Average Error: 6.8 → 0.9
Time: 19.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(z - x\right)\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(z - x\right)\right)
double f(double x, double y, double z, double t) {
        double r305464 = x;
        double r305465 = y;
        double r305466 = z;
        double r305467 = r305466 - r305464;
        double r305468 = r305465 * r305467;
        double r305469 = t;
        double r305470 = r305468 / r305469;
        double r305471 = r305464 + r305470;
        return r305471;
}
↓
double f(double x, double y, double z, double t) {
        double r305472 = x;
        double r305473 = y;
        double r305474 = cbrt(r305473);
        double r305475 = r305474 * r305474;
        double r305476 = t;
        double r305477 = cbrt(r305476);
        double r305478 = r305477 * r305477;
        double r305479 = r305475 / r305478;
        double r305480 = r305474 / r305477;
        double r305481 = z;
        double r305482 = r305481 - r305472;
        double r305483 = r305480 * r305482;
        double r305484 = r305479 * r305483;
        double r305485 = r305472 + r305484;
        return r305485;
}

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

Original6.8
Target2.1
Herbie0.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  3. Applied add-cube-cbrt7.3

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

  4. Applied times-frac3.2

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

  5. Taylor expanded around 0 6.8

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

  6. Simplified6.2

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

  8. Applied div-inv6.2

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

  9. Applied div-inv6.2

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

  10. Applied distribute-rgt-out--6.2

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

  11. Applied associate-*r*2.1

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

  12. Simplified2.1

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

  14. Applied add-cube-cbrt2.6

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

  15. Applied add-cube-cbrt2.7

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

  16. Applied times-frac2.7

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

  17. Applied associate-*l*0.9

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

  18. Final simplification0.9

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

Reproduce

herbie shell --seed 2019303 
(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)))