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

Average Error: 12.08% → 1.23%

Time: 11.2s

Precision: binary64

Cost: 2121

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

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+304} \lor \neg \left(t_1 \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot t + \left(t_1 - z \cdot t\right)}{a}\\ \end{array} \]

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 -5e+304) (not (<= t_1 5e+223)))
     (- (/ x (/ a y)) (* t (/ z a)))
     (/ (+ (* z t) (- t_1 (* z t))) 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 <= -5e+304) || !(t_1 <= 5e+223)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = ((z * t) + (t_1 - (z * t))) / 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 <= (-5d+304)) .or. (.not. (t_1 <= 5d+223))) then
        tmp = (x / (a / y)) - (t * (z / a))
    else
        tmp = ((z * t) + (t_1 - (z * t))) / 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 <= -5e+304) || !(t_1 <= 5e+223)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = ((z * t) + (t_1 - (z * t))) / 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 <= -5e+304) or not (t_1 <= 5e+223):
		tmp = (x / (a / y)) - (t * (z / a))
	else:
		tmp = ((z * t) + (t_1 - (z * t))) / 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 <= -5e+304) || !(t_1 <= 5e+223))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(Float64(Float64(z * t) + Float64(t_1 - Float64(z * t))) / 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 <= -5e+304) || ~((t_1 <= 5e+223)))
		tmp = (x / (a / y)) - (t * (z / a));
	else
		tmp = ((z * t) + (t_1 - (z * t))) / 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, -5e+304], N[Not[LessEqual[t$95$1, 5e+223]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] + N[(t$95$1 - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Target

Original	12.08%
Target	9.31%
Herbie	1.23%

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.9999999999999997e304 or 4.99999999999999985e223 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 68.08

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

   2. Applied egg-rr 0.93

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

   3. Applied egg-rr 1.05

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

   if -4.9999999999999997e304 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.99999999999999985e223

   1. Initial program 1.26

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

   2. Applied egg-rr 1.27

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

4. Final simplification 1.23

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+304} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot t + \left(\left(x \cdot y - z \cdot t\right) - z \cdot t\right)}{a}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.22%
Cost	1737

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+304} \lor \neg \left(t_1 \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \]

Alternative 2
Error	6.47%
Cost	1608

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 3
Error	29.42%
Cost	1292

\[\begin{array}{l} t_1 := t \cdot \left(-\frac{z}{a}\right)\\ \mathbf{if}\;z \cdot t \leq -6 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 10^{-31}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{+166}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{1}{-a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	39.28%
Cost	913

\[\begin{array}{l} t_1 := z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-121} \lor \neg \left(z \leq 2.9 \cdot 10^{-149}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 5
Error	39.54%
Cost	912

\[\begin{array}{l} t_1 := z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 6
Error	39.67%
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+34}:\\ \;\;\;\;\frac{z}{-\frac{a}{t}}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 7
Error	39.65%
Cost	912

\[\begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;\frac{z}{-\frac{a}{t}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-97}:\\ \;\;\;\;\frac{1}{\frac{\frac{a}{y}}{x}}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-149}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{z}{a}\right)\\ \end{array} \]

Alternative 8
Error	51.01%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-162} \lor \neg \left(x \leq 4.5 \cdot 10^{-181}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9
Error	50.93%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-162} \lor \neg \left(x \leq 5.8 \cdot 10^{-175}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10
Error	50.41%
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-258}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11
Error	51.12%
Cost	320

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

Reproduce

herbie shell --seed 2023115 
(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))