Average Error: 10.8 → 1.3
Time: 4.0s
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 r536835 = x;
        double r536836 = y;
        double r536837 = z;
        double r536838 = t;
        double r536839 = r536837 - r536838;
        double r536840 = r536836 * r536839;
        double r536841 = a;
        double r536842 = r536837 - r536841;
        double r536843 = r536840 / r536842;
        double r536844 = r536835 + r536843;
        return r536844;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r536845 = x;
        double r536846 = y;
        double r536847 = z;
        double r536848 = a;
        double r536849 = r536847 - r536848;
        double r536850 = t;
        double r536851 = r536847 - r536850;
        double r536852 = r536849 / r536851;
        double r536853 = r536846 / r536852;
        double r536854 = r536845 + r536853;
        return r536854;
}

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

Original10.8
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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))))