Average Error: 10.4 → 1.2
Time: 15.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r447274 = x;
        double r447275 = y;
        double r447276 = z;
        double r447277 = t;
        double r447278 = r447276 - r447277;
        double r447279 = r447275 * r447278;
        double r447280 = a;
        double r447281 = r447276 - r447280;
        double r447282 = r447279 / r447281;
        double r447283 = r447274 + r447282;
        return r447283;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r447284 = x;
        double r447285 = y;
        double r447286 = z;
        double r447287 = a;
        double r447288 = r447286 - r447287;
        double r447289 = t;
        double r447290 = r447286 - r447289;
        double r447291 = r447288 / r447290;
        double r447292 = r447285 / r447291;
        double r447293 = r447284 + r447292;
        return r447293;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.4
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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