Average Error: 6.0 → 3.2
Time: 15.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -102833585701505768775598385857036288 \lor a \le 27501089785367.6328125:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1} \cdot \frac{\frac{1}{a}}{\frac{\sqrt{1}}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;a \le -102833585701505768775598385857036288 \lor a \le 27501089785367.6328125:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r261391 = x;
        double r261392 = y;
        double r261393 = z;
        double r261394 = t;
        double r261395 = r261393 - r261394;
        double r261396 = r261392 * r261395;
        double r261397 = a;
        double r261398 = r261396 / r261397;
        double r261399 = r261391 - r261398;
        return r261399;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r261400 = a;
        double r261401 = -1.0283358570150577e+35;
        bool r261402 = r261400 <= r261401;
        double r261403 = 27501089785367.633;
        bool r261404 = r261400 <= r261403;
        bool r261405 = r261402 || r261404;
        double r261406 = x;
        double r261407 = y;
        double r261408 = z;
        double r261409 = t;
        double r261410 = r261408 - r261409;
        double r261411 = r261407 * r261410;
        double r261412 = r261411 / r261400;
        double r261413 = r261406 - r261412;
        double r261414 = 1.0;
        double r261415 = r261407 / r261414;
        double r261416 = r261414 / r261400;
        double r261417 = sqrt(r261414);
        double r261418 = r261417 / r261410;
        double r261419 = r261416 / r261418;
        double r261420 = r261415 * r261419;
        double r261421 = r261406 - r261420;
        double r261422 = r261405 ? r261413 : r261421;
        return r261422;
}

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
Target0.7
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if a < -1.0283358570150577e+35

    1. Initial program 9.9

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

    3. Applied associate-/l*0.6

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

    if -1.0283358570150577e+35 < a < 27501089785367.633

    1. Initial program 0.8

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

    if 27501089785367.633 < a

    1. Initial program 9.6

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

    3. Applied associate-/l*0.6

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

    5. Applied div-inv0.6

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

    6. Applied associate-/r*1.7

      \[\leadsto x - \color{blue}{\frac{\frac{y}{a}}{\frac{1}{z - t}}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity1.7

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

    9. Applied add-sqr-sqrt1.7

      \[\leadsto x - \frac{\frac{y}{a}}{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{1 \cdot \left(z - t\right)}}\]

    10. Applied times-frac1.7

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

    11. Applied div-inv1.8

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

    12. Applied times-frac0.5

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

    13. Simplified0.5

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -102833585701505768775598385857036288 \lor a \le 27501089785367.6328125:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1} \cdot \frac{\frac{1}{a}}{\frac{\sqrt{1}}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019297 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.07612662163899753e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.8944268627920891e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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