Average Error: 10.9 → 1.2
Time: 18.2s
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 r395397 = x;
        double r395398 = y;
        double r395399 = z;
        double r395400 = t;
        double r395401 = r395399 - r395400;
        double r395402 = r395398 * r395401;
        double r395403 = a;
        double r395404 = r395403 - r395400;
        double r395405 = r395402 / r395404;
        double r395406 = r395397 + r395405;
        return r395406;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r395407 = x;
        double r395408 = y;
        double r395409 = a;
        double r395410 = t;
        double r395411 = r395409 - r395410;
        double r395412 = z;
        double r395413 = r395412 - r395410;
        double r395414 = r395411 / r395413;
        double r395415 = r395408 / r395414;
        double r395416 = r395407 + r395415;
        return r395416;
}

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

Original10.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
  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 2019303 
(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))))