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

Average Error: 5.27% → 0.45%

Time: 10.2s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+231}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+124}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right) + x \cdot \left(1 - z\right)\\ \end{array} \]

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 -1e+231)
     (* z (* x (+ y -1.0)))
     (if (<= t_0 5e+124)
       (+ x (* x (* z (+ y -1.0))))
       (+ (* y (* z x)) (* x (- 1.0 z)))))))

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 <= -1e+231) {
		tmp = z * (x * (y + -1.0));
	} else if (t_0 <= 5e+124) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = (y * (z * x)) + (x * (1.0 - z));
	}
	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 <= (-1d+231)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (t_0 <= 5d+124) then
        tmp = x + (x * (z * (y + (-1.0d0))))
    else
        tmp = (y * (z * x)) + (x * (1.0d0 - z))
    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 <= -1e+231) {
		tmp = z * (x * (y + -1.0));
	} else if (t_0 <= 5e+124) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = (y * (z * x)) + (x * (1.0 - z));
	}
	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 <= -1e+231:
		tmp = z * (x * (y + -1.0))
	elif t_0 <= 5e+124:
		tmp = x + (x * (z * (y + -1.0)))
	else:
		tmp = (y * (z * x)) + (x * (1.0 - z))
	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 <= -1e+231)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (t_0 <= 5e+124)
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(y * Float64(z * x)) + Float64(x * Float64(1.0 - z)));
	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 <= -1e+231)
		tmp = z * (x * (y + -1.0));
	elseif (t_0 <= 5e+124)
		tmp = x + (x * (z * (y + -1.0)));
	else
		tmp = (y * (z * x)) + (x * (1.0 - z));
	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, -1e+231], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+124], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	5.27%
Target	0.34%
Herbie	0.45%

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -1.0000000000000001e231

   1. Initial program 37.31

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

   2. Taylor expanded in z around inf 0.47

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

   if -1.0000000000000001e231 < (*.f64 (-.f64 1 y) z) < 4.9999999999999996e124

   1. Initial program 0.11

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

   2. Applied egg-rr 0.1

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

   if 4.9999999999999996e124 < (*.f64 (-.f64 1 y) z)

   1. Initial program 17.3

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

   2. Taylor expanded in y around 0 2.34

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

4. Final simplification 0.45

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -1 \cdot 10^{+231}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 5 \cdot 10^{+124}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right) + x \cdot \left(1 - z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	46.54%
Cost	1905

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-206}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+148} \lor \neg \left(y \leq 6.2 \cdot 10^{+169}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	44.47%
Cost	1905

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-161}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-206}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.02 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.95 \cdot 10^{+149} \lor \neg \left(y \leq 5.7 \cdot 10^{+169}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	44.32%
Cost	1905

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-207}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-302}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+149} \lor \neg \left(y \leq 5.7 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	0.17%
Cost	1353

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+231} \lor \neg \left(t_0 \leq 10^{+241}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 5
Error	0.17%
Cost	1353

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+231} \lor \neg \left(t_0 \leq 10^{+241}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 6
Error	18.17%
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+148} \lor \neg \left(y \leq 6.9 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	18.13%
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+72}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{elif}\;y \leq 3.95 \cdot 10^{+149} \lor \neg \left(y \leq 5.7 \cdot 10^{+169}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	1.53%
Cost	844

\[\begin{array}{l} t_0 := z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;z \leq -4.6:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{elif}\;z \leq 220000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	0.26%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-14} \lor \neg \left(z \leq 6.2 \cdot 10^{-54}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 10
Error	30.33%
Cost	521

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

Alternative 11
Error	52.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023089 
(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))))