Average Error: 10.8 → 1.3
Time: 3.5s
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 r516533 = x;
        double r516534 = y;
        double r516535 = z;
        double r516536 = t;
        double r516537 = r516535 - r516536;
        double r516538 = r516534 * r516537;
        double r516539 = a;
        double r516540 = r516535 - r516539;
        double r516541 = r516538 / r516540;
        double r516542 = r516533 + r516541;
        return r516542;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r516543 = x;
        double r516544 = y;
        double r516545 = z;
        double r516546 = a;
        double r516547 = r516545 - r516546;
        double r516548 = t;
        double r516549 = r516545 - r516548;
        double r516550 = r516547 / r516549;
        double r516551 = r516544 / r516550;
        double r516552 = r516543 + r516551;
        return r516552;
}

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

Original10.8
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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))))