Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
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(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
double f(double x) {
        double r94408 = 0.70711;
        double r94409 = 2.30753;
        double r94410 = x;
        double r94411 = 0.27061;
        double r94412 = r94410 * r94411;
        double r94413 = r94409 + r94412;
        double r94414 = 1.0;
        double r94415 = 0.99229;
        double r94416 = 0.04481;
        double r94417 = r94410 * r94416;
        double r94418 = r94415 + r94417;
        double r94419 = r94410 * r94418;
        double r94420 = r94414 + r94419;
        double r94421 = r94413 / r94420;
        double r94422 = r94421 - r94410;
        double r94423 = r94408 * r94422;
        return r94423;
}
↓
double f(double x) {
        double r94424 = 0.70711;
        double r94425 = 2.30753;
        double r94426 = x;
        double r94427 = 0.27061;
        double r94428 = r94426 * r94427;
        double r94429 = r94425 + r94428;
        double r94430 = 1.0;
        double r94431 = 1.0;
        double r94432 = 0.99229;
        double r94433 = 0.04481;
        double r94434 = r94426 * r94433;
        double r94435 = r94432 + r94434;
        double r94436 = r94426 * r94435;
        double r94437 = r94431 + r94436;
        double r94438 = r94430 / r94437;
        double r94439 = r94429 * r94438;
        double r94440 = r94439 - r94426;
        double r94441 = r94424 * r94440;
        return r94441;
}

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 div-inv0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 
(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)))