Average Error: 6.2 → 2.3
Time: 5.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \left(\sqrt[3]{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)} \cdot \sqrt[3]{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \left(\sqrt[3]{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)} \cdot \sqrt[3]{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)}
double f(double x, double y, double z, double t, double a) {
        double r409297 = x;
        double r409298 = y;
        double r409299 = z;
        double r409300 = t;
        double r409301 = r409299 - r409300;
        double r409302 = r409298 * r409301;
        double r409303 = a;
        double r409304 = r409302 / r409303;
        double r409305 = r409297 + r409304;
        return r409305;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r409306 = x;
        double r409307 = y;
        double r409308 = cbrt(r409307);
        double r409309 = r409308 * r409308;
        double r409310 = a;
        double r409311 = cbrt(r409310);
        double r409312 = r409309 / r409311;
        double r409313 = r409308 / r409311;
        double r409314 = z;
        double r409315 = t;
        double r409316 = r409314 - r409315;
        double r409317 = r409316 / r409311;
        double r409318 = r409313 * r409317;
        double r409319 = r409312 * r409318;
        double r409320 = cbrt(r409319);
        double r409321 = r409320 * r409320;
        double r409322 = r409321 * r409320;
        double r409323 = r409306 + r409322;
        return r409323;
}

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

Original6.2
Target0.7
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.2

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

  3. Applied add-cube-cbrt6.6

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

  4. Applied times-frac3.1

    \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt3.2

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

  7. Applied times-frac3.2

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

  8. Applied associate-*l*2.2

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

  10. Applied add-cube-cbrt2.3

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

  11. Final simplification2.3

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

Reproduce

herbie shell --seed 2020047 
(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)))