Average Error: 10.6 → 1.3
Time: 19.7s
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 r490616 = x;
        double r490617 = y;
        double r490618 = z;
        double r490619 = t;
        double r490620 = r490618 - r490619;
        double r490621 = r490617 * r490620;
        double r490622 = a;
        double r490623 = r490622 - r490619;
        double r490624 = r490621 / r490623;
        double r490625 = r490616 + r490624;
        return r490625;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r490626 = x;
        double r490627 = y;
        double r490628 = a;
        double r490629 = t;
        double r490630 = r490628 - r490629;
        double r490631 = z;
        double r490632 = r490631 - r490629;
        double r490633 = r490630 / r490632;
        double r490634 = r490627 / r490633;
        double r490635 = r490626 + r490634;
        return r490635;
}

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

Original10.6
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019208 
(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))))