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

Average Error: 7.8 → 0.8

Time: 13.3s

Precision: binary64

Cost: 1737

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

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+290} \lor \neg \left(t_1 \leq 4 \cdot 10^{+300}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \]

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 -5e+290) (not (<= t_1 4e+300)))
     (- (/ 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 <= -5e+290) || !(t_1 <= 4e+300)) {
		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 <= (-5d+290)) .or. (.not. (t_1 <= 4d+300))) 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 <= -5e+290) || !(t_1 <= 4e+300)) {
		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 <= -5e+290) or not (t_1 <= 4e+300):
		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 <= -5e+290) || !(t_1 <= 4e+300))
		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 <= -5e+290) || ~((t_1 <= 4e+300)))
		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, -5e+290], N[Not[LessEqual[t$95$1, 4e+300]], $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	7.8
Target	6.0
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -4.9999999999999998e290 or 4.0000000000000002e300 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.2

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

   2. Applied egg-rr 0.3

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

   if -4.9999999999999998e290 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.0000000000000002e300

   1. Initial program 0.8

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+290} \lor \neg \left(x \cdot y - z \cdot t \leq 4 \cdot 10^{+300}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternatives

Alternative 1
Error	32.3
Cost	2101

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{x}}\\ t_2 := \frac{x \cdot y}{a}\\ t_3 := \frac{z \cdot \left(-t\right)}{a}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+262}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+193}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-268}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 36:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+97} \lor \neg \left(a \leq 1.6 \cdot 10^{+135}\right):\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	32.4
Cost	2101

\[\begin{array}{l} t_1 := \frac{y}{\frac{a}{x}}\\ t_2 := \frac{x \cdot y}{a}\\ t_3 := \frac{z \cdot \left(-t\right)}{a}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{+261}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+193}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-184}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{\frac{1}{y}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 12:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{+97} \lor \neg \left(a \leq 4.8 \cdot 10^{+135}\right):\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	0.9
Cost	1737

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+196} \lor \neg \left(t_1 \leq 5 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \]

Alternative 4
Error	5.3
Cost	1616

\[\begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq -1 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 10^{-63}:\\ \;\;\;\;x \cdot \frac{y - \frac{t}{\frac{x}{z}}}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \end{array} \]

Alternative 5
Error	4.3
Cost	1608

\[\begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+300}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6
Error	25.0
Cost	1441

\[\begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-42} \lor \neg \left(z \leq 9.2 \cdot 10^{-109}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 7
Error	23.9
Cost	1177

\[\begin{array}{l} t_1 := z \cdot \frac{-t}{a}\\ t_2 := \frac{z}{a} \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+153} \lor \neg \left(t \leq 1.65 \cdot 10^{+286}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	23.8
Cost	1177

\[\begin{array}{l} t_1 := \frac{z}{a} \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 1.28 \cdot 10^{+153} \lor \neg \left(t \leq 4.6 \cdot 10^{+285}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{-a}{t}}\\ \end{array} \]

Alternative 9
Error	31.6
Cost	717

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-23} \lor \neg \left(y \leq 5.5 \cdot 10^{-103}\right) \land y \leq 6 \cdot 10^{+276}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 10
Error	32.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-111} \lor \neg \left(a \leq 1.34 \cdot 10^{+82}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11
Error	32.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-115} \lor \neg \left(a \leq 1000000000000\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 12
Error	32.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-113} \lor \neg \left(a \leq 100000\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 13
Error	32.7
Cost	320

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

Reproduce

herbie shell --seed 2022343 
(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))