Average Error: 0.1 → 0.1
Time: 21.1s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(\left(y + z\right) + z\right) + y\right) \cdot x + \left(t \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(\left(y + z\right) + z\right) + y\right) \cdot x + \left(t \cdot x + y \cdot 5\right)
double f(double x, double y, double z, double t) {
        double r136504 = x;
        double r136505 = y;
        double r136506 = z;
        double r136507 = r136505 + r136506;
        double r136508 = r136507 + r136506;
        double r136509 = r136508 + r136505;
        double r136510 = t;
        double r136511 = r136509 + r136510;
        double r136512 = r136504 * r136511;
        double r136513 = 5.0;
        double r136514 = r136505 * r136513;
        double r136515 = r136512 + r136514;
        return r136515;
}
↓
double f(double x, double y, double z, double t) {
        double r136516 = y;
        double r136517 = z;
        double r136518 = r136516 + r136517;
        double r136519 = r136518 + r136517;
        double r136520 = r136519 + r136516;
        double r136521 = x;
        double r136522 = r136520 * r136521;
        double r136523 = t;
        double r136524 = r136523 * r136521;
        double r136525 = 5.0;
        double r136526 = r136516 * r136525;
        double r136527 = r136524 + r136526;
        double r136528 = r136522 + r136527;
        return r136528;
}

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

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

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)))