Average Error: 11.3 → 2.2
Time: 9.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x}{\frac{t - z}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{\frac{t - z}{y - z}}
double f(double x, double y, double z, double t) {
        double r470907 = x;
        double r470908 = y;
        double r470909 = z;
        double r470910 = r470908 - r470909;
        double r470911 = r470907 * r470910;
        double r470912 = t;
        double r470913 = r470912 - r470909;
        double r470914 = r470911 / r470913;
        return r470914;
}
↓
double f(double x, double y, double z, double t) {
        double r470915 = x;
        double r470916 = t;
        double r470917 = z;
        double r470918 = r470916 - r470917;
        double r470919 = y;
        double r470920 = r470919 - r470917;
        double r470921 = r470918 / r470920;
        double r470922 = r470915 / r470921;
        return r470922;
}

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

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Target

Original11.3
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.3

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

  3. Applied associate-/l*2.2

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

  4. Final simplification2.2

    \[\leadsto \frac{x}{\frac{t - z}{y - z}}\]

Reproduce

herbie shell --seed 2019350 +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)))