Average Error: 0.6 → 0.6
Time: 27.7s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[{e}^{\left(\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
{e}^{\left(\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)\right)}
double f(double v) {
        double r110265 = 1.0;
        double r110266 = 5.0;
        double r110267 = v;
        double r110268 = r110267 * r110267;
        double r110269 = r110266 * r110268;
        double r110270 = r110265 - r110269;
        double r110271 = r110268 - r110265;
        double r110272 = r110270 / r110271;
        double r110273 = acos(r110272);
        return r110273;
}
↓
double f(double v) {
        double r110274 = exp(1.0);
        double r110275 = 1.0;
        double r110276 = 5.0;
        double r110277 = v;
        double r110278 = r110277 * r110277;
        double r110279 = r110276 * r110278;
        double r110280 = r110275 - r110279;
        double r110281 = r110278 - r110275;
        double r110282 = r110280 / r110281;
        double r110283 = acos(r110282);
        double r110284 = log(r110283);
        double r110285 = pow(r110274, r110284);
        return r110285;
}

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 pow10.6

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

  6. Applied log-pow0.6

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

  7. Applied exp-prod0.6

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

  8. Simplified0.6

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

  10. Applied pow10.6

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

  11. Final simplification0.6

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

Reproduce

herbie shell --seed 2019304 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))