Average Error: 0.1 → 0.1
Time: 15.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(2 \cdot \left(z + y\right) + t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(2 \cdot \left(z + y\right) + t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r132278 = x;
        double r132279 = y;
        double r132280 = z;
        double r132281 = r132279 + r132280;
        double r132282 = r132281 + r132280;
        double r132283 = r132282 + r132279;
        double r132284 = t;
        double r132285 = r132283 + r132284;
        double r132286 = r132278 * r132285;
        double r132287 = 5.0;
        double r132288 = r132279 * r132287;
        double r132289 = r132286 + r132288;
        return r132289;
}
↓
double f(double x, double y, double z, double t) {
        double r132290 = x;
        double r132291 = 2.0;
        double r132292 = z;
        double r132293 = y;
        double r132294 = r132292 + r132293;
        double r132295 = r132291 * r132294;
        double r132296 = t;
        double r132297 = r132295 + r132296;
        double r132298 = r132290 * r132297;
        double r132299 = 5.0;
        double r132300 = r132293 * r132299;
        double r132301 = r132298 + r132300;
        return r132301;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 
(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)))