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

Average Error: 3.5 → 0.1

Time: 6.4s

Precision: binary64

Cost: 1352

Math

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

↓

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

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 (- INFINITY))
     (* y (* z x))
     (if (<= t_0 2e+215) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (- (* y x) x))))))

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 <= -((double) INFINITY)) {
		tmp = y * (z * x);
	} else if (t_0 <= 2e+215) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z * x);
	} else if (t_0 <= 2e+215) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * ((y * x) - x);
	}
	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 <= -math.inf:
		tmp = y * (z * x)
	elif t_0 <= 2e+215:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * ((y * x) - x)
	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 <= Float64(-Inf))
		tmp = Float64(y * Float64(z * x));
	elseif (t_0 <= 2e+215)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(Float64(y * x) - x));
	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 <= -Inf)
		tmp = y * (z * x);
	elseif (t_0 <= 2e+215)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * ((y * x) - x);
	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, (-Infinity)], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+215], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.5
Target	0.2
Herbie	0.1

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 0.3

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

   3. Taylor expanded in y around inf 0.3

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 1.99999999999999981e215

   1. Initial program 0.1

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

   if 1.99999999999999981e215 < (*.f64 (-.f64 1 y) z)

   1. Initial program 21.2

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

   2. Simplified 0.7

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

   3. Taylor expanded in z around inf 0.7

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

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+215}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	20.1
Cost	1244

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+195}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -113.13207983602821:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.8835882681962543 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	20.1
Cost	1244

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.18 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -113.13207983602821:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.8835882681962543 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	4.5
Cost	976

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot x - x\right)\\ t_1 := x + z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -527111280153.2585:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.015645786008923 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.015213277955912 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.04776155565695565:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.7
Cost	840

\[\begin{array}{l} t_0 := x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;z \leq -2.0565631925566188 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.118203813164115 \cdot 10^{-99}:\\ \;\;\;\;x + y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	3.8
Cost	712

\[\begin{array}{l} t_0 := x + z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -4673.224789273354:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.867885715714948 \cdot 10^{-5}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	3.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -4673.224789273354:\\ \;\;\;\;x + y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 7.867885715714948 \cdot 10^{-5}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 7
Error	12.3
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.5647560239085615 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	12.3
Cost	584

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.5647560239085615 \cdot 10^{+47}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	18.9
Cost	520

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -113.13207983602821:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.04776155565695565:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	33.4
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(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))))