Average Error: 10.7 → 1.1
Time: 8.6s
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 r624399 = x;
        double r624400 = y;
        double r624401 = z;
        double r624402 = t;
        double r624403 = r624401 - r624402;
        double r624404 = r624400 * r624403;
        double r624405 = a;
        double r624406 = r624401 - r624405;
        double r624407 = r624404 / r624406;
        double r624408 = r624399 + r624407;
        return r624408;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r624409 = x;
        double r624410 = y;
        double r624411 = z;
        double r624412 = a;
        double r624413 = r624411 - r624412;
        double r624414 = t;
        double r624415 = r624411 - r624414;
        double r624416 = r624413 / r624415;
        double r624417 = r624410 / r624416;
        double r624418 = r624409 + r624417;
        return r624418;
}

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

Original10.7
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.1

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

  4. Final simplification1.1

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

Reproduce

herbie shell --seed 2020043 +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))))