Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.044810000000000003 \cdot x + 0.992290000000000005\right)} - x\right)\]
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(0.044810000000000003 \cdot x + 0.992290000000000005\right)} - x\right)
double f(double x) {
        double r165476 = 0.70711;
        double r165477 = 2.30753;
        double r165478 = x;
        double r165479 = 0.27061;
        double r165480 = r165478 * r165479;
        double r165481 = r165477 + r165480;
        double r165482 = 1.0;
        double r165483 = 0.99229;
        double r165484 = 0.04481;
        double r165485 = r165478 * r165484;
        double r165486 = r165483 + r165485;
        double r165487 = r165478 * r165486;
        double r165488 = r165482 + r165487;
        double r165489 = r165481 / r165488;
        double r165490 = r165489 - r165478;
        double r165491 = r165476 * r165490;
        return r165491;
}
↓
double f(double x) {
        double r165492 = 0.70711;
        double r165493 = 2.30753;
        double r165494 = x;
        double r165495 = 0.27061;
        double r165496 = r165494 * r165495;
        double r165497 = r165493 + r165496;
        double r165498 = 1.0;
        double r165499 = 0.04481;
        double r165500 = r165499 * r165494;
        double r165501 = 0.99229;
        double r165502 = r165500 + r165501;
        double r165503 = r165494 * r165502;
        double r165504 = r165498 + r165503;
        double r165505 = r165497 / r165504;
        double r165506 = r165505 - r165494;
        double r165507 = r165492 * r165506;
        return r165507;
}

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. Taylor expanded around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(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)))