Average Error: 0.0 → 0.0
Time: 16.3s
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 r124969 = 0.70711;
        double r124970 = 2.30753;
        double r124971 = x;
        double r124972 = 0.27061;
        double r124973 = r124971 * r124972;
        double r124974 = r124970 + r124973;
        double r124975 = 1.0;
        double r124976 = 0.99229;
        double r124977 = 0.04481;
        double r124978 = r124971 * r124977;
        double r124979 = r124976 + r124978;
        double r124980 = r124971 * r124979;
        double r124981 = r124975 + r124980;
        double r124982 = r124974 / r124981;
        double r124983 = r124982 - r124971;
        double r124984 = r124969 * r124983;
        return r124984;
}
↓
double f(double x) {
        double r124985 = 2.30753;
        double r124986 = x;
        double r124987 = 0.27061;
        double r124988 = r124986 * r124987;
        double r124989 = r124985 + r124988;
        double r124990 = 1.0;
        double r124991 = 0.99229;
        double r124992 = 0.04481;
        double r124993 = r124986 * r124992;
        double r124994 = r124991 + r124993;
        double r124995 = r124986 * r124994;
        double r124996 = r124990 + r124995;
        double r124997 = r124989 / r124996;
        double r124998 = 0.70711;
        double r124999 = r124997 * r124998;
        double r125000 = 3.0;
        double r125001 = pow(r124999, r125000);
        double r125002 = cbrt(r125001);
        double r125003 = -r124986;
        double r125004 = r124998 * r125003;
        double r125005 = r125002 + r125004;
        return r125005;
}

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)))