Average Error: 0.0 → 0.1
Time: 3.6s
Precision: 64
\[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
↓
\[x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}\]
x - \frac{y}{1 + \frac{x \cdot y}{2}}
↓
x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}
double f(double x, double y) {
        double r1212 = x;
        double r1213 = y;
        double r1214 = 1.0;
        double r1215 = r1212 * r1213;
        double r1216 = 2.0;
        double r1217 = r1215 / r1216;
        double r1218 = r1214 + r1217;
        double r1219 = r1213 / r1218;
        double r1220 = r1212 - r1219;
        return r1220;
}
↓
double f(double x, double y) {
        double r1221 = x;
        double r1222 = y;
        double r1223 = 1.0;
        double r1224 = 2.0;
        double r1225 = r1224 / r1222;
        double r1226 = r1221 / r1225;
        double r1227 = r1223 + r1226;
        double r1228 = r1222 / r1227;
        double r1229 = r1221 - r1228;
        return r1229;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{y}{1 + \frac{x \cdot y}{2}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto x - \frac{y}{1 + \color{blue}{\frac{x}{\frac{2}{y}}}}\]

  4. Final simplification0.1

    \[\leadsto x - \frac{y}{1 + \frac{x}{\frac{2}{y}}}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B"
  :precision binary64
  (- x (/ y (+ 1 (/ (* x y) 2)))))