Average Error: 11.0 → 1.2
Time: 47.1s
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 r27296897 = x;
        double r27296898 = y;
        double r27296899 = z;
        double r27296900 = t;
        double r27296901 = r27296899 - r27296900;
        double r27296902 = r27296898 * r27296901;
        double r27296903 = a;
        double r27296904 = r27296899 - r27296903;
        double r27296905 = r27296902 / r27296904;
        double r27296906 = r27296897 + r27296905;
        return r27296906;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27296907 = x;
        double r27296908 = y;
        double r27296909 = z;
        double r27296910 = a;
        double r27296911 = r27296909 - r27296910;
        double r27296912 = t;
        double r27296913 = r27296909 - r27296912;
        double r27296914 = r27296911 / r27296913;
        double r27296915 = r27296908 / r27296914;
        double r27296916 = r27296907 + r27296915;
        return r27296916;
}

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

Original11.0
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 11.0

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  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 2019165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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