Average Error: 11.6 → 2.1
Time: 8.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{\frac{t}{y - z} - \frac{z}{y - z}}
double f(double x, double y, double z, double t) {
        double r389925 = x;
        double r389926 = y;
        double r389927 = z;
        double r389928 = r389926 - r389927;
        double r389929 = r389925 * r389928;
        double r389930 = t;
        double r389931 = r389930 - r389927;
        double r389932 = r389929 / r389931;
        return r389932;
}
↓
double f(double x, double y, double z, double t) {
        double r389933 = x;
        double r389934 = t;
        double r389935 = y;
        double r389936 = z;
        double r389937 = r389935 - r389936;
        double r389938 = r389934 / r389937;
        double r389939 = r389936 / r389937;
        double r389940 = r389938 - r389939;
        double r389941 = r389933 / r389940;
        return r389941;
}

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
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.6

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

  3. Applied associate-/l*2.1

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

  5. Applied div-sub2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2019298 
(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)))