Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)
double f(double x) {
        double r121262 = 0.70711;
        double r121263 = 2.30753;
        double r121264 = x;
        double r121265 = 0.27061;
        double r121266 = r121264 * r121265;
        double r121267 = r121263 + r121266;
        double r121268 = 1.0;
        double r121269 = 0.99229;
        double r121270 = 0.04481;
        double r121271 = r121264 * r121270;
        double r121272 = r121269 + r121271;
        double r121273 = r121264 * r121272;
        double r121274 = r121268 + r121273;
        double r121275 = r121267 / r121274;
        double r121276 = r121275 - r121264;
        double r121277 = r121262 * r121276;
        return r121277;
}
↓
double f(double x) {
        double r121278 = 0.70711;
        double r121279 = 2.30753;
        double r121280 = x;
        double r121281 = 0.27061;
        double r121282 = r121280 * r121281;
        double r121283 = r121279 + r121282;
        double r121284 = 1.0;
        double r121285 = 0.99229;
        double r121286 = 0.04481;
        double r121287 = r121280 * r121286;
        double r121288 = r121285 + r121287;
        double r121289 = r121280 * r121288;
        double r121290 = r121284 + r121289;
        double r121291 = r121283 / r121290;
        double r121292 = r121278 * r121291;
        double r121293 = -r121280;
        double r121294 = r121278 * r121293;
        double r121295 = r121292 + r121294;
        return r121295;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 0.707110000000000016 \cdot \color{blue}{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + \left(-x\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)}\]

  5. Final simplification0.0

    \[\leadsto 0.707110000000000016 \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} + 0.707110000000000016 \cdot \left(-x\right)\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))