Average Error: 11.1 → 1.1
Time: 13.8s
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 r367366 = x;
        double r367367 = y;
        double r367368 = z;
        double r367369 = t;
        double r367370 = r367368 - r367369;
        double r367371 = r367367 * r367370;
        double r367372 = a;
        double r367373 = r367368 - r367372;
        double r367374 = r367371 / r367373;
        double r367375 = r367366 + r367374;
        return r367375;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r367376 = x;
        double r367377 = y;
        double r367378 = z;
        double r367379 = a;
        double r367380 = r367378 - r367379;
        double r367381 = t;
        double r367382 = r367378 - r367381;
        double r367383 = r367380 / r367382;
        double r367384 = r367377 / r367383;
        double r367385 = r367376 + r367384;
        return r367385;
}

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

Original11.1
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.1

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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