Average Error: 0.1 → 0.1
Time: 13.3s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + \left(z + z\right)\right) + y\right) + t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(y + \left(z + z\right)\right) + y\right) + t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r179275 = x;
        double r179276 = y;
        double r179277 = z;
        double r179278 = r179276 + r179277;
        double r179279 = r179278 + r179277;
        double r179280 = r179279 + r179276;
        double r179281 = t;
        double r179282 = r179280 + r179281;
        double r179283 = r179275 * r179282;
        double r179284 = 5.0;
        double r179285 = r179276 * r179284;
        double r179286 = r179283 + r179285;
        return r179286;
}
↓
double f(double x, double y, double z, double t) {
        double r179287 = x;
        double r179288 = y;
        double r179289 = z;
        double r179290 = r179289 + r179289;
        double r179291 = r179288 + r179290;
        double r179292 = r179291 + r179288;
        double r179293 = t;
        double r179294 = r179292 + r179293;
        double r179295 = r179287 * r179294;
        double r179296 = 5.0;
        double r179297 = r179288 * r179296;
        double r179298 = r179295 + r179297;
        return r179298;
}

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 associate-+l+0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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)))