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

Average Error: 3.4 → 0.1

Time: 5.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ t_1 := z \cdot \left(y \cdot x - x\right)\\ \mathbf{if}\;t_0 \leq -2.974458431851716 \cdot 10^{+223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 7.608042687497342 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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)) (t_1 (* z (- (* y x) x))))
   (if (<= t_0 -2.974458431851716e+223)
     t_1
     (if (<= t_0 7.608042687497342e+237) (* x (- 1.0 t_0)) t_1))))

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 t_1 = z * ((y * x) - x);
	double tmp;
	if (t_0 <= -2.974458431851716e+223) {
		tmp = t_1;
	} else if (t_0 <= 7.608042687497342e+237) {
		tmp = x * (1.0 - t_0);
	} 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
    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) :: t_1
    real(8) :: tmp
    t_0 = (1.0d0 - y) * z
    t_1 = z * ((y * x) - x)
    if (t_0 <= (-2.974458431851716d+223)) then
        tmp = t_1
    else if (t_0 <= 7.608042687497342d+237) then
        tmp = x * (1.0d0 - t_0)
    else
        tmp = t_1
    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 t_1 = z * ((y * x) - x);
	double tmp;
	if (t_0 <= -2.974458431851716e+223) {
		tmp = t_1;
	} else if (t_0 <= 7.608042687497342e+237) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = t_1;
	}
	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
	t_1 = z * ((y * x) - x)
	tmp = 0
	if t_0 <= -2.974458431851716e+223:
		tmp = t_1
	elif t_0 <= 7.608042687497342e+237:
		tmp = x * (1.0 - t_0)
	else:
		tmp = t_1
	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)
	t_1 = Float64(z * Float64(Float64(y * x) - x))
	tmp = 0.0
	if (t_0 <= -2.974458431851716e+223)
		tmp = t_1;
	elseif (t_0 <= 7.608042687497342e+237)
		tmp = Float64(x * Float64(1.0 - t_0));
	else
		tmp = t_1;
	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;
	t_1 = z * ((y * x) - x);
	tmp = 0.0;
	if (t_0 <= -2.974458431851716e+223)
		tmp = t_1;
	elseif (t_0 <= 7.608042687497342e+237)
		tmp = x * (1.0 - t_0);
	else
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2.974458431851716e+223], t$95$1, If[LessEqual[t$95$0, 7.608042687497342e+237], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	3.4
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 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -2.97445843185171577e223 or 7.608042687497342e237 < (*.f64 (-.f64 1 y) z)

   1. Initial program 24.1

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

   2. Taylor expanded in y around 0 0.3

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

   3. Taylor expanded in z around inf 0.5

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

   if -2.97445843185171577e223 < (*.f64 (-.f64 1 y) z) < 7.608042687497342e237

   1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -2.974458431851716 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 7.608042687497342 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022131 
(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))))