Average Error: 11.1 → 2.2
Time: 4.9s
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 r723604 = x;
        double r723605 = y;
        double r723606 = z;
        double r723607 = r723605 - r723606;
        double r723608 = r723604 * r723607;
        double r723609 = t;
        double r723610 = r723609 - r723606;
        double r723611 = r723608 / r723610;
        return r723611;
}
↓
double f(double x, double y, double z, double t) {
        double r723612 = x;
        double r723613 = t;
        double r723614 = z;
        double r723615 = r723613 - r723614;
        double r723616 = y;
        double r723617 = r723616 - r723614;
        double r723618 = r723615 / r723617;
        double r723619 = r723612 / r723618;
        return r723619;
}

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

Original11.1
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.1

    \[\frac{x \cdot \left(y - z\right)}{t - z}\]
  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 2020057 +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)))