Average Error: 0.6 → 0.6
Time: 24.5s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)
double f(double v) {
        double r6466612 = 1.0;
        double r6466613 = 5.0;
        double r6466614 = v;
        double r6466615 = r6466614 * r6466614;
        double r6466616 = r6466613 * r6466615;
        double r6466617 = r6466612 - r6466616;
        double r6466618 = r6466615 - r6466612;
        double r6466619 = r6466617 / r6466618;
        double r6466620 = acos(r6466619);
        return r6466620;
}
↓
double f(double v) {
        double r6466621 = 1.0;
        double r6466622 = v;
        double r6466623 = r6466622 * r6466622;
        double r6466624 = 5.0;
        double r6466625 = r6466623 * r6466624;
        double r6466626 = r6466621 - r6466625;
        double r6466627 = r6466623 - r6466621;
        double r6466628 = r6466626 / r6466627;
        double r6466629 = acos(r6466628);
        return r6466629;
}

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 *-commutative0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019132 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))