Average Error: 10.4 → 1.1
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 r1110283 = x;
        double r1110284 = y;
        double r1110285 = z;
        double r1110286 = t;
        double r1110287 = r1110285 - r1110286;
        double r1110288 = r1110284 * r1110287;
        double r1110289 = a;
        double r1110290 = r1110285 - r1110289;
        double r1110291 = r1110288 / r1110290;
        double r1110292 = r1110283 + r1110291;
        return r1110292;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1110293 = x;
        double r1110294 = y;
        double r1110295 = z;
        double r1110296 = a;
        double r1110297 = r1110295 - r1110296;
        double r1110298 = t;
        double r1110299 = r1110295 - r1110298;
        double r1110300 = r1110297 / r1110299;
        double r1110301 = r1110294 / r1110300;
        double r1110302 = r1110293 + r1110301;
        return r1110302;
}

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

Original10.4
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2020065 
(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))))