Average Error: 0.1 → 0.1
Time: 9.4s
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 r178619 = x;
        double r178620 = y;
        double r178621 = z;
        double r178622 = r178620 + r178621;
        double r178623 = r178622 + r178621;
        double r178624 = r178623 + r178620;
        double r178625 = t;
        double r178626 = r178624 + r178625;
        double r178627 = r178619 * r178626;
        double r178628 = 5.0;
        double r178629 = r178620 * r178628;
        double r178630 = r178627 + r178629;
        return r178630;
}
↓
double f(double x, double y, double z, double t) {
        double r178631 = x;
        double r178632 = y;
        double r178633 = z;
        double r178634 = r178632 + r178633;
        double r178635 = r178634 + r178633;
        double r178636 = r178635 + r178632;
        double r178637 = r178631 * r178636;
        double r178638 = t;
        double r178639 = r178638 * r178631;
        double r178640 = 5.0;
        double r178641 = r178632 * r178640;
        double r178642 = r178639 + r178641;
        double r178643 = r178637 + r178642;
        return r178643;
}

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 2019354 
(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)))