Average Error: 10.8 → 1.3
Time: 1.1m
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{y}{\frac{z}{z - t} - \frac{a}{z - t}} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{y}{\frac{z}{z - t} - \frac{a}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r30187616 = x;
        double r30187617 = y;
        double r30187618 = z;
        double r30187619 = t;
        double r30187620 = r30187618 - r30187619;
        double r30187621 = r30187617 * r30187620;
        double r30187622 = a;
        double r30187623 = r30187618 - r30187622;
        double r30187624 = r30187621 / r30187623;
        double r30187625 = r30187616 + r30187624;
        return r30187625;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30187626 = y;
        double r30187627 = z;
        double r30187628 = t;
        double r30187629 = r30187627 - r30187628;
        double r30187630 = r30187627 / r30187629;
        double r30187631 = a;
        double r30187632 = r30187631 / r30187629;
        double r30187633 = r30187630 - r30187632;
        double r30187634 = r30187626 / r30187633;
        double r30187635 = x;
        double r30187636 = r30187634 + r30187635;
        return r30187636;
}

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. Using strategy rm

  5. Applied div-sub1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019200 
(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))))