Average Error: 0.1 → 0.1
Time: 14.0s
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 r137148 = x;
        double r137149 = y;
        double r137150 = z;
        double r137151 = r137149 + r137150;
        double r137152 = r137151 + r137150;
        double r137153 = r137152 + r137149;
        double r137154 = t;
        double r137155 = r137153 + r137154;
        double r137156 = r137148 * r137155;
        double r137157 = 5.0;
        double r137158 = r137149 * r137157;
        double r137159 = r137156 + r137158;
        return r137159;
}
↓
double f(double x, double y, double z, double t) {
        double r137160 = y;
        double r137161 = z;
        double r137162 = r137160 + r137161;
        double r137163 = r137162 + r137161;
        double r137164 = r137163 + r137160;
        double r137165 = x;
        double r137166 = r137164 * r137165;
        double r137167 = t;
        double r137168 = r137167 * r137165;
        double r137169 = 5.0;
        double r137170 = r137160 * r137169;
        double r137171 = r137168 + r137170;
        double r137172 = r137166 + r137171;
        return r137172;
}

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 2020003 
(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)))