Average Error: 11.0 → 1.3
Time: 4.0s
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 r561458 = x;
        double r561459 = y;
        double r561460 = z;
        double r561461 = t;
        double r561462 = r561460 - r561461;
        double r561463 = r561459 * r561462;
        double r561464 = a;
        double r561465 = r561464 - r561461;
        double r561466 = r561463 / r561465;
        double r561467 = r561458 + r561466;
        return r561467;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r561468 = x;
        double r561469 = y;
        double r561470 = a;
        double r561471 = t;
        double r561472 = r561470 - r561471;
        double r561473 = z;
        double r561474 = r561473 - r561471;
        double r561475 = r561472 / r561474;
        double r561476 = r561469 / r561475;
        double r561477 = r561468 + r561476;
        return r561477;
}

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

Original11.0
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020036 
(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))))