Average Error: 3.8 → 0.6
Time: 23.0s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\sqrt[3]{t}}{\sqrt[3]{y}} \cdot \left(\frac{\frac{\sqrt[3]{t}}{z}}{\sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}\right)\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\sqrt[3]{t}}{\sqrt[3]{y}} \cdot \left(\frac{\frac{\sqrt[3]{t}}{z}}{\sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}\right)
double f(double x, double y, double z, double t) {
        double r29421965 = x;
        double r29421966 = y;
        double r29421967 = z;
        double r29421968 = 3.0;
        double r29421969 = r29421967 * r29421968;
        double r29421970 = r29421966 / r29421969;
        double r29421971 = r29421965 - r29421970;
        double r29421972 = t;
        double r29421973 = r29421969 * r29421966;
        double r29421974 = r29421972 / r29421973;
        double r29421975 = r29421971 + r29421974;
        return r29421975;
}
↓
double f(double x, double y, double z, double t) {
        double r29421976 = x;
        double r29421977 = y;
        double r29421978 = z;
        double r29421979 = 3.0;
        double r29421980 = r29421978 * r29421979;
        double r29421981 = r29421977 / r29421980;
        double r29421982 = r29421976 - r29421981;
        double r29421983 = t;
        double r29421984 = cbrt(r29421983);
        double r29421985 = cbrt(r29421977);
        double r29421986 = r29421984 / r29421985;
        double r29421987 = r29421984 / r29421978;
        double r29421988 = r29421987 / r29421985;
        double r29421989 = r29421984 / r29421979;
        double r29421990 = r29421989 / r29421985;
        double r29421991 = r29421988 * r29421990;
        double r29421992 = r29421986 * r29421991;
        double r29421993 = r29421982 + r29421992;
        return r29421993;
}

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

Original3.8
Target1.8
Herbie0.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.8

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt4.1

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

  4. Applied times-frac1.5

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

  6. Applied add-cube-cbrt1.6

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

  7. Applied *-un-lft-identity1.6

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

  8. Applied cbrt-prod1.6

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

  9. Applied times-frac1.6

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

  10. Applied associate-*r*0.9

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

  11. Simplified0.6

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

  12. Final simplification0.6

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))