Average Error: 0.5 → 0.5
Time: 8.5s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\frac{\pi}{2} - \sin^{-1} \left(\frac{\frac{\left(-5 \cdot 5\right) \cdot {v}^{4} + 1 \cdot 1}{1 + 5 \cdot \left(v \cdot v\right)}}{v \cdot v - 1}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\frac{\pi}{2} - \sin^{-1} \left(\frac{\frac{\left(-5 \cdot 5\right) \cdot {v}^{4} + 1 \cdot 1}{1 + 5 \cdot \left(v \cdot v\right)}}{v \cdot v - 1}\right)
double f(double v) {
        double r303149 = 1.0;
        double r303150 = 5.0;
        double r303151 = v;
        double r303152 = r303151 * r303151;
        double r303153 = r303150 * r303152;
        double r303154 = r303149 - r303153;
        double r303155 = r303152 - r303149;
        double r303156 = r303154 / r303155;
        double r303157 = acos(r303156);
        return r303157;
}
↓
double f(double v) {
        double r303158 = atan2(1.0, 0.0);
        double r303159 = 2.0;
        double r303160 = r303158 / r303159;
        double r303161 = 5.0;
        double r303162 = r303161 * r303161;
        double r303163 = -r303162;
        double r303164 = v;
        double r303165 = 4.0;
        double r303166 = pow(r303164, r303165);
        double r303167 = r303163 * r303166;
        double r303168 = 1.0;
        double r303169 = r303168 * r303168;
        double r303170 = r303167 + r303169;
        double r303171 = r303164 * r303164;
        double r303172 = r303161 * r303171;
        double r303173 = r303168 + r303172;
        double r303174 = r303170 / r303173;
        double r303175 = r303171 - r303168;
        double r303176 = r303174 / r303175;
        double r303177 = asin(r303176);
        double r303178 = r303160 - r303177;
        return r303178;
}

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 flip--0.5

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

  4. Simplified0.5

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

  6. Applied acos-asin0.5

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

  7. Final simplification0.5

    \[\leadsto \frac{\pi}{2} - \sin^{-1} \left(\frac{\frac{\left(-5 \cdot 5\right) \cdot {v}^{4} + 1 \cdot 1}{1 + 5 \cdot \left(v \cdot v\right)}}{v \cdot v - 1}\right)\]

Reproduce

herbie shell --seed 2019322 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))