Average Error: 1.7 → 1.7
Time: 10.3s
Precision: 64
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]
↓
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]
\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}
↓
\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}
double f(double l, double Om, double kx, double ky) {
        double r19598 = 1.0;
        double r19599 = 2.0;
        double r19600 = r19598 / r19599;
        double r19601 = l;
        double r19602 = r19599 * r19601;
        double r19603 = Om;
        double r19604 = r19602 / r19603;
        double r19605 = pow(r19604, r19599);
        double r19606 = kx;
        double r19607 = sin(r19606);
        double r19608 = pow(r19607, r19599);
        double r19609 = ky;
        double r19610 = sin(r19609);
        double r19611 = pow(r19610, r19599);
        double r19612 = r19608 + r19611;
        double r19613 = r19605 * r19612;
        double r19614 = r19598 + r19613;
        double r19615 = sqrt(r19614);
        double r19616 = r19598 / r19615;
        double r19617 = r19598 + r19616;
        double r19618 = r19600 * r19617;
        double r19619 = sqrt(r19618);
        return r19619;
}
↓
double f(double l, double Om, double kx, double ky) {
        double r19620 = 1.0;
        double r19621 = 2.0;
        double r19622 = r19620 / r19621;
        double r19623 = l;
        double r19624 = r19621 * r19623;
        double r19625 = Om;
        double r19626 = r19624 / r19625;
        double r19627 = pow(r19626, r19621);
        double r19628 = kx;
        double r19629 = sin(r19628);
        double r19630 = pow(r19629, r19621);
        double r19631 = ky;
        double r19632 = sin(r19631);
        double r19633 = pow(r19632, r19621);
        double r19634 = r19630 + r19633;
        double r19635 = r19627 * r19634;
        double r19636 = r19620 + r19635;
        double r19637 = sqrt(r19636);
        double r19638 = r19620 / r19637;
        double r19639 = r19620 + r19638;
        double r19640 = r19622 * r19639;
        double r19641 = sqrt(r19640);
        return r19641;
}

Error

Bits error versus l

Bits error versus Om

Bits error versus kx

Bits error versus ky

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.7

    \[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]

  2. Final simplification1.7

    \[\leadsto \sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (l Om kx ky)
  :name "Toniolo and Linder, Equation (3a)"
  (sqrt (* (/ 1.0 2.0) (+ 1.0 (/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))))