Average Error: 12.0 → 2.2
Time: 12.5s
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 r407407 = x;
        double r407408 = y;
        double r407409 = z;
        double r407410 = r407408 - r407409;
        double r407411 = r407407 * r407410;
        double r407412 = t;
        double r407413 = r407412 - r407409;
        double r407414 = r407411 / r407413;
        return r407414;
}
↓
double f(double x, double y, double z, double t) {
        double r407415 = x;
        double r407416 = t;
        double r407417 = z;
        double r407418 = r407416 - r407417;
        double r407419 = y;
        double r407420 = r407419 - r407417;
        double r407421 = r407418 / r407420;
        double r407422 = r407415 / r407421;
        return r407422;
}

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
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 12.0

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

  3. Applied associate-/l*2.2

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

  4. Final simplification2.2

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

Reproduce

herbie shell --seed 2019303 +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)))