Average Error: 0.5 → 0.5
Time: 18.3s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\log \left(\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
e^{\log \left(\cos^{-1} \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)\right)}
double f(double v) {
        double r5433561 = 1.0;
        double r5433562 = 5.0;
        double r5433563 = v;
        double r5433564 = r5433563 * r5433563;
        double r5433565 = r5433562 * r5433564;
        double r5433566 = r5433561 - r5433565;
        double r5433567 = r5433564 - r5433561;
        double r5433568 = r5433566 / r5433567;
        double r5433569 = acos(r5433568);
        return r5433569;
}
↓
double f(double v) {
        double r5433570 = 1.0;
        double r5433571 = v;
        double r5433572 = r5433571 * r5433571;
        double r5433573 = 5.0;
        double r5433574 = r5433572 * r5433573;
        double r5433575 = r5433570 - r5433574;
        double r5433576 = r5433572 - r5433570;
        double r5433577 = r5433575 / r5433576;
        double r5433578 = acos(r5433577);
        double r5433579 = log(r5433578);
        double r5433580 = exp(r5433579);
        return r5433580;
}

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-exp-log0.5

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

  4. Taylor expanded around -inf 0.5

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

  5. Simplified0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019153 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))