Average Error: 0.1 → 0.1
Time: 6.5s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)
double f(double x, double y, double z, double t) {
        double r126209 = x;
        double r126210 = y;
        double r126211 = z;
        double r126212 = r126210 + r126211;
        double r126213 = r126212 + r126211;
        double r126214 = r126213 + r126210;
        double r126215 = t;
        double r126216 = r126214 + r126215;
        double r126217 = r126209 * r126216;
        double r126218 = 5.0;
        double r126219 = r126210 * r126218;
        double r126220 = r126217 + r126219;
        return r126220;
}
↓
double f(double x, double y, double z, double t) {
        double r126221 = x;
        double r126222 = y;
        double r126223 = z;
        double r126224 = r126222 + r126223;
        double r126225 = r126224 + r126223;
        double r126226 = r126225 + r126222;
        double r126227 = r126221 * r126226;
        double r126228 = t;
        double r126229 = r126228 * r126221;
        double r126230 = 5.0;
        double r126231 = r126222 * r126230;
        double r126232 = r126229 + r126231;
        double r126233 = r126227 + r126232;
        return r126233;
}

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 distribute-lft-in0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020056 
(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)))