Average Error: 1.4 → 1.3
Time: 3.6s
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 r651527 = x;
        double r651528 = y;
        double r651529 = z;
        double r651530 = t;
        double r651531 = r651529 - r651530;
        double r651532 = a;
        double r651533 = r651529 - r651532;
        double r651534 = r651531 / r651533;
        double r651535 = r651528 * r651534;
        double r651536 = r651527 + r651535;
        return r651536;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r651537 = x;
        double r651538 = y;
        double r651539 = z;
        double r651540 = a;
        double r651541 = r651539 - r651540;
        double r651542 = t;
        double r651543 = r651539 - r651542;
        double r651544 = r651541 / r651543;
        double r651545 = r651538 / r651544;
        double r651546 = r651537 + r651545;
        return r651546;
}

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 +o rules:numerics
(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)))))