Average Error: 0.5 → 0.5
Time: 9.8s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\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)}
↓
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r246547 = 1.0;
        double r246548 = 5.0;
        double r246549 = v;
        double r246550 = r246549 * r246549;
        double r246551 = r246548 * r246550;
        double r246552 = r246547 - r246551;
        double r246553 = atan2(1.0, 0.0);
        double r246554 = t;
        double r246555 = r246553 * r246554;
        double r246556 = 2.0;
        double r246557 = 3.0;
        double r246558 = r246557 * r246550;
        double r246559 = r246547 - r246558;
        double r246560 = r246556 * r246559;
        double r246561 = sqrt(r246560);
        double r246562 = r246555 * r246561;
        double r246563 = r246547 - r246550;
        double r246564 = r246562 * r246563;
        double r246565 = r246552 / r246564;
        return r246565;
}
↓
double f(double v, double t) {
        double r246566 = 1.0;
        double r246567 = 5.0;
        double r246568 = v;
        double r246569 = r246568 * r246568;
        double r246570 = r246567 * r246569;
        double r246571 = r246566 - r246570;
        double r246572 = atan2(1.0, 0.0);
        double r246573 = t;
        double r246574 = 2.0;
        double r246575 = 3.0;
        double r246576 = r246575 * r246569;
        double r246577 = r246566 - r246576;
        double r246578 = r246574 * r246577;
        double r246579 = sqrt(r246578);
        double r246580 = r246573 * r246579;
        double r246581 = r246572 * r246580;
        double r246582 = r246566 - r246569;
        double r246583 = r246581 * r246582;
        double r246584 = r246571 / r246583;
        return r246584;
}

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. Using strategy rm

  3. Applied associate-*l*0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020001 
(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)))))