Average Error: 6.0 → 0.8
Time: 3.2s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.0637893463441613 \cdot 10^{62} \lor \neg \left(y \le 8.1614470454838748 \cdot 10^{-13}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.0637893463441613 \cdot 10^{62} \lor \neg \left(y \le 8.1614470454838748 \cdot 10^{-13}\right):\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r264590 = x;
        double r264591 = y;
        double r264592 = z;
        double r264593 = t;
        double r264594 = r264592 - r264593;
        double r264595 = r264591 * r264594;
        double r264596 = a;
        double r264597 = r264595 / r264596;
        double r264598 = r264590 - r264597;
        return r264598;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r264599 = y;
        double r264600 = -3.0637893463441613e+62;
        bool r264601 = r264599 <= r264600;
        double r264602 = 8.161447045483875e-13;
        bool r264603 = r264599 <= r264602;
        double r264604 = !r264603;
        bool r264605 = r264601 || r264604;
        double r264606 = x;
        double r264607 = a;
        double r264608 = z;
        double r264609 = t;
        double r264610 = r264608 - r264609;
        double r264611 = r264607 / r264610;
        double r264612 = r264599 / r264611;
        double r264613 = r264606 - r264612;
        double r264614 = r264599 * r264608;
        double r264615 = -r264609;
        double r264616 = r264599 * r264615;
        double r264617 = r264614 + r264616;
        double r264618 = r264617 / r264607;
        double r264619 = r264606 - r264618;
        double r264620 = r264605 ? r264613 : r264619;
        return r264620;
}

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

Original6.0
Target0.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.0637893463441613e+62 or 8.161447045483875e-13 < y

    1. Initial program 16.1

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

    3. Applied associate-/l*0.9

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

    if -3.0637893463441613e+62 < y < 8.161447045483875e-13

    1. Initial program 0.8

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

    3. Applied sub-neg0.8

      \[\leadsto x - \frac{y \cdot \color{blue}{\left(z + \left(-t\right)\right)}}{a}\]

    4. Applied distribute-lft-in0.8

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.0637893463441613 \cdot 10^{62} \lor \neg \left(y \le 8.1614470454838748 \cdot 10^{-13}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))