Average Error: 0.5 → 0.1
Time: 50.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\left(1 - v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}{t}\]
\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)}
↓
\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\left(1 - v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}{t}
double f(double v, double t) {
        double r6648802 = 1.0;
        double r6648803 = 5.0;
        double r6648804 = v;
        double r6648805 = r6648804 * r6648804;
        double r6648806 = r6648803 * r6648805;
        double r6648807 = r6648802 - r6648806;
        double r6648808 = atan2(1.0, 0.0);
        double r6648809 = t;
        double r6648810 = r6648808 * r6648809;
        double r6648811 = 2.0;
        double r6648812 = 3.0;
        double r6648813 = r6648812 * r6648805;
        double r6648814 = r6648802 - r6648813;
        double r6648815 = r6648811 * r6648814;
        double r6648816 = sqrt(r6648815);
        double r6648817 = r6648810 * r6648816;
        double r6648818 = r6648802 - r6648805;
        double r6648819 = r6648817 * r6648818;
        double r6648820 = r6648807 / r6648819;
        return r6648820;
}
↓
double f(double v, double t) {
        double r6648821 = 1.0;
        double r6648822 = v;
        double r6648823 = r6648822 * r6648822;
        double r6648824 = 5.0;
        double r6648825 = r6648823 * r6648824;
        double r6648826 = r6648821 - r6648825;
        double r6648827 = r6648821 - r6648823;
        double r6648828 = atan2(1.0, 0.0);
        double r6648829 = r6648827 * r6648828;
        double r6648830 = r6648826 / r6648829;
        double r6648831 = -6.0;
        double r6648832 = r6648831 * r6648823;
        double r6648833 = 2.0;
        double r6648834 = r6648832 + r6648833;
        double r6648835 = sqrt(r6648834);
        double r6648836 = r6648830 / r6648835;
        double r6648837 = t;
        double r6648838 = r6648836 / r6648837;
        return r6648838;
}

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 0.5

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\color{blue}{1 \cdot \pi}}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

  5. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\color{blue}{1 \cdot \left(1 - v \cdot v\right)}}}{1 \cdot \pi}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

  6. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\frac{\frac{\color{blue}{1 \cdot \left(1 - \left(v \cdot v\right) \cdot 5\right)}}{1 \cdot \left(1 - v \cdot v\right)}}{1 \cdot \pi}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

  7. Applied times-frac0.3

    \[\leadsto \frac{\frac{\color{blue}{\frac{1}{1} \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}}{1 \cdot \pi}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

  8. Applied times-frac0.3

    \[\leadsto \frac{\color{blue}{\frac{\frac{1}{1}}{1} \cdot \frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}}{t \cdot \sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

  9. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1}{1}}{1}}{t} \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}\]

  10. Simplified0.3

    \[\leadsto \color{blue}{\frac{1}{t}} \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]
  11. Using strategy rm

  12. Applied associate-*l/0.1

    \[\leadsto \color{blue}{\frac{1 \cdot \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}{t}}\]

  13. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 + -6 \cdot \left(v \cdot v\right)}}}}{t}\]

  14. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\left(1 - v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}}{t}\]

Reproduce

herbie shell --seed 2019146 
(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)))))