Average Error: 10.4 → 1.4
Time: 22.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}
double f(double x, double y, double z, double t, double a) {
        double r30101359 = x;
        double r30101360 = y;
        double r30101361 = z;
        double r30101362 = t;
        double r30101363 = r30101361 - r30101362;
        double r30101364 = r30101360 * r30101363;
        double r30101365 = a;
        double r30101366 = r30101365 - r30101362;
        double r30101367 = r30101364 / r30101366;
        double r30101368 = r30101359 + r30101367;
        return r30101368;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r30101369 = x;
        double r30101370 = 1.0;
        double r30101371 = a;
        double r30101372 = t;
        double r30101373 = r30101371 - r30101372;
        double r30101374 = z;
        double r30101375 = r30101374 - r30101372;
        double r30101376 = r30101373 / r30101375;
        double r30101377 = y;
        double r30101378 = r30101376 / r30101377;
        double r30101379 = r30101370 / r30101378;
        double r30101380 = r30101369 + r30101379;
        return r30101380;
}

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

Original10.4
Target1.3
Herbie1.4
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  3. Applied associate-/l*1.3

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

  5. Applied clear-num1.4

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y}}}\]

  6. Final simplification1.4

    \[\leadsto x + \frac{1}{\frac{\frac{a - t}{z - t}}{y}}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))