Average Error: 10.6 → 1.2
Time: 23.6s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r331596 = x;
        double r331597 = y;
        double r331598 = z;
        double r331599 = t;
        double r331600 = r331598 - r331599;
        double r331601 = r331597 * r331600;
        double r331602 = a;
        double r331603 = r331602 - r331599;
        double r331604 = r331601 / r331603;
        double r331605 = r331596 + r331604;
        return r331605;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r331606 = x;
        double r331607 = y;
        double r331608 = a;
        double r331609 = z;
        double r331610 = t;
        double r331611 = r331609 - r331610;
        double r331612 = r331608 / r331611;
        double r331613 = r331610 / r331611;
        double r331614 = r331612 - r331613;
        double r331615 = r331607 / r331614;
        double r331616 = r331606 + r331615;
        return r331616;
}

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

Original10.6
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.2

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

  5. Applied div-sub1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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