Average Error: 11.5 → 2.1
Time: 11.5s
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 r344401 = x;
        double r344402 = y;
        double r344403 = z;
        double r344404 = r344402 - r344403;
        double r344405 = r344401 * r344404;
        double r344406 = t;
        double r344407 = r344406 - r344403;
        double r344408 = r344405 / r344407;
        return r344408;
}
↓
double f(double x, double y, double z, double t) {
        double r344409 = x;
        double r344410 = t;
        double r344411 = z;
        double r344412 = r344410 - r344411;
        double r344413 = y;
        double r344414 = r344413 - r344411;
        double r344415 = r344412 / r344414;
        double r344416 = r344409 / r344415;
        return r344416;
}

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)))