Average Error: 6.1 → 1.0
Time: 4.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right) + x\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(z - t\right)\right) + x
double f(double x, double y, double z, double t, double a) {
        double r279507 = x;
        double r279508 = y;
        double r279509 = z;
        double r279510 = t;
        double r279511 = r279509 - r279510;
        double r279512 = r279508 * r279511;
        double r279513 = a;
        double r279514 = r279512 / r279513;
        double r279515 = r279507 + r279514;
        return r279515;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r279516 = y;
        double r279517 = cbrt(r279516);
        double r279518 = r279517 * r279517;
        double r279519 = a;
        double r279520 = cbrt(r279519);
        double r279521 = r279520 * r279520;
        double r279522 = r279518 / r279521;
        double r279523 = r279517 / r279520;
        double r279524 = z;
        double r279525 = t;
        double r279526 = r279524 - r279525;
        double r279527 = r279523 * r279526;
        double r279528 = r279522 * r279527;
        double r279529 = x;
        double r279530 = r279528 + r279529;
        return r279530;
}

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
Target0.7
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.1

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

  2. Simplified2.9

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.9

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

  6. Applied add-cube-cbrt3.4

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

  7. Applied add-cube-cbrt3.6

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

  8. Applied times-frac3.6

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

  9. Applied associate-*l*1.0

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

  10. Final simplification1.0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))