Average Error: 0.1 → 0.1
Time: 18.2s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[y \cdot 5 + \left(\left(2 \cdot x\right) \cdot \left(y + z\right) + t \cdot x\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
y \cdot 5 + \left(\left(2 \cdot x\right) \cdot \left(y + z\right) + t \cdot x\right)
double f(double x, double y, double z, double t) {
        double r153240 = x;
        double r153241 = y;
        double r153242 = z;
        double r153243 = r153241 + r153242;
        double r153244 = r153243 + r153242;
        double r153245 = r153244 + r153241;
        double r153246 = t;
        double r153247 = r153245 + r153246;
        double r153248 = r153240 * r153247;
        double r153249 = 5.0;
        double r153250 = r153241 * r153249;
        double r153251 = r153248 + r153250;
        return r153251;
}
↓
double f(double x, double y, double z, double t) {
        double r153252 = y;
        double r153253 = 5.0;
        double r153254 = r153252 * r153253;
        double r153255 = 2.0;
        double r153256 = x;
        double r153257 = r153255 * r153256;
        double r153258 = z;
        double r153259 = r153252 + r153258;
        double r153260 = r153257 * r153259;
        double r153261 = t;
        double r153262 = r153261 * r153256;
        double r153263 = r153260 + r153262;
        double r153264 = r153254 + r153263;
        return r153264;
}

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

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

  3. Taylor expanded around inf 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 
(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)))