e+223) {
		tmp = x * t_0;
	} else {
		tmp = (-x * z) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 1.0 - (y * z)
	tmp = 0
	if t_0 <= 5e+223:
		tmp = x * t_0
	else:
		tmp = (-x * z) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	tmp = 0.0
	if (t_0 <= 5e+223)
		tmp = Float64(x * t_0);
	else
		tmp = Float64(Float64(Float64(-x) * z) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	tmp = 0.0;
	if (t_0 <= 5e+223)
		tmp = x * t_0;
	else
		tmp = (-x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+223], N[(x * t$95$0), $MachinePrecision], N[(N[((-x) * z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < 4.99999999999999985e223

   1. Initial program 98.3%

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

   if 4.99999999999999985e223 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 79.5%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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-rgt-in N/A

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

      7. *-lft-identity N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-neg.f64 79.5

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

   4. Applied rewrites 79.5%

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

   6. Applied rewrites 43.9%

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

   7. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(y \cdot z\right)\right)} \]
   8. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. *-rgt-identity N/A

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

      8. *-inverses N/A

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

      9. associate-/l* N/A

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

      10. associate-*l/ N/A

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

      11. distribute-neg-frac N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. lower-neg.f64 N/A

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

      15. mul-1-neg N/A

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

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

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

      17. remove-double-neg N/A

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

      18. associate-*l/ N/A

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

      19. associate-/l* N/A

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

      20. *-inverses N/A

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

      21. *-rgt-identity 99.9

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

   9. Applied rewrites 99.9%

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

Alternative 5: 50.2% 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 96.6%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 55.0%

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

Reproduce

herbie shell --seed 2024340 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))