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

Percentage Accurate: 96.2% → 98.0%

Time: 11.0s

Alternatives: 5

Speedup: 0.6×

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: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-1}{z \cdot x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+181) (* x (- 1.0 (* y z))) (/ y (/ -1.0 (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+181) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y / (-1.0 / (z * x));
	}
	return tmp;
}

Fortran

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) <= 5d+181) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y / ((-1.0d0) / (z * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+181) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y / (-1.0 / (z * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+181:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y / (-1.0 / (z * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+181)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y / Float64(-1.0 / Float64(z * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+181)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y / (-1.0 / (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+181], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(-1.0 / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.0000000000000003e181

   1. Initial program 98.3%

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

   if 5.0000000000000003e181 < (*.f64 y z)

   1. Initial program 80.3%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 80.3

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

   5. Applied rewrites 80.3%

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

      1. distribute-rgt-neg-out N/A

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

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

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

      3. lift-neg.f64 N/A

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

      4. associate-*l* N/A

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

      5. lift-*.f64 N/A

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

      6. lower-*.f64 99.8

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-neg.f64 N/A

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

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

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

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

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

      12. lift-neg.f64 N/A

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

      13. lower-*.f64 99.8

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

   7. Applied rewrites 99.8%

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

      1. distribute-rgt-neg-out N/A

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

      2. *-commutative N/A

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

      3. lift-*.f64 N/A

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

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

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

      5. neg-mul-1 N/A

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

      6. *-commutative N/A

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

      7. metadata-eval N/A

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

      8. *-inverses N/A

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

      9. distribute-frac-neg N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

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

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

      13. lift-*.f64 N/A

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

      14. lift-neg.f64 N/A

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

      15. associate-/l* N/A

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

      16. clear-num N/A

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

      17. un-div-inv N/A

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

      18. lift-neg.f64 N/A

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

      19. lift-*.f64 N/A

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

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

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

      21. associate-/r* N/A

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

      22. *-inverses N/A

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

      23. lower-/.f64 N/A

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

      24. lift-*.f64 N/A

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

      25. *-commutative N/A

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

      26. lower-*.f64 N/A

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

      27. neg-mul-1 N/A

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

   9. Applied rewrites 99.8%

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

   11. Applied rewrites 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+181}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-1}{z \cdot x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\left(y \cdot z\right) \cdot x\\ \mathbf{if}\;y \cdot z \leq -2:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+131}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (* y z) x))))
   (if (<= (* y z) -2.0)
     t_0
     (if (<= (* y z) 1e-7) x (if (<= (* y z) 5e+131) t_0 (- (* y (* z x))))))))

C

double code(double x, double y, double z) {
	double t_0 = -((y * z) * x);
	double tmp;
	if ((y * z) <= -2.0) {
		tmp = t_0;
	} else if ((y * z) <= 1e-7) {
		tmp = x;
	} else if ((y * z) <= 5e+131) {
		tmp = t_0;
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -((y * z) * x)
    if ((y * z) <= (-2.0d0)) then
        tmp = t_0
    else if ((y * z) <= 1d-7) then
        tmp = x
    else if ((y * z) <= 5d+131) then
        tmp = t_0
    else
        tmp = -(y * (z * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -((y * z) * x);
	double tmp;
	if ((y * z) <= -2.0) {
		tmp = t_0;
	} else if ((y * z) <= 1e-7) {
		tmp = x;
	} else if ((y * z) <= 5e+131) {
		tmp = t_0;
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -((y * z) * x)
	tmp = 0
	if (y * z) <= -2.0:
		tmp = t_0
	elif (y * z) <= 1e-7:
		tmp = x
	elif (y * z) <= 5e+131:
		tmp = t_0
	else:
		tmp = -(y * (z * x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(Float64(y * z) * x))
	tmp = 0.0
	if (Float64(y * z) <= -2.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 1e-7)
		tmp = x;
	elseif (Float64(y * z) <= 5e+131)
		tmp = t_0;
	else
		tmp = Float64(-Float64(y * Float64(z * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -((y * z) * x);
	tmp = 0.0;
	if ((y * z) <= -2.0)
		tmp = t_0;
	elseif ((y * z) <= 1e-7)
		tmp = x;
	elseif ((y * z) <= 5e+131)
		tmp = t_0;
	else
		tmp = -(y * (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -2.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 1e-7], x, If[LessEqual[N[(y * z), $MachinePrecision], 5e+131], t$95$0, (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -2 or 9.9999999999999995e-8 < (*.f64 y z) < 4.99999999999999995e131

   1. Initial program 95.4%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 92.3

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

   5. Applied rewrites 92.3%

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

   if -2 < (*.f64 y z) < 9.9999999999999995e-8

   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 97.3%

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

      1. *-rgt-identity 97.3

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

   7. Applied rewrites 97.3%

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

   if 4.99999999999999995e131 < (*.f64 y z)

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -2:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;y \cdot z \leq 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+131}:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - y \cdot z\\ t_1 := -\left(y \cdot z\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* y z))) (t_1 (- (* (* y z) x))))
   (if (<= t_0 -0.5) t_1 (if (<= t_0 2.0) x t_1))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = -((y * z) * x);
	double tmp;
	if (t_0 <= -0.5) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (y * z)
    t_1 = -((y * z) * x)
    if (t_0 <= (-0.5d0)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 - (y * z);
	double t_1 = -((y * z) * x);
	double tmp;
	if (t_0 <= -0.5) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (y * z)
	t_1 = -((y * z) * x)
	tmp = 0
	if t_0 <= -0.5:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(y * z))
	t_1 = Float64(-Float64(Float64(y * z) * x))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (y * z);
	t_1 = -((y * z) * x);
	tmp = 0.0;
	if (t_0 <= -0.5)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision])}, If[LessEqual[t$95$0, -0.5], t$95$1, If[LessEqual[t$95$0, 2.0], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (*.f64 y z)) < -0.5 or 2 < (-.f64 #s(literal 1 binary64) (*.f64 y z))

   1. Initial program 92.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   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. mul-1-neg N/A

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

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

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 89.9

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

   5. Applied rewrites 89.9%

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

   if -0.5 < (-.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 97.3%

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

      1. *-rgt-identity 97.3

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

   7. Applied rewrites 97.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \cdot z \leq -0.5:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \mathbf{elif}\;1 - y \cdot z \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-\left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+131) (* x (- 1.0 (* y z))) (- (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+131) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Fortran

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) <= 5d+131) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = -(y * (z * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+131) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = -(y * (z * x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+131:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = -(y * (z * x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+131)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(-Float64(y * Float64(z * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+131)
		tmp = x * (1.0 - (y * z));
	else
		tmp = -(y * (z * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+131], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 4.99999999999999995e131

   1. Initial program 98.2%

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

   if 4.99999999999999995e131 < (*.f64 y z)

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. associate-*r* N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 99.8

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

   5. Applied rewrites 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% accurate, 14.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around 0

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

5. Applied rewrites 52.6%

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

   1. *-rgt-identity 52.6

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

7. Applied rewrites 52.6%

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

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))