Average Error: 6.5 → 1.7
Time: 58.8s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} \cdot \left(\left(\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}\right) \cdot \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}} \cdot \left(\left(\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}\right) \cdot \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)
double f(double x, double y, double z, double t) {
        double r17948980 = x;
        double r17948981 = y;
        double r17948982 = z;
        double r17948983 = r17948982 - r17948980;
        double r17948984 = r17948981 * r17948983;
        double r17948985 = t;
        double r17948986 = r17948984 / r17948985;
        double r17948987 = r17948980 + r17948986;
        return r17948987;
}
↓
double f(double x, double y, double z, double t) {
        double r17948988 = x;
        double r17948989 = z;
        double r17948990 = r17948989 - r17948988;
        double r17948991 = cbrt(r17948990);
        double r17948992 = t;
        double r17948993 = cbrt(r17948992);
        double r17948994 = r17948991 / r17948993;
        double r17948995 = r17948991 * r17948991;
        double r17948996 = y;
        double r17948997 = r17948993 * r17948993;
        double r17948998 = r17948996 / r17948997;
        double r17948999 = r17948995 * r17948998;
        double r17949000 = r17948994 * r17948999;
        double r17949001 = r17948988 + r17949000;
        return r17949001;
}

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

Original6.5
Target2.1
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.5

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

  3. Applied add-cube-cbrt7.0

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

  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. Using strategy rm

  6. Applied *-un-lft-identity3.2

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

  7. Applied cbrt-prod3.2

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

  8. Applied add-cube-cbrt3.3

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

  9. Applied times-frac3.3

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

  10. Applied associate-*r*1.7

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

  11. Simplified1.4

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

  13. Applied frac-times1.4

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

  14. Applied associate-/r/1.7

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

  15. Final simplification1.7

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

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

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