Average Error: 1.4 → 1.3
Time: 3.3s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r589480 = x;
        double r589481 = y;
        double r589482 = z;
        double r589483 = t;
        double r589484 = r589482 - r589483;
        double r589485 = a;
        double r589486 = r589482 - r589485;
        double r589487 = r589484 / r589486;
        double r589488 = r589481 * r589487;
        double r589489 = r589480 + r589488;
        return r589489;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r589490 = x;
        double r589491 = y;
        double r589492 = z;
        double r589493 = a;
        double r589494 = r589492 - r589493;
        double r589495 = t;
        double r589496 = r589492 - r589495;
        double r589497 = r589494 / r589496;
        double r589498 = r589491 / r589497;
        double r589499 = r589490 + r589498;
        return r589499;
}

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

Original1.4
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.4

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

  3. Applied associate-*r/10.9

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

  5. Applied associate-/l*1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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