Average Error: 0.6 → 0.6
Time: 25.4s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\sqrt{\log \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{v \cdot v - 1}\right)\right)}}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
e^{\sqrt{\log \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{v \cdot v - 1}\right)\right)}}
double f(double v) {
        double r27966966 = 1.0;
        double r27966967 = 5.0;
        double r27966968 = v;
        double r27966969 = r27966968 * r27966968;
        double r27966970 = r27966967 * r27966969;
        double r27966971 = r27966966 - r27966970;
        double r27966972 = r27966969 - r27966966;
        double r27966973 = r27966971 / r27966972;
        double r27966974 = acos(r27966973);
        return r27966974;
}
↓
double f(double v) {
        double r27966975 = 1.0;
        double r27966976 = v;
        double r27966977 = r27966976 * r27966976;
        double r27966978 = 5.0;
        double r27966979 = r27966977 * r27966978;
        double r27966980 = r27966975 - r27966979;
        double r27966981 = r27966977 - r27966975;
        double r27966982 = r27966980 / r27966981;
        double r27966983 = acos(r27966982);
        double r27966984 = cbrt(r27966983);
        double r27966985 = r27966984 * r27966984;
        double r27966986 = r27966984 * r27966985;
        double r27966987 = log(r27966986);
        double r27966988 = sqrt(r27966987);
        double r27966989 = exp(r27966979);
        double r27966990 = log(r27966989);
        double r27966991 = r27966975 - r27966990;
        double r27966992 = r27966991 / r27966981;
        double r27966993 = acos(r27966992);
        double r27966994 = log(r27966993);
        double r27966995 = sqrt(r27966994);
        double r27966996 = r27966988 * r27966995;
        double r27966997 = exp(r27966996);
        return r27966997;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
  2. Using strategy rm

  3. Applied add-exp-log0.6

    \[\leadsto \color{blue}{e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.6

    \[\leadsto e^{\color{blue}{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}}}\]
  6. Using strategy rm

  7. Applied add-log-exp0.6

    \[\leadsto e^{\sqrt{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \color{blue}{\log \left(e^{5 \cdot \left(v \cdot v\right)}\right)}}{v \cdot v - 1}\right)\right)}}\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.6

    \[\leadsto e^{\sqrt{\log \color{blue}{\left(\left(\sqrt[3]{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right) \cdot \sqrt[3]{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{5 \cdot \left(v \cdot v\right)}\right)}{v \cdot v - 1}\right)\right)}}\]

  10. Final simplification0.6

    \[\leadsto e^{\sqrt{\log \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)\right)} \cdot \sqrt{\log \left(\cos^{-1} \left(\frac{1 - \log \left(e^{\left(v \cdot v\right) \cdot 5}\right)}{v \cdot v - 1}\right)\right)}}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))