Average Error: 0.4 → 0.3
Time: 30.7s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi}}{t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
\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 - 5 \cdot \left(v \cdot v\right)}{\pi}}{t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r146572 = 1.0;
        double r146573 = 5.0;
        double r146574 = v;
        double r146575 = r146574 * r146574;
        double r146576 = r146573 * r146575;
        double r146577 = r146572 - r146576;
        double r146578 = atan2(1.0, 0.0);
        double r146579 = t;
        double r146580 = r146578 * r146579;
        double r146581 = 2.0;
        double r146582 = 3.0;
        double r146583 = r146582 * r146575;
        double r146584 = r146572 - r146583;
        double r146585 = r146581 * r146584;
        double r146586 = sqrt(r146585);
        double r146587 = r146580 * r146586;
        double r146588 = r146572 - r146575;
        double r146589 = r146587 * r146588;
        double r146590 = r146577 / r146589;
        return r146590;
}
↓
double f(double v, double t) {
        double r146591 = 1.0;
        double r146592 = 5.0;
        double r146593 = v;
        double r146594 = r146593 * r146593;
        double r146595 = r146592 * r146594;
        double r146596 = r146591 - r146595;
        double r146597 = atan2(1.0, 0.0);
        double r146598 = r146596 / r146597;
        double r146599 = t;
        double r146600 = 2.0;
        double r146601 = 3.0;
        double r146602 = r146601 * r146594;
        double r146603 = r146591 - r146602;
        double r146604 = r146600 * r146603;
        double r146605 = sqrt(r146604);
        double r146606 = r146599 * r146605;
        double r146607 = r146598 / r146606;
        double r146608 = r146591 - r146594;
        double r146609 = r146607 / r146608;
        return r146609;
}

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 associate-/r*0.4

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

  5. Applied associate-*l*0.4

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

  7. Applied associate-/r*0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))