Average Error: 0.0 → 0.0
Time: 28.7s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(x \cdot \left(\sqrt[3]{0.992290000000000005 + x \cdot 0.044810000000000003} \cdot \sqrt[3]{0.992290000000000005 + x \cdot 0.044810000000000003}\right)\right) \cdot \sqrt[3]{0.992290000000000005 + x \cdot 0.044810000000000003}} - x\right)\]
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 + \left(x \cdot \left(\sqrt[3]{0.992290000000000005 + x \cdot 0.044810000000000003} \cdot \sqrt[3]{0.992290000000000005 + x \cdot 0.044810000000000003}\right)\right) \cdot \sqrt[3]{0.992290000000000005 + x \cdot 0.044810000000000003}} - x\right)
double f(double x) {
        double r110627 = 0.70711;
        double r110628 = 2.30753;
        double r110629 = x;
        double r110630 = 0.27061;
        double r110631 = r110629 * r110630;
        double r110632 = r110628 + r110631;
        double r110633 = 1.0;
        double r110634 = 0.99229;
        double r110635 = 0.04481;
        double r110636 = r110629 * r110635;
        double r110637 = r110634 + r110636;
        double r110638 = r110629 * r110637;
        double r110639 = r110633 + r110638;
        double r110640 = r110632 / r110639;
        double r110641 = r110640 - r110629;
        double r110642 = r110627 * r110641;
        return r110642;
}
↓
double f(double x) {
        double r110643 = 0.70711;
        double r110644 = 2.30753;
        double r110645 = x;
        double r110646 = 0.27061;
        double r110647 = r110645 * r110646;
        double r110648 = r110644 + r110647;
        double r110649 = 1.0;
        double r110650 = 0.99229;
        double r110651 = 0.04481;
        double r110652 = r110645 * r110651;
        double r110653 = r110650 + r110652;
        double r110654 = cbrt(r110653);
        double r110655 = r110654 * r110654;
        double r110656 = r110645 * r110655;
        double r110657 = r110656 * r110654;
        double r110658 = r110649 + r110657;
        double r110659 = r110648 / r110658;
        double r110660 = r110659 - r110645;
        double r110661 = r110643 * r110660;
        return r110661;
}

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 add-cube-cbrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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)))