Average Error: 7.6 → 1.2
Time: 4.8s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2.7268203083758326 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{z \cdot t}{a}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2.7268203083758326 \cdot 10^{+140}\right):\\
\;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot y}{a} - \frac{z \cdot t}{a}\\

\end{array}
(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- (* x y) (* z t)) (- INFINITY))
         (not (<= (- (* x y) (* z t)) 2.7268203083758326e+140)))
   (- (/ x (/ a y)) (* z (/ t a)))
   (- (/ (* x y) a) (/ (* z t) a))))
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 tmp;
	if ((((x * y) - (z * t)) <= -((double) INFINITY)) || !(((x * y) - (z * t)) <= 2.7268203083758326e+140)) {
		tmp = (x / (a / y)) - (z * (t / a));
	} else {
		tmp = ((x * y) / a) - ((z * t) / a);
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.6
Target6.0
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 2.7268203083758326e140 < (-.f64 (*.f64 x y) (*.f64 z t))

    1. Initial program 30.2

      \[\frac{x \cdot y - z \cdot t}{a}\]
    2. Using strategy rm

    3. Applied div-sub_binary64_2224830.2

      \[\leadsto \color{blue}{\frac{x \cdot y}{a} - \frac{z \cdot t}{a}}\]
    4. Using strategy rm

    5. Applied associate-/l*_binary64_2218817.1

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} - \frac{z \cdot t}{a}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity_binary64_2224317.1

      \[\leadsto \frac{x}{\frac{a}{y}} - \frac{z \cdot t}{\color{blue}{1 \cdot a}}\]

    8. Applied times-frac_binary64_222492.1

      \[\leadsto \frac{x}{\frac{a}{y}} - \color{blue}{\frac{z}{1} \cdot \frac{t}{a}}\]

    9. Simplified2.1

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

    if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.7268203083758326e140

    1. Initial program 0.9

      \[\frac{x \cdot y - z \cdot t}{a}\]
    2. Using strategy rm

    3. Applied div-sub_binary64_222480.9

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 2.7268203083758326 \cdot 10^{+140}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a} - \frac{z \cdot t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(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))