Average Error: 0.1 → 0.1
Time: 50.1s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[y \cdot 5 + \left(2 \cdot \left(x \cdot z\right) + \left(t \cdot x + 2 \cdot \left(x \cdot y\right)\right)\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
y \cdot 5 + \left(2 \cdot \left(x \cdot z\right) + \left(t \cdot x + 2 \cdot \left(x \cdot y\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r38155327 = x;
        double r38155328 = y;
        double r38155329 = z;
        double r38155330 = r38155328 + r38155329;
        double r38155331 = r38155330 + r38155329;
        double r38155332 = r38155331 + r38155328;
        double r38155333 = t;
        double r38155334 = r38155332 + r38155333;
        double r38155335 = r38155327 * r38155334;
        double r38155336 = 5.0;
        double r38155337 = r38155328 * r38155336;
        double r38155338 = r38155335 + r38155337;
        return r38155338;
}
↓
double f(double x, double y, double z, double t) {
        double r38155339 = y;
        double r38155340 = 5.0;
        double r38155341 = r38155339 * r38155340;
        double r38155342 = 2.0;
        double r38155343 = x;
        double r38155344 = z;
        double r38155345 = r38155343 * r38155344;
        double r38155346 = r38155342 * r38155345;
        double r38155347 = t;
        double r38155348 = r38155347 * r38155343;
        double r38155349 = r38155343 * r38155339;
        double r38155350 = r38155342 * r38155349;
        double r38155351 = r38155348 + r38155350;
        double r38155352 = r38155346 + r38155351;
        double r38155353 = r38155341 + r38155352;
        return r38155353;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(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)))