Data.Colour.Matrix:inverse from colour-2.3.3, B

Average Error: 7.4 → 0.7

Time: 8.7s

Precision: binary64

Cost: 1737

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\frac{x \cdot y - z \cdot t}{a} \]

↓

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+282} \lor \neg \left(t_1 \leq 2 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 -2e+282) (not (<= t_1 2e+305)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ t_1 a))))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+282) || !(t_1 <= 2e+305)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

↓

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (z * t)
    if ((t_1 <= (-2d+282)) .or. (.not. (t_1 <= 2d+305))) then
        tmp = (x / (a / y)) - (z / (a / t))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -2e+282) || !(t_1 <= 2e+305)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

↓

def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -2e+282) or not (t_1 <= 2e+305):
		tmp = (x / (a / y)) - (z / (a / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

↓

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -2e+282) || !(t_1 <= 2e+305))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -2e+282) || ~((t_1 <= 2e+305)))
		tmp = (x / (a / y)) - (z / (a / t));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+282], N[Not[LessEqual[t$95$1, 2e+305]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Target

Original	7.4
Target	6.0
Herbie	0.7

\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -2.00000000000000007e282 or 1.9999999999999999e305 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 55.7

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Applied egg-rr 0.3

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}} \]

   if -2.00000000000000007e282 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.9999999999999999e305

   1. Initial program 0.8

      \[\frac{x \cdot y - z \cdot t}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+282} \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+305}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternatives

Alternative 1
Error	20.7
Cost	2724

\[\begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := \left(z \cdot t\right) \cdot \frac{1}{-a}\\ t_3 := z \cdot \frac{-t}{a}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \cdot t \leq 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+215}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 2
Error	4.6
Cost	1864

\[\begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3
Error	25.7
Cost	1176

\[\begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;t \leq 29000000:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+247}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+260}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	25.0
Cost	912

\[\begin{array}{l} t_1 := \frac{-t}{\frac{a}{z}}\\ \mathbf{if}\;y \leq -2 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5
Error	25.1
Cost	912

\[\begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+128}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 6
Error	25.2
Cost	912

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+26}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+183}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 7
Error	32.5
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 1.08 \cdot 10^{+150}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 8
Error	32.5
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 9
Error	32.2
Cost	452

\[\begin{array}{l} \mathbf{if}\;a \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 10
Error	32.7
Cost	320

\[y \cdot \frac{x}{a} \]

Reproduce

herbie shell --seed 2022364 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))