Average Error: 11.6 → 1.4
Time: 11.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \sqrt[3]{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\left(x \cdot \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \sqrt[3]{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}
double f(double x, double y, double z, double t) {
        double r348957 = x;
        double r348958 = y;
        double r348959 = z;
        double r348960 = r348958 - r348959;
        double r348961 = r348957 * r348960;
        double r348962 = t;
        double r348963 = r348962 - r348959;
        double r348964 = r348961 / r348963;
        return r348964;
}
↓
double f(double x, double y, double z, double t) {
        double r348965 = x;
        double r348966 = y;
        double r348967 = z;
        double r348968 = r348966 - r348967;
        double r348969 = cbrt(r348968);
        double r348970 = r348969 * r348969;
        double r348971 = t;
        double r348972 = r348971 - r348967;
        double r348973 = cbrt(r348972);
        double r348974 = r348973 * r348973;
        double r348975 = r348970 / r348974;
        double r348976 = r348965 * r348975;
        double r348977 = cbrt(r348970);
        double r348978 = cbrt(r348969);
        double r348979 = r348977 * r348978;
        double r348980 = r348979 / r348973;
        double r348981 = r348976 * r348980;
        return r348981;
}

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

Original11.6
Target2.2
Herbie1.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.6

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

  3. Applied *-un-lft-identity11.6

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

  4. Applied times-frac2.2

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

  5. Simplified2.2

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

  7. Applied add-cube-cbrt3.2

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

  8. Applied add-cube-cbrt2.9

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

  9. Applied times-frac2.9

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

  10. Applied associate-*r*1.1

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

  12. Applied add-cube-cbrt1.2

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

  13. Applied cbrt-prod1.4

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

  14. Final simplification1.4

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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