Average Error: 0.1 → 0.1
Time: 23.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)\]
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) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)
double f(double x, double y, double z, double t) {
        double r145457 = x;
        double r145458 = y;
        double r145459 = z;
        double r145460 = r145458 + r145459;
        double r145461 = r145460 + r145459;
        double r145462 = r145461 + r145458;
        double r145463 = t;
        double r145464 = r145462 + r145463;
        double r145465 = r145457 * r145464;
        double r145466 = 5.0;
        double r145467 = r145458 * r145466;
        double r145468 = r145465 + r145467;
        return r145468;
}
↓
double f(double x, double y, double z, double t) {
        double r145469 = x;
        double r145470 = y;
        double r145471 = z;
        double r145472 = r145470 + r145471;
        double r145473 = r145472 + r145471;
        double r145474 = r145473 + r145470;
        double r145475 = r145469 * r145474;
        double r145476 = t;
        double r145477 = r145476 * r145469;
        double r145478 = 5.0;
        double r145479 = r145470 * r145478;
        double r145480 = r145477 + r145479;
        double r145481 = r145475 + r145480;
        return r145481;
}

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 distribute-lft-in0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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)))