Average Error: 0.1 → 0.1
Time: 3.8s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(\left(y + z\right) + z\right) + y\right) \cdot x + \left(t \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(\left(y + z\right) + z\right) + y\right) \cdot x + \left(t \cdot x + y \cdot 5\right)
double f(double x, double y, double z, double t) {
        double r233958 = x;
        double r233959 = y;
        double r233960 = z;
        double r233961 = r233959 + r233960;
        double r233962 = r233961 + r233960;
        double r233963 = r233962 + r233959;
        double r233964 = t;
        double r233965 = r233963 + r233964;
        double r233966 = r233958 * r233965;
        double r233967 = 5.0;
        double r233968 = r233959 * r233967;
        double r233969 = r233966 + r233968;
        return r233969;
}
↓
double f(double x, double y, double z, double t) {
        double r233970 = y;
        double r233971 = z;
        double r233972 = r233970 + r233971;
        double r233973 = r233972 + r233971;
        double r233974 = r233973 + r233970;
        double r233975 = x;
        double r233976 = r233974 * r233975;
        double r233977 = t;
        double r233978 = r233977 * r233975;
        double r233979 = 5.0;
        double r233980 = r233970 * r233979;
        double r233981 = r233978 + r233980;
        double r233982 = r233976 + r233981;
        return r233982;
}

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-rgt-in0.1

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

  4. Applied associate-+l+0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))