Average Error: 0.6 → 0.6
Time: 18.0s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\frac{1}{v \cdot v - 1} - \frac{\left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\frac{1}{v \cdot v - 1} - \frac{\left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)
double f(double v) {
        double r7334154 = 1.0;
        double r7334155 = 5.0;
        double r7334156 = v;
        double r7334157 = r7334156 * r7334156;
        double r7334158 = r7334155 * r7334157;
        double r7334159 = r7334154 - r7334158;
        double r7334160 = r7334157 - r7334154;
        double r7334161 = r7334159 / r7334160;
        double r7334162 = acos(r7334161);
        return r7334162;
}
↓
double f(double v) {
        double r7334163 = 1.0;
        double r7334164 = v;
        double r7334165 = r7334164 * r7334164;
        double r7334166 = r7334165 - r7334163;
        double r7334167 = r7334163 / r7334166;
        double r7334168 = 5.0;
        double r7334169 = r7334165 * r7334168;
        double r7334170 = r7334169 / r7334166;
        double r7334171 = r7334167 - r7334170;
        double r7334172 = acos(r7334171);
        return r7334172;
}

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 div-sub0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019164 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))