Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
\[0.707110000000000016 \cdot \left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\right)\]
↓
\[0.707110000000000016 \cdot \left(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)\]
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(\sqrt[3]{{\left(\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}\right)}^{3}} - x\right)
double f(double x) {
        double r94994 = 0.70711;
        double r94995 = 2.30753;
        double r94996 = x;
        double r94997 = 0.27061;
        double r94998 = r94996 * r94997;
        double r94999 = r94995 + r94998;
        double r95000 = 1.0;
        double r95001 = 0.99229;
        double r95002 = 0.04481;
        double r95003 = r94996 * r95002;
        double r95004 = r95001 + r95003;
        double r95005 = r94996 * r95004;
        double r95006 = r95000 + r95005;
        double r95007 = r94999 / r95006;
        double r95008 = r95007 - r94996;
        double r95009 = r94994 * r95008;
        return r95009;
}
↓
double f(double x) {
        double r95010 = 0.70711;
        double r95011 = 2.30753;
        double r95012 = x;
        double r95013 = 0.27061;
        double r95014 = r95012 * r95013;
        double r95015 = r95011 + r95014;
        double r95016 = 1.0;
        double r95017 = 0.99229;
        double r95018 = 0.04481;
        double r95019 = r95012 * r95018;
        double r95020 = r95017 + r95019;
        double r95021 = r95012 * r95020;
        double r95022 = r95016 + r95021;
        double r95023 = r95015 / r95022;
        double r95024 = 3.0;
        double r95025 = pow(r95023, r95024);
        double r95026 = cbrt(r95025);
        double r95027 = r95026 - r95012;
        double r95028 = r95010 * r95027;
        return r95028;
}

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-cbrt-cube0.0

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

  4. Applied add-cbrt-cube21.7

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

  5. Applied cbrt-undiv21.7

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))