Average Error: 11.2 → 1.2
Time: 19.6s
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 r33502892 = x;
        double r33502893 = y;
        double r33502894 = z;
        double r33502895 = t;
        double r33502896 = r33502894 - r33502895;
        double r33502897 = r33502893 * r33502896;
        double r33502898 = a;
        double r33502899 = r33502894 - r33502898;
        double r33502900 = r33502897 / r33502899;
        double r33502901 = r33502892 + r33502900;
        return r33502901;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r33502902 = x;
        double r33502903 = y;
        double r33502904 = z;
        double r33502905 = a;
        double r33502906 = r33502904 - r33502905;
        double r33502907 = t;
        double r33502908 = r33502904 - r33502907;
        double r33502909 = r33502906 / r33502908;
        double r33502910 = r33502903 / r33502909;
        double r33502911 = r33502902 + r33502910;
        return r33502911;
}

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

Derivation

  1. Initial program 11.2

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))