Average Error: 0.5 → 0.5
Time: 21.5s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\frac{\pi}{2} - \sin^{-1} \left(\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\left(1 \cdot 1 + \left(5 \cdot \left(v \cdot v\right)\right) \cdot \left(5 \cdot \left(v \cdot v\right) + 1\right)\right) \cdot \left(v \cdot v - 1\right)}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\frac{\pi}{2} - \sin^{-1} \left(\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\left(1 \cdot 1 + \left(5 \cdot \left(v \cdot v\right)\right) \cdot \left(5 \cdot \left(v \cdot v\right) + 1\right)\right) \cdot \left(v \cdot v - 1\right)}\right)
double f(double v) {
        double r133660 = 1.0;
        double r133661 = 5.0;
        double r133662 = v;
        double r133663 = r133662 * r133662;
        double r133664 = r133661 * r133663;
        double r133665 = r133660 - r133664;
        double r133666 = r133663 - r133660;
        double r133667 = r133665 / r133666;
        double r133668 = acos(r133667);
        return r133668;
}
↓
double f(double v) {
        double r133669 = atan2(1.0, 0.0);
        double r133670 = 2.0;
        double r133671 = r133669 / r133670;
        double r133672 = 1.0;
        double r133673 = 3.0;
        double r133674 = pow(r133672, r133673);
        double r133675 = 5.0;
        double r133676 = v;
        double r133677 = r133676 * r133676;
        double r133678 = r133675 * r133677;
        double r133679 = pow(r133678, r133673);
        double r133680 = r133674 - r133679;
        double r133681 = r133672 * r133672;
        double r133682 = r133678 + r133672;
        double r133683 = r133678 * r133682;
        double r133684 = r133681 + r133683;
        double r133685 = r133677 - r133672;
        double r133686 = r133684 * r133685;
        double r133687 = r133680 / r133686;
        double r133688 = asin(r133687);
        double r133689 = r133671 - r133688;
        return r133689;
}

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 acos-asin0.5

    \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]
  4. Using strategy rm

  5. Applied flip3--0.5

    \[\leadsto \frac{\pi}{2} - \sin^{-1} \left(\frac{\color{blue}{\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{1 \cdot 1 + \left(\left(5 \cdot \left(v \cdot v\right)\right) \cdot \left(5 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(5 \cdot \left(v \cdot v\right)\right)\right)}}}{v \cdot v - 1}\right)\]

  6. Applied associate-/l/0.5

    \[\leadsto \frac{\pi}{2} - \sin^{-1} \color{blue}{\left(\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\left(v \cdot v - 1\right) \cdot \left(1 \cdot 1 + \left(\left(5 \cdot \left(v \cdot v\right)\right) \cdot \left(5 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(5 \cdot \left(v \cdot v\right)\right)\right)\right)}\right)}\]

  7. Simplified0.5

    \[\leadsto \frac{\pi}{2} - \sin^{-1} \left(\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\color{blue}{\left(1 \cdot 1 + \left(5 \cdot \left(v \cdot v\right)\right) \cdot \left(5 \cdot \left(v \cdot v\right) + 1\right)\right) \cdot \left(v \cdot v - 1\right)}}\right)\]

  8. Final simplification0.5

    \[\leadsto \frac{\pi}{2} - \sin^{-1} \left(\frac{{1}^{3} - {\left(5 \cdot \left(v \cdot v\right)\right)}^{3}}{\left(1 \cdot 1 + \left(5 \cdot \left(v \cdot v\right)\right) \cdot \left(5 \cdot \left(v \cdot v\right) + 1\right)\right) \cdot \left(v \cdot v - 1\right)}\right)\]

Reproduce

herbie shell --seed 2019199 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))