Average Error: 0.1 → 0.1
Time: 21.4s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[z + \left(\left(\left(y + x\right) + \left(y + x\right)\right) + x\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
z + \left(\left(\left(y + x\right) + \left(y + x\right)\right) + x\right)
double f(double x, double y, double z) {
        double r12190205 = x;
        double r12190206 = y;
        double r12190207 = r12190205 + r12190206;
        double r12190208 = r12190207 + r12190206;
        double r12190209 = r12190208 + r12190205;
        double r12190210 = z;
        double r12190211 = r12190209 + r12190210;
        double r12190212 = r12190211 + r12190205;
        return r12190212;
}
↓
double f(double x, double y, double z) {
        double r12190213 = z;
        double r12190214 = y;
        double r12190215 = x;
        double r12190216 = r12190214 + r12190215;
        double r12190217 = r12190216 + r12190216;
        double r12190218 = r12190217 + r12190215;
        double r12190219 = r12190213 + r12190218;
        return r12190219;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]

  2. Simplified0.1

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

  4. Applied +-commutative0.1

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

  5. Applied associate-+r+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  (+ (+ (+ (+ (+ x y) y) x) z) x))