Average Error: 6.6 → 1.7
Time: 23.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \left(\left(y \cdot \left(\sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \left(\left(y \cdot \left(\sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}} \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}}\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}
double f(double x, double y, double z, double t) {
        double r375698 = x;
        double r375699 = y;
        double r375700 = z;
        double r375701 = r375700 - r375698;
        double r375702 = r375699 * r375701;
        double r375703 = t;
        double r375704 = r375702 / r375703;
        double r375705 = r375698 + r375704;
        return r375705;
}
↓
double f(double x, double y, double z, double t) {
        double r375706 = x;
        double r375707 = y;
        double r375708 = z;
        double r375709 = r375708 - r375706;
        double r375710 = cbrt(r375709);
        double r375711 = r375710 * r375710;
        double r375712 = t;
        double r375713 = cbrt(r375712);
        double r375714 = r375713 * r375713;
        double r375715 = r375711 / r375714;
        double r375716 = cbrt(r375715);
        double r375717 = r375716 * r375716;
        double r375718 = r375707 * r375717;
        double r375719 = r375718 * r375716;
        double r375720 = r375710 / r375713;
        double r375721 = r375719 * r375720;
        double r375722 = r375706 + r375721;
        return r375722;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.6
Target2.0
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  3. Applied *-un-lft-identity6.6

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

  4. Applied times-frac6.9

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

  5. Simplified6.9

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

  7. Applied add-cube-cbrt7.3

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

  8. Applied add-cube-cbrt7.5

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

  9. Applied times-frac7.5

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

  10. Applied associate-*r*1.6

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

  12. Applied add-cube-cbrt1.7

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

  13. Applied associate-*r*1.7

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

  14. Final simplification1.7

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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