Average Error: 10.8 → 1.2
Time: 11.8s
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 r345264 = x;
        double r345265 = y;
        double r345266 = z;
        double r345267 = t;
        double r345268 = r345266 - r345267;
        double r345269 = r345265 * r345268;
        double r345270 = a;
        double r345271 = r345270 - r345267;
        double r345272 = r345269 / r345271;
        double r345273 = r345264 + r345272;
        return r345273;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r345274 = x;
        double r345275 = y;
        double r345276 = a;
        double r345277 = t;
        double r345278 = r345276 - r345277;
        double r345279 = z;
        double r345280 = r345279 - r345277;
        double r345281 = r345278 / r345280;
        double r345282 = r345275 / r345281;
        double r345283 = r345274 + r345282;
        return r345283;
}

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. Final simplification1.2

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

Reproduce

herbie shell --seed 2019298 
(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))))