Average Error: 0.1 → 0.1
Time: 21.5s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(\left(\left(z + y\right) + \left(z + y\right)\right) + t\right) \cdot x + y \cdot 5\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(\left(\left(z + y\right) + \left(z + y\right)\right) + t\right) \cdot x + y \cdot 5
double f(double x, double y, double z, double t) {
        double r9115216 = x;
        double r9115217 = y;
        double r9115218 = z;
        double r9115219 = r9115217 + r9115218;
        double r9115220 = r9115219 + r9115218;
        double r9115221 = r9115220 + r9115217;
        double r9115222 = t;
        double r9115223 = r9115221 + r9115222;
        double r9115224 = r9115216 * r9115223;
        double r9115225 = 5.0;
        double r9115226 = r9115217 * r9115225;
        double r9115227 = r9115224 + r9115226;
        return r9115227;
}
↓
double f(double x, double y, double z, double t) {
        double r9115228 = z;
        double r9115229 = y;
        double r9115230 = r9115228 + r9115229;
        double r9115231 = r9115230 + r9115230;
        double r9115232 = t;
        double r9115233 = r9115231 + r9115232;
        double r9115234 = x;
        double r9115235 = r9115233 * r9115234;
        double r9115236 = 5.0;
        double r9115237 = r9115229 * r9115236;
        double r9115238 = r9115235 + r9115237;
        return r9115238;
}

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. Simplified0.1

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

  3. Taylor expanded around inf 0.1

    \[\leadsto y \cdot 5 + \color{blue}{\left(2 \cdot \left(x \cdot z\right) + \left(t \cdot x + 2 \cdot \left(x \cdot y\right)\right)\right)}\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5.0)))