Average Error: 1.3 → 1.1
Time: 4.6s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r525932 = x;
        double r525933 = y;
        double r525934 = z;
        double r525935 = t;
        double r525936 = r525934 - r525935;
        double r525937 = a;
        double r525938 = r525934 - r525937;
        double r525939 = r525936 / r525938;
        double r525940 = r525933 * r525939;
        double r525941 = r525932 + r525940;
        return r525941;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r525942 = x;
        double r525943 = y;
        double r525944 = z;
        double r525945 = a;
        double r525946 = r525944 - r525945;
        double r525947 = t;
        double r525948 = r525944 - r525947;
        double r525949 = r525946 / r525948;
        double r525950 = r525943 / r525949;
        double r525951 = r525942 + r525950;
        return r525951;
}

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

Original1.3
Target1.1
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied associate-*r/11.2

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

  5. Applied associate-/l*1.1

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

  6. 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:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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