Average Error: 10.7 → 1.4
Time: 13.8s
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 r427507 = x;
        double r427508 = y;
        double r427509 = z;
        double r427510 = t;
        double r427511 = r427509 - r427510;
        double r427512 = r427508 * r427511;
        double r427513 = a;
        double r427514 = r427513 - r427510;
        double r427515 = r427512 / r427514;
        double r427516 = r427507 + r427515;
        return r427516;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r427517 = x;
        double r427518 = y;
        double r427519 = a;
        double r427520 = t;
        double r427521 = r427519 - r427520;
        double r427522 = z;
        double r427523 = r427522 - r427520;
        double r427524 = r427521 / r427523;
        double r427525 = r427518 / r427524;
        double r427526 = r427517 + r427525;
        return r427526;
}

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

Original10.7
Target1.4
Herbie1.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019297 
(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))))