Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
x \cdot \left(\left(\left(y + z\right) + z\right) + y\right) + \left(t \cdot x + y \cdot 5\right)
double f(double x, double y, double z, double t) {
        double r164159 = x;
        double r164160 = y;
        double r164161 = z;
        double r164162 = r164160 + r164161;
        double r164163 = r164162 + r164161;
        double r164164 = r164163 + r164160;
        double r164165 = t;
        double r164166 = r164164 + r164165;
        double r164167 = r164159 * r164166;
        double r164168 = 5.0;
        double r164169 = r164160 * r164168;
        double r164170 = r164167 + r164169;
        return r164170;
}
↓
double f(double x, double y, double z, double t) {
        double r164171 = x;
        double r164172 = y;
        double r164173 = z;
        double r164174 = r164172 + r164173;
        double r164175 = r164174 + r164173;
        double r164176 = r164175 + r164172;
        double r164177 = r164171 * r164176;
        double r164178 = t;
        double r164179 = r164178 * r164171;
        double r164180 = 5.0;
        double r164181 = r164172 * r164180;
        double r164182 = r164179 + r164181;
        double r164183 = r164177 + r164182;
        return r164183;
}

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. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))