Average Error: 0.0 → 0.5
Time: 17.1s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}{\frac{x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) + 1}{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}} - x\right)\]
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{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}{\frac{x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) + 1}{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}} - x\right)
double f(double x) {
        double r6435497 = 0.70711;
        double r6435498 = 2.30753;
        double r6435499 = x;
        double r6435500 = 0.27061;
        double r6435501 = r6435499 * r6435500;
        double r6435502 = r6435498 + r6435501;
        double r6435503 = 1.0;
        double r6435504 = 0.99229;
        double r6435505 = 0.04481;
        double r6435506 = r6435499 * r6435505;
        double r6435507 = r6435504 + r6435506;
        double r6435508 = r6435499 * r6435507;
        double r6435509 = r6435503 + r6435508;
        double r6435510 = r6435502 / r6435509;
        double r6435511 = r6435510 - r6435499;
        double r6435512 = r6435497 * r6435511;
        return r6435512;
}
↓
double f(double x) {
        double r6435513 = 0.70711;
        double r6435514 = 2.30753;
        double r6435515 = x;
        double r6435516 = 0.27061;
        double r6435517 = r6435515 * r6435516;
        double r6435518 = r6435514 + r6435517;
        double r6435519 = cbrt(r6435518);
        double r6435520 = r6435519 * r6435519;
        double r6435521 = 0.04481;
        double r6435522 = r6435515 * r6435521;
        double r6435523 = 0.99229;
        double r6435524 = r6435522 + r6435523;
        double r6435525 = r6435515 * r6435524;
        double r6435526 = 1.0;
        double r6435527 = r6435525 + r6435526;
        double r6435528 = r6435527 / r6435519;
        double r6435529 = r6435520 / r6435528;
        double r6435530 = r6435529 - r6435515;
        double r6435531 = r6435513 * r6435530;
        return r6435531;
}

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-cube-cbrt0.5

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{\color{blue}{\left(\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}\right) \cdot \sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]

  4. Applied associate-/l*0.5

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\color{blue}{\frac{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}{\frac{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}}} - x\right)\]

  5. Final simplification0.5

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812} \cdot \sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}{\frac{x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) + 1}{\sqrt[3]{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}} - x\right)\]

Reproduce

herbie shell --seed 2019192 
(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)))