Average Error: 11.7 → 2.1
Time: 2.8s
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 r628199 = x;
        double r628200 = y;
        double r628201 = z;
        double r628202 = r628200 - r628201;
        double r628203 = r628199 * r628202;
        double r628204 = t;
        double r628205 = r628204 - r628201;
        double r628206 = r628203 / r628205;
        return r628206;
}
↓
double f(double x, double y, double z, double t) {
        double r628207 = x;
        double r628208 = t;
        double r628209 = z;
        double r628210 = r628208 - r628209;
        double r628211 = y;
        double r628212 = r628211 - r628209;
        double r628213 = r628210 / r628212;
        double r628214 = r628207 / r628213;
        return r628214;
}

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

Original11.7
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.7

    \[\frac{x \cdot \left(y - z\right)}{t - z}\]
  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 2020001 +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)))