Average Error: 10.9 → 1.3
Time: 5.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r586376 = x;
        double r586377 = y;
        double r586378 = z;
        double r586379 = t;
        double r586380 = r586378 - r586379;
        double r586381 = r586377 * r586380;
        double r586382 = a;
        double r586383 = r586378 - r586382;
        double r586384 = r586381 / r586383;
        double r586385 = r586376 + r586384;
        return r586385;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r586386 = x;
        double r586387 = y;
        double r586388 = z;
        double r586389 = t;
        double r586390 = r586388 - r586389;
        double r586391 = r586388 / r586390;
        double r586392 = a;
        double r586393 = r586392 / r586390;
        double r586394 = r586391 - r586393;
        double r586395 = r586387 / r586394;
        double r586396 = r586386 + r586395;
        return r586396;
}

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

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.3

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

  5. Applied div-sub1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020039 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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