Average Error: 0.5 → 0.5
Time: 6.3s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}
double f(double v) {
        double r217975 = 1.0;
        double r217976 = 5.0;
        double r217977 = v;
        double r217978 = r217977 * r217977;
        double r217979 = r217976 * r217978;
        double r217980 = r217975 - r217979;
        double r217981 = r217978 - r217975;
        double r217982 = r217980 / r217981;
        double r217983 = acos(r217982);
        return r217983;
}
↓
double f(double v) {
        double r217984 = 1.0;
        double r217985 = 5.0;
        double r217986 = v;
        double r217987 = r217986 * r217986;
        double r217988 = r217985 * r217987;
        double r217989 = r217984 - r217988;
        double r217990 = r217987 - r217984;
        double r217991 = r217989 / r217990;
        double r217992 = acos(r217991);
        double r217993 = log(r217992);
        double r217994 = exp(r217993);
        return r217994;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

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

  3. Applied add-exp-log0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020033 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))