Average Error: 12.0 → 2.3
Time: 11.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{y - z}{t - z} \cdot x\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{y - z}{t - z} \cdot x
double f(double x, double y, double z, double t) {
        double r513255 = x;
        double r513256 = y;
        double r513257 = z;
        double r513258 = r513256 - r513257;
        double r513259 = r513255 * r513258;
        double r513260 = t;
        double r513261 = r513260 - r513257;
        double r513262 = r513259 / r513261;
        return r513262;
}
↓
double f(double x, double y, double z, double t) {
        double r513263 = y;
        double r513264 = z;
        double r513265 = r513263 - r513264;
        double r513266 = t;
        double r513267 = r513266 - r513264;
        double r513268 = r513265 / r513267;
        double r513269 = x;
        double r513270 = r513268 * r513269;
        return r513270;
}

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

Original12.0
Target2.2
Herbie2.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 12.0

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

  2. Simplified11.4

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

  4. Applied associate-/r/2.3

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

  5. Final simplification2.3

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))