Average Error: 10.6 → 1.2
Time: 3.2s
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 r570298 = x;
        double r570299 = y;
        double r570300 = z;
        double r570301 = t;
        double r570302 = r570300 - r570301;
        double r570303 = r570299 * r570302;
        double r570304 = a;
        double r570305 = r570300 - r570304;
        double r570306 = r570303 / r570305;
        double r570307 = r570298 + r570306;
        return r570307;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r570308 = x;
        double r570309 = y;
        double r570310 = z;
        double r570311 = a;
        double r570312 = r570310 - r570311;
        double r570313 = t;
        double r570314 = r570310 - r570313;
        double r570315 = r570312 / r570314;
        double r570316 = r570309 / r570315;
        double r570317 = r570308 + r570316;
        return r570317;
}

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

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019354 
(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))))