Average Error: 0.0 → 0.0
Time: 13.6s
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 r94352 = 0.70711;
        double r94353 = 2.30753;
        double r94354 = x;
        double r94355 = 0.27061;
        double r94356 = r94354 * r94355;
        double r94357 = r94353 + r94356;
        double r94358 = 1.0;
        double r94359 = 0.99229;
        double r94360 = 0.04481;
        double r94361 = r94354 * r94360;
        double r94362 = r94359 + r94361;
        double r94363 = r94354 * r94362;
        double r94364 = r94358 + r94363;
        double r94365 = r94357 / r94364;
        double r94366 = r94365 - r94354;
        double r94367 = r94352 * r94366;
        return r94367;
}
↓
double f(double x) {
        double r94368 = 0.70711;
        double r94369 = 2.30753;
        double r94370 = x;
        double r94371 = 0.27061;
        double r94372 = r94370 * r94371;
        double r94373 = r94369 + r94372;
        double r94374 = 1.0;
        double r94375 = 0.99229;
        double r94376 = 0.04481;
        double r94377 = r94370 * r94376;
        double r94378 = r94375 + r94377;
        double r94379 = r94370 * r94378;
        double r94380 = r94374 + r94379;
        double r94381 = r94373 / r94380;
        double r94382 = r94381 - r94370;
        double r94383 = r94368 * r94382;
        return r94383;
}

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 2019198 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))