Average Error: 7.5 → 0.7
Time: 3.2s
Precision: 64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \le -9.5074592501627567 \cdot 10^{262} \lor \neg \left(x \cdot y - z \cdot t \le 1.1430705439765695 \cdot 10^{260}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{a} - \frac{t \cdot z}{a}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \le -9.5074592501627567 \cdot 10^{262} \lor \neg \left(x \cdot y - z \cdot t \le 1.1430705439765695 \cdot 10^{260}\right):\\
\;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (((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)))) <= -9.507459250162757e+262) || !(((double) (((double) (x * y)) - ((double) (z * t)))) <= 1.1430705439765695e+260))) {
		VAR = ((double) (((double) (x * ((double) (y / a)))) - ((double) (t / ((double) (a / z))))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) * ((double) (1.0 / a)))) - ((double) (((double) (t * z)) / 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

Original7.5
Target5.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z t)) < -9.507459250162757e+262 or 1.1430705439765695e+260 < (- (* x y) (* z t))

    1. Initial program 43.1

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

    3. Applied div-sub43.1

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

    4. Simplified43.1

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

    6. Applied associate-/l*22.5

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

    8. Applied *-un-lft-identity22.5

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

    9. Applied times-frac0.3

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

    10. Simplified0.3

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

    if -9.507459250162757e+262 < (- (* x y) (* z t)) < 1.1430705439765695e+260

    1. Initial program 0.7

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

    3. Applied div-sub0.7

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

    4. Simplified0.7

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

    6. Applied div-inv0.7

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \le -9.5074592501627567 \cdot 10^{262} \lor \neg \left(x \cdot y - z \cdot t \le 1.1430705439765695 \cdot 10^{260}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{a} - \frac{t \cdot z}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020129 
(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))