Average Error: 0.1 → 0.1
Time: 22.6s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
y \cdot 5 + x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right)
double f(double x, double y, double z, double t) {
        double r140522 = x;
        double r140523 = y;
        double r140524 = z;
        double r140525 = r140523 + r140524;
        double r140526 = r140525 + r140524;
        double r140527 = r140526 + r140523;
        double r140528 = t;
        double r140529 = r140527 + r140528;
        double r140530 = r140522 * r140529;
        double r140531 = 5.0;
        double r140532 = r140523 * r140531;
        double r140533 = r140530 + r140532;
        return r140533;
}
↓
double f(double x, double y, double z, double t) {
        double r140534 = y;
        double r140535 = 5.0;
        double r140536 = r140534 * r140535;
        double r140537 = x;
        double r140538 = z;
        double r140539 = r140534 + r140538;
        double r140540 = r140539 + r140538;
        double r140541 = r140540 + r140534;
        double r140542 = t;
        double r140543 = r140541 + r140542;
        double r140544 = r140537 * r140543;
        double r140545 = r140536 + r140544;
        return r140545;
}

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-rgt-in0.1

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

  4. Applied associate-+l+0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))