Average Error: 11.5 → 2.4
Time: 13.5s
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 r1102047 = x;
        double r1102048 = y;
        double r1102049 = z;
        double r1102050 = r1102048 - r1102049;
        double r1102051 = r1102047 * r1102050;
        double r1102052 = t;
        double r1102053 = r1102052 - r1102049;
        double r1102054 = r1102051 / r1102053;
        return r1102054;
}
↓
double f(double x, double y, double z, double t) {
        double r1102055 = x;
        double r1102056 = t;
        double r1102057 = z;
        double r1102058 = r1102056 - r1102057;
        double r1102059 = y;
        double r1102060 = r1102059 - r1102057;
        double r1102061 = r1102058 / r1102060;
        double r1102062 = r1102055 / r1102061;
        return r1102062;
}

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
Target2.4
Herbie2.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.5

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

  3. Applied associate-/l*2.4

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

  4. Final simplification2.4

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

Reproduce

herbie shell --seed 2019235 +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)))