Average Error: 0.5 → 0.5
Time: 35.6s
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 r6843231 = 1.0;
        double r6843232 = 5.0;
        double r6843233 = v;
        double r6843234 = r6843233 * r6843233;
        double r6843235 = r6843232 * r6843234;
        double r6843236 = r6843231 - r6843235;
        double r6843237 = r6843234 - r6843231;
        double r6843238 = r6843236 / r6843237;
        double r6843239 = acos(r6843238);
        return r6843239;
}
↓
double f(double v) {
        double r6843240 = 1.0;
        double r6843241 = v;
        double r6843242 = r6843241 * r6843241;
        double r6843243 = 5.0;
        double r6843244 = r6843242 * r6843243;
        double r6843245 = r6843240 - r6843244;
        double r6843246 = r6843242 - r6843240;
        double r6843247 = r6843245 / r6843246;
        double r6843248 = acos(r6843247);
        return r6843248;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019142 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))