Average Error: 33.1 → 29.6
Time: 50.1s
Precision: 64
\[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]
↓
\[\sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \left(2 \cdot \ell - \left(-\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right)\right)\right) \cdot \frac{\ell}{Om}\right)}} \cdot \sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \left(2 \cdot \ell - \left(-\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right)\right)\right) \cdot \frac{\ell}{Om}\right)}}\]
\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}
↓
\sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \left(2 \cdot \ell - \left(-\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right)\right)\right) \cdot \frac{\ell}{Om}\right)}} \cdot \sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \left(2 \cdot \ell - \left(-\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right)\right)\right) \cdot \frac{\ell}{Om}\right)}}
double f(double n, double U, double t, double l, double Om, double U_) {
        double r2581556 = 2.0;
        double r2581557 = n;
        double r2581558 = r2581556 * r2581557;
        double r2581559 = U;
        double r2581560 = r2581558 * r2581559;
        double r2581561 = t;
        double r2581562 = l;
        double r2581563 = r2581562 * r2581562;
        double r2581564 = Om;
        double r2581565 = r2581563 / r2581564;
        double r2581566 = r2581556 * r2581565;
        double r2581567 = r2581561 - r2581566;
        double r2581568 = r2581562 / r2581564;
        double r2581569 = pow(r2581568, r2581556);
        double r2581570 = r2581557 * r2581569;
        double r2581571 = U_;
        double r2581572 = r2581559 - r2581571;
        double r2581573 = r2581570 * r2581572;
        double r2581574 = r2581567 - r2581573;
        double r2581575 = r2581560 * r2581574;
        double r2581576 = sqrt(r2581575);
        return r2581576;
}
↓
double f(double n, double U, double t, double l, double Om, double U_) {
        double r2581577 = U;
        double r2581578 = n;
        double r2581579 = r2581577 * r2581578;
        double r2581580 = 2.0;
        double r2581581 = r2581579 * r2581580;
        double r2581582 = t;
        double r2581583 = l;
        double r2581584 = r2581580 * r2581583;
        double r2581585 = U_;
        double r2581586 = r2581577 - r2581585;
        double r2581587 = Om;
        double r2581588 = r2581583 / r2581587;
        double r2581589 = r2581588 * r2581578;
        double r2581590 = r2581586 * r2581589;
        double r2581591 = -r2581590;
        double r2581592 = r2581584 - r2581591;
        double r2581593 = r2581592 * r2581588;
        double r2581594 = r2581582 - r2581593;
        double r2581595 = r2581581 * r2581594;
        double r2581596 = sqrt(r2581595);
        double r2581597 = sqrt(r2581596);
        double r2581598 = r2581597 * r2581597;
        return r2581598;
}

Error

Bits error versus n

Bits error versus U

Bits error versus t

Bits error versus l

Bits error versus Om

Bits error versus U*

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 33.1

    \[\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)}\]

  2. Simplified29.5

    \[\leadsto \color{blue}{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \frac{\ell}{Om} \cdot \left(2 \cdot \ell - \left(-\left(n \cdot \frac{\ell}{Om}\right) \cdot \left(U - U*\right)\right)\right)\right)}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt29.6

    \[\leadsto \color{blue}{\sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \frac{\ell}{Om} \cdot \left(2 \cdot \ell - \left(-\left(n \cdot \frac{\ell}{Om}\right) \cdot \left(U - U*\right)\right)\right)\right)}} \cdot \sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \frac{\ell}{Om} \cdot \left(2 \cdot \ell - \left(-\left(n \cdot \frac{\ell}{Om}\right) \cdot \left(U - U*\right)\right)\right)\right)}}}\]

  5. Final simplification29.6

    \[\leadsto \sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \left(2 \cdot \ell - \left(-\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right)\right)\right) \cdot \frac{\ell}{Om}\right)}} \cdot \sqrt{\sqrt{\left(\left(U \cdot n\right) \cdot 2\right) \cdot \left(t - \left(2 \cdot \ell - \left(-\left(U - U*\right) \cdot \left(\frac{\ell}{Om} \cdot n\right)\right)\right) \cdot \frac{\ell}{Om}\right)}}\]

Reproduce

herbie shell --seed 2019134 
(FPCore (n U t l Om U*)
  :name "Toniolo and Linder, Equation (13)"
  (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))))