Average Error: 6.1 → 1.1
Time: 25.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.7432637471506773 \cdot 10^{-180}:\\ \;\;\;\;x + \frac{z - t}{\sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\\ \mathbf{elif}\;y \le 1.593765271222455 \cdot 10^{-09}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.7432637471506773 \cdot 10^{-180}:\\
\;\;\;\;x + \frac{z - t}{\sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\\

\mathbf{elif}\;y \le 1.593765271222455 \cdot 10^{-09}:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r19014477 = x;
        double r19014478 = y;
        double r19014479 = z;
        double r19014480 = t;
        double r19014481 = r19014479 - r19014480;
        double r19014482 = r19014478 * r19014481;
        double r19014483 = a;
        double r19014484 = r19014482 / r19014483;
        double r19014485 = r19014477 + r19014484;
        return r19014485;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19014486 = y;
        double r19014487 = -1.7432637471506773e-180;
        bool r19014488 = r19014486 <= r19014487;
        double r19014489 = x;
        double r19014490 = z;
        double r19014491 = t;
        double r19014492 = r19014490 - r19014491;
        double r19014493 = a;
        double r19014494 = cbrt(r19014493);
        double r19014495 = r19014492 / r19014494;
        double r19014496 = r19014494 * r19014494;
        double r19014497 = r19014486 / r19014496;
        double r19014498 = r19014495 * r19014497;
        double r19014499 = r19014489 + r19014498;
        double r19014500 = 1.593765271222455e-09;
        bool r19014501 = r19014486 <= r19014500;
        double r19014502 = 1.0;
        double r19014503 = r19014486 * r19014492;
        double r19014504 = r19014493 / r19014503;
        double r19014505 = r19014502 / r19014504;
        double r19014506 = r19014489 + r19014505;
        double r19014507 = r19014493 / r19014492;
        double r19014508 = r19014486 / r19014507;
        double r19014509 = r19014489 + r19014508;
        double r19014510 = r19014501 ? r19014506 : r19014509;
        double r19014511 = r19014488 ? r19014499 : r19014510;
        return r19014511;
}

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

Original6.1
Target0.6
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.7432637471506773e-180

    1. Initial program 8.4

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

    3. Applied add-cube-cbrt8.9

      \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

    4. Applied times-frac2.1

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}}\]

    if -1.7432637471506773e-180 < y < 1.593765271222455e-09

    1. Initial program 0.4

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

    3. Applied clear-num0.5

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

    if 1.593765271222455e-09 < y

    1. Initial program 14.4

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

    3. Applied associate-/l*0.7

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.7432637471506773 \cdot 10^{-180}:\\ \;\;\;\;x + \frac{z - t}{\sqrt[3]{a}} \cdot \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\\ \mathbf{elif}\;y \le 1.593765271222455 \cdot 10^{-09}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"

  :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)))