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

Average Error: 3.4 → 1.2

Time: 6.8s

Precision: binary64

Cost: 840

Math

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

↓

\[\begin{array}{l} t_0 := x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.5524451704913054 \cdot 10^{-168}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (+ y -1.0))))))
   (if (<= x -1e+138)
     t_0
     (if (<= x 1.5524451704913054e-168) (+ x (* z (- (* x y) x))) t_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 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (x <= -1e+138) {
		tmp = t_0;
	} else if (x <= 1.5524451704913054e-168) {
		tmp = x + (z * ((x * y) - x));
	} else {
		tmp = t_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 = x * (1.0d0 + (z * (y + (-1.0d0))))
    if (x <= (-1d+138)) then
        tmp = t_0
    else if (x <= 1.5524451704913054d-168) then
        tmp = x + (z * ((x * y) - x))
    else
        tmp = t_0
    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 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (x <= -1e+138) {
		tmp = t_0;
	} else if (x <= 1.5524451704913054e-168) {
		tmp = x + (z * ((x * y) - x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = x * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if x <= -1e+138:
		tmp = t_0
	elif x <= 1.5524451704913054e-168:
		tmp = x + (z * ((x * y) - x))
	else:
		tmp = t_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(x * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (x <= -1e+138)
		tmp = t_0;
	elseif (x <= 1.5524451704913054e-168)
		tmp = Float64(x + Float64(z * Float64(Float64(x * y) - x)));
	else
		tmp = t_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 = x * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (x <= -1e+138)
		tmp = t_0;
	elseif (x <= 1.5524451704913054e-168)
		tmp = x + (z * ((x * y) - x));
	else
		tmp = t_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[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+138], t$95$0, If[LessEqual[x, 1.5524451704913054e-168], N[(x + N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	3.4
Target	0.2
Herbie	1.2

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

Derivation

1. Split input into 2 regimes

2. if x < -1e138 or 1.5524451704913054e-168 < x

   1. Initial program 1.5

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

   if -1e138 < x < 1.5524451704913054e-168

   1. Initial program 4.9

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

   2. Simplified 1.0

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

   3. Applied egg-rr 1.0

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

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;x \leq 1.5524451704913054 \cdot 10^{-168}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	20.6
Cost	980

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -58000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.3208976595093053 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1100:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	20.7
Cost	980

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -58000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.3208976595093053 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1100:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.2
Cost	840

\[\begin{array}{l} t_0 := x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{if}\;z \leq -4.0483219142097575 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{-20}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	2.2
Cost	712

\[\begin{array}{l} t_0 := x + y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;y \leq -2.285844912751982:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.014191937481997147:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	3.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.285844912751982:\\ \;\;\;\;x + y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 0.014191937481997147:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6
Error	1.0
Cost	712

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

Alternative 7
Error	12.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 51746012972654550:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8
Error	12.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 51746012972654550:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9
Error	19.2
Cost	520

\[\begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1100:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	33.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022216 
(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))))