Average Error: 7.5 → 1.0
Time: 4.3s
Precision: binary64
\[\frac{x \cdot y - z \cdot t}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \le -1.0318458523111846 \cdot 10^{212} \lor \neg \left(x \cdot y - z \cdot t \le 7.39728386618436135 \cdot 10^{257}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y - z \cdot t}}\\ \end{array}\]
\frac{x \cdot y - z \cdot t}{a}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - z \cdot t \le -1.0318458523111846 \cdot 10^{212} \lor \neg \left(x \cdot y - z \cdot t \le 7.39728386618436135 \cdot 10^{257}\right):\\
\;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\

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

\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)))) <= -1.0318458523111846e+212) || !(((double) (((double) (x * y)) - ((double) (z * t)))) <= 7.397283866184361e+257))) {
		VAR = ((double) (((double) (x / ((double) (a / y)))) - ((double) (t * ((double) (z / a))))));
	} else {
		VAR = ((double) (1.0 / ((double) (a / ((double) (((double) (x * y)) - ((double) (z * t))))))));
	}
	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
Target6.3
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.46868496869954822 \cdot 10^{170}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{elif}\;z \lt 6.30983112197837121 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* z t)) < -1.0318458523111846e212 or 7.39728386618436135e257 < (- (* x y) (* z t))

    1. Initial program 34.7

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

    3. Applied div-sub34.7

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

    4. Simplified34.7

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

    6. Applied associate-/l*18.1

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

    8. Applied *-un-lft-identity18.1

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

    9. Applied times-frac0.6

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

    10. Simplified0.6

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

    if -1.0318458523111846e212 < (- (* x y) (* z t)) < 7.39728386618436135e257

    1. Initial program 0.8

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

    3. Applied clear-num1.1

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \le -1.0318458523111846 \cdot 10^{212} \lor \neg \left(x \cdot y - z \cdot t \le 7.39728386618436135 \cdot 10^{257}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{x \cdot y - z \cdot t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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))