Average Error: 0.0 → 0.0
Time: 9.3s
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 r116346 = 0.70711;
        double r116347 = 2.30753;
        double r116348 = x;
        double r116349 = 0.27061;
        double r116350 = r116348 * r116349;
        double r116351 = r116347 + r116350;
        double r116352 = 1.0;
        double r116353 = 0.99229;
        double r116354 = 0.04481;
        double r116355 = r116348 * r116354;
        double r116356 = r116353 + r116355;
        double r116357 = r116348 * r116356;
        double r116358 = r116352 + r116357;
        double r116359 = r116351 / r116358;
        double r116360 = r116359 - r116348;
        double r116361 = r116346 * r116360;
        return r116361;
}
↓
double f(double x) {
        double r116362 = 0.70711;
        double r116363 = 2.30753;
        double r116364 = x;
        double r116365 = 0.27061;
        double r116366 = r116364 * r116365;
        double r116367 = r116363 + r116366;
        double r116368 = 1.0;
        double r116369 = 0.99229;
        double r116370 = 0.04481;
        double r116371 = r116364 * r116370;
        double r116372 = r116369 + r116371;
        double r116373 = r116364 * r116372;
        double r116374 = r116368 + r116373;
        double r116375 = r116367 / r116374;
        double r116376 = r116375 - r116364;
        double r116377 = r116362 * r116376;
        return r116377;
}

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)))