Average Error: 0.5 → 0.6
Time: 19.4s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\left(\sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}} \cdot \sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\left(\sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}} \cdot \sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}
double f(double v) {
        double r143371 = 1.0;
        double r143372 = 5.0;
        double r143373 = v;
        double r143374 = r143373 * r143373;
        double r143375 = r143372 * r143374;
        double r143376 = r143371 - r143375;
        double r143377 = r143374 - r143371;
        double r143378 = r143376 / r143377;
        double r143379 = acos(r143378);
        return r143379;
}
↓
double f(double v) {
        double r143380 = 1.0;
        double r143381 = 5.0;
        double r143382 = v;
        double r143383 = r143382 * r143382;
        double r143384 = r143381 * r143383;
        double r143385 = r143380 - r143384;
        double r143386 = r143383 - r143380;
        double r143387 = r143385 / r143386;
        double r143388 = acos(r143387);
        double r143389 = sqrt(r143388);
        double r143390 = 3.0;
        double r143391 = 2.0;
        double r143392 = r143390 / r143391;
        double r143393 = pow(r143389, r143392);
        double r143394 = cbrt(r143393);
        double r143395 = r143394 * r143394;
        double r143396 = r143395 * r143389;
        return r143396;
}

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-cbrt-cube1.5

    \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}}} \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]

  6. Simplified1.5

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{3}}} \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]
  7. Using strategy rm

  8. Applied sqr-pow1.5

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}}} \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]

  9. Applied cbrt-prod0.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}} \cdot \sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}}\right)} \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]

  10. Final simplification0.6

    \[\leadsto \left(\sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}} \cdot \sqrt[3]{{\left(\sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\right)}^{\left(\frac{3}{2}\right)}}\right) \cdot \sqrt{\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))