Average Error: 0.4 → 0.4
Time: 23.7s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(t \cdot \left(\sqrt{2} \cdot \pi\right)\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
\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(\left(t \cdot \left(\sqrt{2} \cdot \pi\right)\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r228698 = 1.0;
        double r228699 = 5.0;
        double r228700 = v;
        double r228701 = r228700 * r228700;
        double r228702 = r228699 * r228701;
        double r228703 = r228698 - r228702;
        double r228704 = atan2(1.0, 0.0);
        double r228705 = t;
        double r228706 = r228704 * r228705;
        double r228707 = 2.0;
        double r228708 = 3.0;
        double r228709 = r228708 * r228701;
        double r228710 = r228698 - r228709;
        double r228711 = r228707 * r228710;
        double r228712 = sqrt(r228711);
        double r228713 = r228706 * r228712;
        double r228714 = r228698 - r228701;
        double r228715 = r228713 * r228714;
        double r228716 = r228703 / r228715;
        return r228716;
}
↓
double f(double v, double t) {
        double r228717 = 1.0;
        double r228718 = 5.0;
        double r228719 = v;
        double r228720 = r228719 * r228719;
        double r228721 = r228718 * r228720;
        double r228722 = r228717 - r228721;
        double r228723 = t;
        double r228724 = 2.0;
        double r228725 = sqrt(r228724);
        double r228726 = atan2(1.0, 0.0);
        double r228727 = r228725 * r228726;
        double r228728 = r228723 * r228727;
        double r228729 = 3.0;
        double r228730 = r228729 * r228720;
        double r228731 = r228717 - r228730;
        double r228732 = sqrt(r228731);
        double r228733 = r228728 * r228732;
        double r228734 = r228717 - r228720;
        double r228735 = r228733 * r228734;
        double r228736 = r228722 / r228735;
        return r228736;
}

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 sqrt-prod0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019304 
(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)))))