Average Error: 0.5 → 0.5
Time: 45.5s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\left(\sqrt{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}} \cdot \sqrt{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\left(\sqrt{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}} \cdot \sqrt{\sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}
double f(double v) {
        double r49546371 = 1.0;
        double r49546372 = 5.0;
        double r49546373 = v;
        double r49546374 = r49546373 * r49546373;
        double r49546375 = r49546372 * r49546374;
        double r49546376 = r49546371 - r49546375;
        double r49546377 = r49546374 - r49546371;
        double r49546378 = r49546376 / r49546377;
        double r49546379 = acos(r49546378);
        return r49546379;
}
↓
double f(double v) {
        double r49546380 = 1.0;
        double r49546381 = v;
        double r49546382 = r49546381 * r49546381;
        double r49546383 = 5.0;
        double r49546384 = r49546382 * r49546383;
        double r49546385 = r49546380 - r49546384;
        double r49546386 = r49546382 - r49546380;
        double r49546387 = r49546385 / r49546386;
        double r49546388 = acos(r49546387);
        double r49546389 = sqrt(r49546388);
        double r49546390 = sqrt(r49546389);
        double r49546391 = r49546390 * r49546390;
        double r49546392 = r49546391 * r49546389;
        return r49546392;
}

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 add-sqr-sqrt1.5

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

  5. Applied add-sqr-sqrt0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019121 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))