Average Error: 0.1 → 0.1
Time: 7.9s
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 r164090 = x;
        double r164091 = y;
        double r164092 = z;
        double r164093 = r164091 + r164092;
        double r164094 = r164093 + r164092;
        double r164095 = r164094 + r164091;
        double r164096 = t;
        double r164097 = r164095 + r164096;
        double r164098 = r164090 * r164097;
        double r164099 = 5.0;
        double r164100 = r164091 * r164099;
        double r164101 = r164098 + r164100;
        return r164101;
}
↓
double f(double x, double y, double z, double t) {
        double r164102 = y;
        double r164103 = z;
        double r164104 = r164102 + r164103;
        double r164105 = r164104 + r164103;
        double r164106 = r164105 + r164102;
        double r164107 = x;
        double r164108 = r164106 * r164107;
        double r164109 = t;
        double r164110 = r164109 * r164107;
        double r164111 = 5.0;
        double r164112 = r164102 * r164111;
        double r164113 = r164110 + r164112;
        double r164114 = r164108 + r164113;
        return r164114;
}

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 2019353 
(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)))