Average Error: 10.8 → 1.2
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r568286 = x;
        double r568287 = y;
        double r568288 = z;
        double r568289 = t;
        double r568290 = r568288 - r568289;
        double r568291 = r568287 * r568290;
        double r568292 = a;
        double r568293 = r568292 - r568289;
        double r568294 = r568291 / r568293;
        double r568295 = r568286 + r568294;
        return r568295;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r568296 = x;
        double r568297 = y;
        double r568298 = a;
        double r568299 = z;
        double r568300 = t;
        double r568301 = r568299 - r568300;
        double r568302 = r568298 / r568301;
        double r568303 = r568300 / r568301;
        double r568304 = r568302 - r568303;
        double r568305 = r568297 / r568304;
        double r568306 = r568296 + r568305;
        return r568306;
}

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

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.2

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

  5. Applied div-sub1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020018 
(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))))