Average Error: 0.0 → 0.0
Time: 6.9s
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 r442 = 0.70711;
        double r443 = 2.30753;
        double r444 = x;
        double r445 = 0.27061;
        double r446 = r444 * r445;
        double r447 = r443 + r446;
        double r448 = 1.0;
        double r449 = 0.99229;
        double r450 = 0.04481;
        double r451 = r444 * r450;
        double r452 = r449 + r451;
        double r453 = r444 * r452;
        double r454 = r448 + r453;
        double r455 = r447 / r454;
        double r456 = r455 - r444;
        double r457 = r442 * r456;
        return r457;
}
↓
double f(double x) {
        double r458 = 0.70711;
        double r459 = 2.30753;
        double r460 = x;
        double r461 = 0.27061;
        double r462 = r460 * r461;
        double r463 = r459 + r462;
        double r464 = 1.0;
        double r465 = 0.99229;
        double r466 = 0.04481;
        double r467 = r460 * r466;
        double r468 = r465 + r467;
        double r469 = r460 * r468;
        double r470 = r464 + r469;
        double r471 = r463 / r470;
        double r472 = r458 * r471;
        double r473 = -r460;
        double r474 = r458 * r473;
        double r475 = r472 + r474;
        return r475;
}

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 2020025 
(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)))