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

Average Accuracy: 94.9% → 99.5%

Time: 9.5s

Precision: binary64

Cost: 1352

Math

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

↓

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x - t_0 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 -5e+306)
     (* y (* z x))
     (if (<= t_0 4e+130) (- x (* t_0 x)) (* z (* x (+ y -1.0)))))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+306) {
		tmp = y * (z * x);
	} else if (t_0 <= 4e+130) {
		tmp = x - (t_0 * x);
	} else {
		tmp = z * (x * (y + -1.0));
	}
	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
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end 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+306)) then
        tmp = y * (z * x)
    else if (t_0 <= 4d+130) then
        tmp = x - (t_0 * x)
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - 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+306) {
		tmp = y * (z * x);
	} else if (t_0 <= 4e+130) {
		tmp = x - (t_0 * x);
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -5e+306:
		tmp = y * (z * x)
	elif t_0 <= 4e+130:
		tmp = x - (t_0 * x)
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= -5e+306)
		tmp = Float64(y * Float64(z * x));
	elseif (t_0 <= 4e+130)
		tmp = Float64(x - Float64(t_0 * x));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -5e+306)
		tmp = y * (z * x);
	elseif (t_0 <= 4e+130)
		tmp = x - (t_0 * x);
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+306], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+130], N[(x - N[(t$95$0 * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	94.9%
Target	99.7%
Herbie	99.5%

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.99999999999999993e306

   1. Initial program 2.4%

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

   2. Taylor expanded in y around inf 98.5%

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

   if -4.99999999999999993e306 < (*.f64 (-.f64 1 y) z) < 4.0000000000000002e130

   1. Initial program 99.9%

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

   2. Applied egg-rr 99.9%

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

      [Start] 99.9	\[ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
      sub-neg [=>] 99.9	\[ x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]
      +-commutative [=>] 99.9	\[ x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]
      distribute-lft-in [=>] 99.9	\[ \color{blue}{x \cdot \left(-\left(1 - y\right) \cdot z\right) + x \cdot 1} \]
      distribute-lft-neg-in [=>] 99.9	\[ x \cdot \color{blue}{\left(\left(-\left(1 - y\right)\right) \cdot z\right)} + x \cdot 1 \]
      *-commutative [=>] 99.9	\[ x \cdot \color{blue}{\left(z \cdot \left(-\left(1 - y\right)\right)\right)} + x \cdot 1 \]
      sub-neg [=>] 99.9	\[ x \cdot \left(z \cdot \left(-\color{blue}{\left(1 + \left(-y\right)\right)}\right)\right) + x \cdot 1 \]
      distribute-neg-in [=>] 99.9	\[ x \cdot \left(z \cdot \color{blue}{\left(\left(-1\right) + \left(-\left(-y\right)\right)\right)}\right) + x \cdot 1 \]
      +-commutative [=>] 99.9	\[ x \cdot \left(z \cdot \color{blue}{\left(\left(-\left(-y\right)\right) + \left(-1\right)\right)}\right) + x \cdot 1 \]
      *-un-lft-identity [=>] 99.9	\[ x \cdot \left(z \cdot \left(\left(-\left(-\color{blue}{1 \cdot y}\right)\right) + \left(-1\right)\right)\right) + x \cdot 1 \]
      distribute-lft-neg-in [=>] 99.9	\[ x \cdot \left(z \cdot \left(\left(-\color{blue}{\left(-1\right) \cdot y}\right) + \left(-1\right)\right)\right) + x \cdot 1 \]
      distribute-lft-neg-in [=>] 99.9	\[ x \cdot \left(z \cdot \left(\color{blue}{\left(-\left(-1\right)\right) \cdot y} + \left(-1\right)\right)\right) + x \cdot 1 \]
      metadata-eval [=>] 99.9	\[ x \cdot \left(z \cdot \left(\left(-\color{blue}{-1}\right) \cdot y + \left(-1\right)\right)\right) + x \cdot 1 \]
      metadata-eval [=>] 99.9	\[ x \cdot \left(z \cdot \left(\color{blue}{1} \cdot y + \left(-1\right)\right)\right) + x \cdot 1 \]
      *-un-lft-identity [<=] 99.9	\[ x \cdot \left(z \cdot \left(\color{blue}{y} + \left(-1\right)\right)\right) + x \cdot 1 \]
      metadata-eval [=>] 99.9	\[ x \cdot \left(z \cdot \left(y + \color{blue}{-1}\right)\right) + x \cdot 1 \]
      *-commutative [<=] 99.9	\[ x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{1 \cdot x} \]
      *-un-lft-identity [<=] 99.9	\[ x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{x} \]

   if 4.0000000000000002e130 < (*.f64 (-.f64 1 y) z)

   1. Initial program 83.2%

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

   2. Taylor expanded in z around inf 97.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+306}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x - \left(\left(1 - y\right) \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.5%
Cost	1352

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	99.5%
Cost	1352

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 4 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(\left(1 + y \cdot z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	81.0%
Cost	1113

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+175} \lor \neg \left(y \leq 2 \cdot 10^{+207}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	98.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 49000\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5
Accuracy	69.7%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 49000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Accuracy	48.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))