Average Error: 6.0 → 0.9
Time: 9.2s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x - \frac{1}{\frac{\frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - t}{\frac{\sqrt[3]{a}}{\sqrt[3]{y}}}}}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
x - \frac{1}{\frac{\frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - t}{\frac{\sqrt[3]{a}}{\sqrt[3]{y}}}}}
double f(double x, double y, double z, double t, double a) {
        double r365719 = x;
        double r365720 = y;
        double r365721 = z;
        double r365722 = t;
        double r365723 = r365721 - r365722;
        double r365724 = r365720 * r365723;
        double r365725 = a;
        double r365726 = r365724 / r365725;
        double r365727 = r365719 - r365726;
        return r365727;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r365728 = x;
        double r365729 = 1.0;
        double r365730 = a;
        double r365731 = cbrt(r365730);
        double r365732 = r365731 * r365731;
        double r365733 = y;
        double r365734 = cbrt(r365733);
        double r365735 = r365734 * r365734;
        double r365736 = r365732 / r365735;
        double r365737 = z;
        double r365738 = t;
        double r365739 = r365737 - r365738;
        double r365740 = r365731 / r365734;
        double r365741 = r365739 / r365740;
        double r365742 = r365736 / r365741;
        double r365743 = r365729 / r365742;
        double r365744 = r365728 - r365743;
        return r365744;
}

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
Target0.6
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.0

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

  3. Applied sub-neg6.0

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

  4. Applied distribute-lft-in6.0

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

  6. Applied clear-num6.1

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

  7. Simplified2.6

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

  9. Applied add-cube-cbrt3.0

    \[\leadsto x - \frac{1}{\frac{\frac{a}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}}{z - t}}\]

  10. Applied add-cube-cbrt3.2

    \[\leadsto x - \frac{1}{\frac{\frac{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{z - t}}\]

  11. Applied times-frac3.2

    \[\leadsto x - \frac{1}{\frac{\color{blue}{\frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{a}}{\sqrt[3]{y}}}}{z - t}}\]

  12. Applied associate-/l*0.9

    \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - t}{\frac{\sqrt[3]{a}}{\sqrt[3]{y}}}}}}\]

  13. Final simplification0.9

    \[\leadsto x - \frac{1}{\frac{\frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\frac{z - t}{\frac{\sqrt[3]{a}}{\sqrt[3]{y}}}}}\]

Reproduce

herbie shell --seed 2020049 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-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)))