Average Error: 0.4 → 0.3
Time: 19.0s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\left(1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + v \cdot v\right)\right) \cdot \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\left(1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + v \cdot v\right)\right) \cdot \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)}
double f(double v, double t) {
        double r3310802 = 1.0;
        double r3310803 = 5.0;
        double r3310804 = v;
        double r3310805 = r3310804 * r3310804;
        double r3310806 = r3310803 * r3310805;
        double r3310807 = r3310802 - r3310806;
        double r3310808 = atan2(1.0, 0.0);
        double r3310809 = t;
        double r3310810 = r3310808 * r3310809;
        double r3310811 = 2.0;
        double r3310812 = 3.0;
        double r3310813 = r3310812 * r3310805;
        double r3310814 = r3310802 - r3310813;
        double r3310815 = r3310811 * r3310814;
        double r3310816 = sqrt(r3310815);
        double r3310817 = r3310810 * r3310816;
        double r3310818 = r3310802 - r3310805;
        double r3310819 = r3310817 * r3310818;
        double r3310820 = r3310807 / r3310819;
        return r3310820;
}
↓
double f(double v, double t) {
        double r3310821 = 1.0;
        double r3310822 = v;
        double r3310823 = r3310822 * r3310822;
        double r3310824 = r3310823 * r3310823;
        double r3310825 = r3310824 + r3310823;
        double r3310826 = r3310821 + r3310825;
        double r3310827 = 5.0;
        double r3310828 = r3310823 * r3310827;
        double r3310829 = r3310821 - r3310828;
        double r3310830 = atan2(1.0, 0.0);
        double r3310831 = r3310829 / r3310830;
        double r3310832 = t;
        double r3310833 = r3310831 / r3310832;
        double r3310834 = 2.0;
        double r3310835 = 3.0;
        double r3310836 = r3310835 * r3310823;
        double r3310837 = r3310821 - r3310836;
        double r3310838 = r3310834 * r3310837;
        double r3310839 = sqrt(r3310838);
        double r3310840 = r3310833 / r3310839;
        double r3310841 = r3310824 * r3310823;
        double r3310842 = r3310821 - r3310841;
        double r3310843 = r3310840 / r3310842;
        double r3310844 = r3310826 * r3310843;
        return r3310844;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
  2. Using strategy rm

  3. Applied flip3--0.4

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

  4. Applied associate-*r/0.4

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

  5. Applied associate-/r/0.4

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

  6. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi \cdot t}}{\sqrt{2 \cdot \left(1 - \left(v \cdot v\right) \cdot 3\right)}}}{1 - \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)}} \cdot \left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)\right)\]
  7. Using strategy rm

  8. Applied associate-/r*0.3

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

  9. Final simplification0.3

    \[\leadsto \left(1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + v \cdot v\right)\right) \cdot \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot v\right)}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))