Average Error: 11.5 → 2.1
Time: 12.2s
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 r324083 = x;
        double r324084 = y;
        double r324085 = z;
        double r324086 = r324084 - r324085;
        double r324087 = r324083 * r324086;
        double r324088 = t;
        double r324089 = r324088 - r324085;
        double r324090 = r324087 / r324089;
        return r324090;
}
↓
double f(double x, double y, double z, double t) {
        double r324091 = x;
        double r324092 = t;
        double r324093 = z;
        double r324094 = r324092 - r324093;
        double r324095 = y;
        double r324096 = r324095 - r324093;
        double r324097 = r324094 / r324096;
        double r324098 = r324091 / r324097;
        return r324098;
}

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

Original11.5
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.5

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

  3. Applied associate-/l*2.1

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

  4. Final simplification2.1

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

Reproduce

herbie shell --seed 2019326 +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)))