Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(\frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} - x\right) \cdot \frac{6369080665019903}{9007199254740992}\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(\frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} - x\right) \cdot \frac{6369080665019903}{9007199254740992}
double f(double x) {
        double r79495 = 0.70711;
        double r79496 = 2.30753;
        double r79497 = x;
        double r79498 = 0.27061;
        double r79499 = r79497 * r79498;
        double r79500 = r79496 + r79499;
        double r79501 = 1.0;
        double r79502 = 0.99229;
        double r79503 = 0.04481;
        double r79504 = r79497 * r79503;
        double r79505 = r79502 + r79504;
        double r79506 = r79497 * r79505;
        double r79507 = r79501 + r79506;
        double r79508 = r79500 / r79507;
        double r79509 = r79508 - r79497;
        double r79510 = r79495 * r79509;
        return r79510;
}
↓
double f(double x) {
        double r79511 = 162377988252285.0;
        double r79512 = 70368744177664.0;
        double r79513 = r79511 / r79512;
        double r79514 = x;
        double r79515 = 609359547581365.0;
        double r79516 = 2251799813685248.0;
        double r79517 = r79515 / r79516;
        double r79518 = r79514 * r79517;
        double r79519 = r79513 + r79518;
        double r79520 = 1.0;
        double r79521 = 8937753748486939.0;
        double r79522 = 9007199254740992.0;
        double r79523 = r79521 / r79522;
        double r79524 = 3228900788839551.0;
        double r79525 = 7.205759403792794e+16;
        double r79526 = r79524 / r79525;
        double r79527 = r79514 * r79526;
        double r79528 = r79523 + r79527;
        double r79529 = r79514 * r79528;
        double r79530 = r79520 + r79529;
        double r79531 = r79519 / r79530;
        double r79532 = r79531 - r79514;
        double r79533 = 6369080665019903.0;
        double r79534 = r79533 / r79522;
        double r79535 = r79532 * r79534;
        return r79535;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\frac{6369080665019903}{9007199254740992} \cdot \left(\frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} - x\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto \frac{6369080665019903}{9007199254740992} \cdot \color{blue}{\left(\frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} + \left(-x\right)\right)}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\frac{6369080665019903}{9007199254740992} \cdot \frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} + \frac{6369080665019903}{9007199254740992} \cdot \left(-x\right)}\]

  6. Final simplification0.0

    \[\leadsto \left(\frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + x \cdot \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right)} - x\right) \cdot \frac{6369080665019903}{9007199254740992}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.707110000000000016 (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x)))