Average Error: 0.1 → 0.1
Time: 4.0s
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 r123555 = x;
        double r123556 = y;
        double r123557 = z;
        double r123558 = r123556 + r123557;
        double r123559 = r123558 + r123557;
        double r123560 = r123559 + r123556;
        double r123561 = t;
        double r123562 = r123560 + r123561;
        double r123563 = r123555 * r123562;
        double r123564 = 5.0;
        double r123565 = r123556 * r123564;
        double r123566 = r123563 + r123565;
        return r123566;
}
↓
double f(double x, double y, double z, double t) {
        double r123567 = x;
        double r123568 = y;
        double r123569 = z;
        double r123570 = r123568 + r123569;
        double r123571 = r123570 + r123569;
        double r123572 = r123571 + r123568;
        double r123573 = r123567 * r123572;
        double r123574 = t;
        double r123575 = r123574 * r123567;
        double r123576 = 5.0;
        double r123577 = r123568 * r123576;
        double r123578 = r123575 + r123577;
        double r123579 = r123573 + r123578;
        return r123579;
}

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 2020062 
(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)))