Average Error: 11.2 → 1.1
Time: 13.9s
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 r384266 = x;
        double r384267 = y;
        double r384268 = z;
        double r384269 = t;
        double r384270 = r384268 - r384269;
        double r384271 = r384267 * r384270;
        double r384272 = a;
        double r384273 = r384268 - r384272;
        double r384274 = r384271 / r384273;
        double r384275 = r384266 + r384274;
        return r384275;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r384276 = x;
        double r384277 = y;
        double r384278 = z;
        double r384279 = a;
        double r384280 = r384278 - r384279;
        double r384281 = t;
        double r384282 = r384278 - r384281;
        double r384283 = r384280 / r384282;
        double r384284 = r384277 / r384283;
        double r384285 = r384276 + r384284;
        return r384285;
}

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

Original11.2
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.2

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019322 
(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))))