Average Error: 11.1 → 1.3
Time: 4.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r632431 = x;
        double r632432 = y;
        double r632433 = z;
        double r632434 = t;
        double r632435 = r632433 - r632434;
        double r632436 = r632432 * r632435;
        double r632437 = a;
        double r632438 = r632437 - r632434;
        double r632439 = r632436 / r632438;
        double r632440 = r632431 + r632439;
        return r632440;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r632441 = x;
        double r632442 = y;
        double r632443 = a;
        double r632444 = t;
        double r632445 = r632443 - r632444;
        double r632446 = z;
        double r632447 = r632446 - r632444;
        double r632448 = r632445 / r632447;
        double r632449 = r632442 / r632448;
        double r632450 = r632441 + r632449;
        return r632450;
}

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
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.1

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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