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 r611408 = x;
        double r611409 = y;
        double r611410 = z;
        double r611411 = r611409 - r611410;
        double r611412 = r611408 * r611411;
        double r611413 = t;
        double r611414 = r611413 - r611410;
        double r611415 = r611412 / r611414;
        return r611415;
}
↓
double f(double x, double y, double z, double t) {
        double r611416 = x;
        double r611417 = t;
        double r611418 = z;
        double r611419 = r611417 - r611418;
        double r611420 = y;
        double r611421 = r611420 - r611418;
        double r611422 = r611419 / r611421;
        double r611423 = r611416 / r611422;
        return r611423;
}

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)))