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

Percentage Accurate: 96.1% → 99.7%

Time: 11.7s

Alternatives: 6

Speedup: 1.0×

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: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \mathsf{fma}\left(0 - y, x \cdot z, x\right)\\ \mathbf{if}\;z \cdot y \leq -\infty:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \cdot y \leq 10^{+141}:\\ \;\;\;\;x - x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (fma (- 0.0 y) (* x z) x)))
   (if (<= (* z y) (- INFINITY))
     t_0
     (if (<= (* z y) 1e+141) (- x (* x (* z y))) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = fma((0.0 - y), (x * z), x);
	double tmp;
	if ((z * y) <= -((double) INFINITY)) {
		tmp = t_0;
	} else if ((z * y) <= 1e+141) {
		tmp = x - (x * (z * y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = fma(Float64(0.0 - y), Float64(x * z), x)
	tmp = 0.0
	if (Float64(z * y) <= Float64(-Inf))
		tmp = t_0;
	elseif (Float64(z * y) <= 1e+141)
		tmp = Float64(x - Float64(x * Float64(z * y)));
	else
		tmp = t_0;
	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[(N[(0.0 - y), $MachinePrecision] * N[(x * z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], (-Infinity)], t$95$0, If[LessEqual[N[(z * y), $MachinePrecision], 1e+141], N[(x - N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0 or 1.00000000000000002e141 < (*.f64 y z)

   1. Initial program 84.6%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

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

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

      5. associate-*l* N/A

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

      6. *-lft-identity N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. neg-sub0 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 98.3

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

   4. Applied egg-rr 98.3%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 98.3

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

   6. Applied egg-rr 98.3%

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

   if -inf.0 < (*.f64 y z) < 1.00000000000000002e141

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

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

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

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

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

      8. *-lowering-*.f64 99.8

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(0 - y, x \cdot z, x\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{+141}:\\ \;\;\;\;x - x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0 - y, x \cdot z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0 - x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \cdot y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \cdot y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 0.0 (* x (* z y)))))
   (if (<= (* z y) -1.0) t_0 (if (<= (* z y) 1.0) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.0 - (x * (z * y));
	double tmp;
	if ((z * y) <= -1.0) {
		tmp = t_0;
	} else if ((z * y) <= 1.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.0d0 - (x * (z * y))
    if ((z * y) <= (-1.0d0)) then
        tmp = t_0
    else if ((z * y) <= 1.0d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 0.0 - (x * (z * y));
	double tmp;
	if ((z * y) <= -1.0) {
		tmp = t_0;
	} else if ((z * y) <= 1.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 0.0 - (x * (z * y))
	tmp = 0
	if (z * y) <= -1.0:
		tmp = t_0
	elif (z * y) <= 1.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(0.0 - N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * y), $MachinePrecision], -1.0], t$95$0, If[LessEqual[N[(z * y), $MachinePrecision], 1.0], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

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

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

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

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

      8. *-lowering-*.f64 92.7

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

   4. Applied egg-rr 92.7%

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

      1. associate-*l* N/A

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

      2. cancel-sign-sub-inv N/A

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

      3. sub0-neg N/A

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

      4. associate-*r* N/A

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

      5. distribute-rgt1-in N/A

         \[\leadsto \color{blue}{\left(\left(0 - y\right) \cdot z + 1\right) \cdot x} \]

      6. sub0-neg N/A

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

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

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

      8. neg-sub0 N/A

         \[\leadsto \left(\color{blue}{\left(0 - y \cdot z\right)} + 1\right) \cdot x \]

      9. associate-+l- N/A

         \[\leadsto \color{blue}{\left(0 - \left(y \cdot z - 1\right)\right)} \cdot x \]

      10. flip-- N/A

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

      11. metadata-eval N/A

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

      12. sub-neg N/A

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

      13. swap-sqr N/A

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

      14. metadata-eval N/A

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

      15. associate-*r* N/A

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

      16. neg-sub0 N/A

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

      17. distribute-frac-neg N/A

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in y around inf

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

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

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

      2. *-lowering-*.f64 89.9

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

   9. Simplified 89.9%

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

       1. clear-num N/A

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

       2. associate-/l/ N/A

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

       3. frac-2neg N/A

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

       4. metadata-eval N/A

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

       5. div-inv N/A

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

       6. neg-mul-1 N/A

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

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

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

       8. distribute-frac-neg2 N/A

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

       9. associate-/r/ N/A

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

       10. metadata-eval N/A

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

       11. neg-mul-1 N/A

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

       12. remove-double-neg N/A

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

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

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

       14. *-lowering-*.f64 90.0

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

   11. Applied egg-rr 90.0%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Simplified 97.4%

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

4. Final simplification 93.5%

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

Alternative 3: 95.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 20000000000:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 20000000000.0) (fma (- 0.0 z) (* x y) x) (- x (* x (* z y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 20000000000.0) {
		tmp = fma((0.0 - z), (x * y), x);
	} else {
		tmp = x - (x * (z * y));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 20000000000.0)
		tmp = fma(Float64(0.0 - z), Float64(x * y), x);
	else
		tmp = Float64(x - Float64(x * Float64(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[x, 20000000000.0], N[(N[(0.0 - z), $MachinePrecision] * N[(x * y), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2e10

   1. Initial program 94.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-commutative N/A

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

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

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

      6. associate-*l* N/A

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

      7. *-lft-identity N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. neg-sub0 N/A

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

      10. --lowering--.f64 N/A

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

      11. *-lowering-*.f64 95.7

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

   4. Applied egg-rr 95.7%

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

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 95.7

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

   6. Applied egg-rr 95.7%

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

   if 2e10 < x

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

      3. *-lft-identity N/A

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

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

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

      5. unsub-neg N/A

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

      6. --lowering--.f64 N/A

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

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

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

      8. *-lowering-*.f64 99.8

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 20000000000:\\ \;\;\;\;\mathsf{fma}\left(0 - z, x \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (x * (z * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

   1. sub-neg N/A

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

   2. distribute-rgt-in N/A

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

   3. *-lft-identity N/A

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

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

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

   5. unsub-neg N/A

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

   6. --lowering--.f64 N/A

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

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

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

   8. *-lowering-*.f64 96.1

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

4. Applied egg-rr 96.1%

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

5. Final simplification 96.1%

   \[\leadsto x - x \cdot \left(z \cdot y\right) \]
6. Add Preprocessing

Alternative 5: 96.1% accurate, 1.0× speedup

Math

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

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 (* z y))))

C

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

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 - (z * y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.1%

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

3. Final simplification 96.1%

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

Alternative 6: 51.0% accurate, 14.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 96.1%

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

3. Taylor expanded in y around 0

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

5. Simplified 47.8%

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

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))