Average Error: 6.3 → 0.9
Time: 13.7s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x - \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
x - \left(\left(z - t\right) \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{a}}\right) \cdot \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}
double f(double x, double y, double z, double t, double a) {
        double r15390652 = x;
        double r15390653 = y;
        double r15390654 = z;
        double r15390655 = t;
        double r15390656 = r15390654 - r15390655;
        double r15390657 = r15390653 * r15390656;
        double r15390658 = a;
        double r15390659 = r15390657 / r15390658;
        double r15390660 = r15390652 - r15390659;
        return r15390660;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15390661 = x;
        double r15390662 = z;
        double r15390663 = t;
        double r15390664 = r15390662 - r15390663;
        double r15390665 = y;
        double r15390666 = cbrt(r15390665);
        double r15390667 = a;
        double r15390668 = cbrt(r15390667);
        double r15390669 = r15390666 / r15390668;
        double r15390670 = r15390664 * r15390669;
        double r15390671 = r15390666 * r15390666;
        double r15390672 = r15390668 * r15390668;
        double r15390673 = r15390671 / r15390672;
        double r15390674 = r15390670 * r15390673;
        double r15390675 = r15390661 - r15390674;
        return r15390675;
}

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

Original6.3
Target0.6
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.3

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

  3. Applied associate-/l*5.8

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

  5. Applied associate-/r/2.6

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

  7. Applied add-cube-cbrt3.1

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

  8. Applied add-cube-cbrt3.3

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

  9. Applied times-frac3.3

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

  10. Applied associate-*l*0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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