Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(2 \cdot \left(x \cdot y\right) + 2 \cdot \left(x \cdot z\right)\right) + x \cdot t\right) + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(2 \cdot \left(x \cdot y\right) + 2 \cdot \left(x \cdot z\right)\right) + x \cdot t\right) + y \cdot 5
double f(double x, double y, double z, double t) {
        double r160309 = x;
        double r160310 = y;
        double r160311 = z;
        double r160312 = r160310 + r160311;
        double r160313 = r160312 + r160311;
        double r160314 = r160313 + r160310;
        double r160315 = t;
        double r160316 = r160314 + r160315;
        double r160317 = r160309 * r160316;
        double r160318 = 5.0;
        double r160319 = r160310 * r160318;
        double r160320 = r160317 + r160319;
        return r160320;
}
↓
double f(double x, double y, double z, double t) {
        double r160321 = 2.0;
        double r160322 = x;
        double r160323 = y;
        double r160324 = r160322 * r160323;
        double r160325 = r160321 * r160324;
        double r160326 = z;
        double r160327 = r160322 * r160326;
        double r160328 = r160321 * r160327;
        double r160329 = r160325 + r160328;
        double r160330 = t;
        double r160331 = r160322 * r160330;
        double r160332 = r160329 + r160331;
        double r160333 = 5.0;
        double r160334 = r160323 * r160333;
        double r160335 = r160332 + r160334;
        return r160335;
}

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. Simplified0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 
(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)))