Average Error: 10.5 → 1.2
Time: 3.7s
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 r531315 = x;
        double r531316 = y;
        double r531317 = z;
        double r531318 = t;
        double r531319 = r531317 - r531318;
        double r531320 = r531316 * r531319;
        double r531321 = a;
        double r531322 = r531317 - r531321;
        double r531323 = r531320 / r531322;
        double r531324 = r531315 + r531323;
        return r531324;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r531325 = x;
        double r531326 = y;
        double r531327 = z;
        double r531328 = a;
        double r531329 = r531327 - r531328;
        double r531330 = t;
        double r531331 = r531327 - r531330;
        double r531332 = r531329 / r531331;
        double r531333 = r531326 / r531332;
        double r531334 = r531325 + r531333;
        return r531334;
}

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

Original10.5
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.5

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2020064 
(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))))