Average Error: 0.0 → 0.0
Time: 16.5s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot 0.707110000000000016\right)}^{3}} + 0.707110000000000016 \cdot \left(-x\right)\]
0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)
↓
\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot 0.707110000000000016\right)}^{3}} + 0.707110000000000016 \cdot \left(-x\right)
double f(double x) {
        double r141534 = 0.70711;
        double r141535 = 2.30753;
        double r141536 = x;
        double r141537 = 0.27061;
        double r141538 = r141536 * r141537;
        double r141539 = r141535 + r141538;
        double r141540 = 1.0;
        double r141541 = 0.99229;
        double r141542 = 0.04481;
        double r141543 = r141536 * r141542;
        double r141544 = r141541 + r141543;
        double r141545 = r141536 * r141544;
        double r141546 = r141540 + r141545;
        double r141547 = r141539 / r141546;
        double r141548 = r141547 - r141536;
        double r141549 = r141534 * r141548;
        return r141549;
}
↓
double f(double x) {
        double r141550 = 2.30753;
        double r141551 = x;
        double r141552 = 0.27061;
        double r141553 = r141551 * r141552;
        double r141554 = r141550 + r141553;
        double r141555 = 1.0;
        double r141556 = 0.99229;
        double r141557 = 0.04481;
        double r141558 = r141551 * r141557;
        double r141559 = r141556 + r141558;
        double r141560 = r141551 * r141559;
        double r141561 = r141555 + r141560;
        double r141562 = r141554 / r141561;
        double r141563 = 0.70711;
        double r141564 = r141562 * r141563;
        double r141565 = 3.0;
        double r141566 = pow(r141564, r141565);
        double r141567 = cbrt(r141566);
        double r141568 = -r141551;
        double r141569 = r141563 * r141568;
        double r141570 = r141567 + r141569;
        return r141570;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  7. Applied add-cbrt-cube0.5

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \color{blue}{\sqrt[3]{\left(0.707110000000000016 \cdot 0.707110000000000016\right) \cdot 0.707110000000000016}} + 0.707110000000000016 \cdot \left(-x\right)\]

  8. Applied add-cbrt-cube0.5

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}} \cdot \sqrt[3]{\left(0.707110000000000016 \cdot 0.707110000000000016\right) \cdot 0.707110000000000016} + 0.707110000000000016 \cdot \left(-x\right)\]

  9. Applied add-cbrt-cube21.9

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}} \cdot \sqrt[3]{\left(0.707110000000000016 \cdot 0.707110000000000016\right) \cdot 0.707110000000000016} + 0.707110000000000016 \cdot \left(-x\right)\]

  10. Applied cbrt-undiv21.9

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)}}} \cdot \sqrt[3]{\left(0.707110000000000016 \cdot 0.707110000000000016\right) \cdot 0.707110000000000016} + 0.707110000000000016 \cdot \left(-x\right)\]

  11. Applied cbrt-unprod21.4

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}{\left(\left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)\right)} \cdot \left(\left(0.707110000000000016 \cdot 0.707110000000000016\right) \cdot 0.707110000000000016\right)}} + 0.707110000000000016 \cdot \left(-x\right)\]

  12. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot 0.707110000000000016\right)}^{3}}} + 0.707110000000000016 \cdot \left(-x\right)\]

  13. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot 0.707110000000000016\right)}^{3}} + 0.707110000000000016 \cdot \left(-x\right)\]

Reproduce

herbie shell --seed 2020042 
(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)))