Average Error: 0.0 → 0.2
Time: 25.4s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \log \left(e^{x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}\right)} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \log \left(e^{x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}\right)} - x\right)
double f(double x) {
        double r65532 = 0.70711;
        double r65533 = 2.30753;
        double r65534 = x;
        double r65535 = 0.27061;
        double r65536 = r65534 * r65535;
        double r65537 = r65533 + r65536;
        double r65538 = 1.0;
        double r65539 = 0.99229;
        double r65540 = 0.04481;
        double r65541 = r65534 * r65540;
        double r65542 = r65539 + r65541;
        double r65543 = r65534 * r65542;
        double r65544 = r65538 + r65543;
        double r65545 = r65537 / r65544;
        double r65546 = r65545 - r65534;
        double r65547 = r65532 * r65546;
        return r65547;
}
↓
double f(double x) {
        double r65548 = 0.70711;
        double r65549 = 2.30753;
        double r65550 = x;
        double r65551 = 0.27061;
        double r65552 = r65550 * r65551;
        double r65553 = r65549 + r65552;
        double r65554 = 1.0;
        double r65555 = 0.99229;
        double r65556 = 0.04481;
        double r65557 = r65550 * r65556;
        double r65558 = r65555 + r65557;
        double r65559 = r65550 * r65558;
        double r65560 = exp(r65559);
        double r65561 = log(r65560);
        double r65562 = r65554 + r65561;
        double r65563 = r65553 / r65562;
        double r65564 = r65563 - r65550;
        double r65565 = r65548 * r65564;
        return r65565;
}

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

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.2

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\log \left(e^{x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}\right)}} - x\right)\]

  4. Final simplification0.2

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \log \left(e^{x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}\right)} - x\right)\]

Reproduce

herbie shell --seed 2019323 
(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)))