Average Error: 7.4 → 1.6
Time: 5.4s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -1.9625962662264828 \cdot 10^{+135} \lor \neg \left(x \cdot y - z \cdot t \leq 3.7551065759873035 \cdot 10^{+182}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \leq -1.9625962662264828 \cdot 10^{+135} \lor \neg \left(x \cdot y - z \cdot t \leq 3.7551065759873035 \cdot 10^{+182}\right):\\
\;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (((double) (((double) (x * y)) - ((double) (z * t)))) / a);
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((double) (((double) (x * y)) - ((double) (z * t)))) <= -1.9625962662264828e+135) || !(((double) (((double) (x * y)) - ((double) (z * t)))) <= 3.7551065759873035e+182))) {
		VAR = ((double) (((double) (x * (y / a))) - ((double) (z * (t / a)))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) - ((double) (z * t)))) * (1.0 / a)));
	}
	return VAR;
}

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

Original7.4
Target6.0
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z t)) < -1.9625962662264828e135 or 3.7551065759873035e182 < (- (* x y) (* z t))

    1. Initial program 21.1

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

    3. Applied div-sub21.1

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

    4. Simplified13.2

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

    5. Simplified2.6

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

    if -1.9625962662264828e135 < (- (* x y) (* z t)) < 3.7551065759873035e182

    1. Initial program 1.1

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

    3. Applied div-inv1.2

      \[\leadsto \color{blue}{\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -1.9625962662264828 \cdot 10^{+135} \lor \neg \left(x \cdot y - z \cdot t \leq 3.7551065759873035 \cdot 10^{+182}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - z \cdot t\right) \cdot \frac{1}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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))