Average Error: 0.0 → 0.0
Time: 28.9s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
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 \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
double f(double x) {
        double r105443 = 0.70711;
        double r105444 = 2.30753;
        double r105445 = x;
        double r105446 = 0.27061;
        double r105447 = r105445 * r105446;
        double r105448 = r105444 + r105447;
        double r105449 = 1.0;
        double r105450 = 0.99229;
        double r105451 = 0.04481;
        double r105452 = r105445 * r105451;
        double r105453 = r105450 + r105452;
        double r105454 = r105445 * r105453;
        double r105455 = r105449 + r105454;
        double r105456 = r105448 / r105455;
        double r105457 = r105456 - r105445;
        double r105458 = r105443 * r105457;
        return r105458;
}
↓
double f(double x) {
        double r105459 = 0.70711;
        double r105460 = 2.30753;
        double r105461 = x;
        double r105462 = 0.27061;
        double r105463 = r105461 * r105462;
        double r105464 = r105460 + r105463;
        double r105465 = 1.0;
        double r105466 = 0.99229;
        double r105467 = 0.04481;
        double r105468 = r105461 * r105467;
        double r105469 = r105466 + r105468;
        double r105470 = r105461 * r105469;
        double r105471 = r105465 + r105470;
        double r105472 = r105464 / r105471;
        double r105473 = r105472 - r105461;
        double r105474 = r105459 * r105473;
        return r105474;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(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)))