Average Error: 0.5 → 0.5
Time: 15.2s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\left(\sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot 5\right) \cdot v}{{v}^{2} - 1}\right)}} \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot 5\right) \cdot v}{{v}^{2} - 1}\right)}}\right) \cdot \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{{v}^{2} - 1}\right)}} \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{{v}^{2} - 1}\right)}}\right)\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\left(\sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot 5\right) \cdot v}{{v}^{2} - 1}\right)}} \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot 5\right) \cdot v}{{v}^{2} - 1}\right)}}\right) \cdot \left(\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)} \cdot \left(\sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{{v}^{2} - 1}\right)}} \cdot \sqrt{\sqrt[3]{\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{{v}^{2} - 1}\right)}}\right)\right)
double f(double v) {
        double r128388 = 1.0;
        double r128389 = 5.0;
        double r128390 = v;
        double r128391 = r128390 * r128390;
        double r128392 = r128389 * r128391;
        double r128393 = r128388 - r128392;
        double r128394 = r128391 - r128388;
        double r128395 = r128393 / r128394;
        double r128396 = acos(r128395);
        return r128396;
}
↓
double f(double v) {
        double r128397 = 1.0;
        double r128398 = v;
        double r128399 = 5.0;
        double r128400 = r128398 * r128399;
        double r128401 = r128400 * r128398;
        double r128402 = r128397 - r128401;
        double r128403 = 2.0;
        double r128404 = pow(r128398, r128403);
        double r128405 = r128404 - r128397;
        double r128406 = r128402 / r128405;
        double r128407 = acos(r128406);
        double r128408 = cbrt(r128407);
        double r128409 = sqrt(r128408);
        double r128410 = r128409 * r128409;
        double r128411 = r128398 * r128398;
        double r128412 = r128411 * r128399;
        double r128413 = r128397 - r128412;
        double r128414 = r128411 - r128397;
        double r128415 = r128413 / r128414;
        double r128416 = acos(r128415);
        double r128417 = cbrt(r128416);
        double r128418 = r128413 / r128405;
        double r128419 = acos(r128418);
        double r128420 = cbrt(r128419);
        double r128421 = sqrt(r128420);
        double r128422 = r128421 * r128421;
        double r128423 = r128417 * r128422;
        double r128424 = r128410 * r128423;
        return r128424;
}

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. Simplified0.5

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

  4. Applied add-cube-cbrt2.0

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

  5. Simplified2.0

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

  6. Simplified2.0

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

  8. Applied add-sqr-sqrt1.5

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

  9. Simplified1.5

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

  10. Simplified1.5

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

  12. Applied add-sqr-sqrt0.5

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

  13. Simplified0.5

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

  14. Simplified0.5

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

  15. Final simplification0.5

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

Reproduce

herbie shell --seed 2019196 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))