Average Error: 0.1 → 0.1
Time: 41.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(x \cdot t + \left(\left(y + z\right) + \left(y + z\right)\right) \cdot x\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(x \cdot t + \left(\left(y + z\right) + \left(y + z\right)\right) \cdot x\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r9372568 = x;
        double r9372569 = y;
        double r9372570 = z;
        double r9372571 = r9372569 + r9372570;
        double r9372572 = r9372571 + r9372570;
        double r9372573 = r9372572 + r9372569;
        double r9372574 = t;
        double r9372575 = r9372573 + r9372574;
        double r9372576 = r9372568 * r9372575;
        double r9372577 = 5.0;
        double r9372578 = r9372569 * r9372577;
        double r9372579 = r9372576 + r9372578;
        return r9372579;
}
↓
double f(double x, double y, double z, double t) {
        double r9372580 = x;
        double r9372581 = t;
        double r9372582 = r9372580 * r9372581;
        double r9372583 = y;
        double r9372584 = z;
        double r9372585 = r9372583 + r9372584;
        double r9372586 = r9372585 + r9372585;
        double r9372587 = r9372586 * r9372580;
        double r9372588 = r9372582 + r9372587;
        double r9372589 = 5.0;
        double r9372590 = r9372583 * r9372589;
        double r9372591 = r9372588 + r9372590;
        return r9372591;
}

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. Simplified0.1

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

  3. Taylor expanded around inf 0.1

    \[\leadsto y \cdot 5 + \color{blue}{\left(2 \cdot \left(x \cdot z\right) + \left(t \cdot x + 2 \cdot \left(x \cdot y\right)\right)\right)}\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))