Average Error: 0.1 → 0.1
Time: 8.6s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + z\right) + \left(y + z\right)\right) + t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(y + z\right) + \left(y + z\right)\right) + t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r186461 = x;
        double r186462 = y;
        double r186463 = z;
        double r186464 = r186462 + r186463;
        double r186465 = r186464 + r186463;
        double r186466 = r186465 + r186462;
        double r186467 = t;
        double r186468 = r186466 + r186467;
        double r186469 = r186461 * r186468;
        double r186470 = 5.0;
        double r186471 = r186462 * r186470;
        double r186472 = r186469 + r186471;
        return r186472;
}
↓
double f(double x, double y, double z, double t) {
        double r186473 = x;
        double r186474 = y;
        double r186475 = z;
        double r186476 = r186474 + r186475;
        double r186477 = r186476 + r186476;
        double r186478 = t;
        double r186479 = r186477 + r186478;
        double r186480 = r186473 * r186479;
        double r186481 = 5.0;
        double r186482 = r186474 * r186481;
        double r186483 = r186480 + r186482;
        return r186483;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
  2. Using strategy rm

  3. Applied associate-+l+0.1

    \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5\]

  4. Simplified0.1

    \[\leadsto x \cdot \left(\left(\left(y + z\right) + \color{blue}{\left(y + z\right)}\right) + t\right) + y \cdot 5\]

  5. Final simplification0.1

    \[\leadsto x \cdot \left(\left(\left(y + z\right) + \left(y + z\right)\right) + t\right) + y \cdot 5\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5)))