Average Error: 10.6 → 1.2
Time: 3.0s
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 r559472 = x;
        double r559473 = y;
        double r559474 = z;
        double r559475 = t;
        double r559476 = r559474 - r559475;
        double r559477 = r559473 * r559476;
        double r559478 = a;
        double r559479 = r559474 - r559478;
        double r559480 = r559477 / r559479;
        double r559481 = r559472 + r559480;
        return r559481;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r559482 = x;
        double r559483 = y;
        double r559484 = z;
        double r559485 = t;
        double r559486 = r559484 - r559485;
        double r559487 = r559484 / r559486;
        double r559488 = a;
        double r559489 = r559488 / r559486;
        double r559490 = r559487 - r559489;
        double r559491 = r559483 / r559490;
        double r559492 = r559482 + r559491;
        return r559492;
}

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

Original10.6
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.2

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

  5. Applied div-sub1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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))))