Average Error: 10.9 → 1.2
Time: 13.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r411717 = x;
        double r411718 = y;
        double r411719 = z;
        double r411720 = t;
        double r411721 = r411719 - r411720;
        double r411722 = r411718 * r411721;
        double r411723 = a;
        double r411724 = r411723 - r411720;
        double r411725 = r411722 / r411724;
        double r411726 = r411717 + r411725;
        return r411726;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r411727 = x;
        double r411728 = y;
        double r411729 = a;
        double r411730 = t;
        double r411731 = r411729 - r411730;
        double r411732 = z;
        double r411733 = r411732 - r411730;
        double r411734 = r411731 / r411733;
        double r411735 = r411728 / r411734;
        double r411736 = r411727 + r411735;
        return r411736;
}

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

Original10.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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