Average Error: 11.6 → 11.6
Time: 4.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x \cdot \left(y - z\right)}{t - z}
double f(double x, double y, double z, double t) {
        double r430837 = x;
        double r430838 = y;
        double r430839 = z;
        double r430840 = r430838 - r430839;
        double r430841 = r430837 * r430840;
        double r430842 = t;
        double r430843 = r430842 - r430839;
        double r430844 = r430841 / r430843;
        return r430844;
}
↓
double f(double x, double y, double z, double t) {
        double r430845 = x;
        double r430846 = y;
        double r430847 = z;
        double r430848 = r430846 - r430847;
        double r430849 = r430845 * r430848;
        double r430850 = t;
        double r430851 = r430850 - r430847;
        double r430852 = r430849 / r430851;
        return r430852;
}

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
Target2.3
Herbie11.6
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.6

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

  3. Applied associate-/l*2.3

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

  5. Applied add-cube-cbrt3.3

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

  6. Applied add-cube-cbrt3.0

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

  7. Applied times-frac3.0

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

  8. Applied associate-/r*1.1

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

  9. Final simplification11.6

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

Reproduce

herbie shell --seed 1978988140 
(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)))