Average Error: 25.7 → 18.8
Time: 24.8s
Precision: binary64
\[\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}} = -inf.0 \lor \neg \left(\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}} \le 1.99476301360708469 \cdot 10^{295}\right):\\ \;\;\;\;2 \cdot \left(\frac{l1}{\frac{{a}^{2}}{p1}} + \left(\frac{l3}{\frac{{b}^{2}}{p3}} + \frac{l2}{\frac{{a}^{2}}{p2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}\\ \end{array}\]
\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}
↓
\begin{array}{l}
\mathbf{if}\;\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}} = -inf.0 \lor \neg \left(\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}} \le 1.99476301360708469 \cdot 10^{295}\right):\\
\;\;\;\;2 \cdot \left(\frac{l1}{\frac{{a}^{2}}{p1}} + \left(\frac{l3}{\frac{{b}^{2}}{p3}} + \frac{l2}{\frac{{a}^{2}}{p2}}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}\\

\end{array}
double code(double l1, double p1, double a, double l2, double p2, double l3, double p3, double b) {
	return ((double) (((double) (((double) (((double) (((double) (2.0 * l1)) * p1)) / ((double) pow(a, 2.0)))) + ((double) (((double) (((double) (2.0 * l2)) * p2)) / ((double) pow(a, 2.0)))))) + ((double) (((double) (((double) (2.0 * l3)) * p3)) / ((double) pow(b, 2.0))))));
}
↓
double code(double l1, double p1, double a, double l2, double p2, double l3, double p3, double b) {
	double VAR;
	if (((((double) (((double) (((double) (((double) (((double) (2.0 * l1)) * p1)) / ((double) pow(a, 2.0)))) + ((double) (((double) (((double) (2.0 * l2)) * p2)) / ((double) pow(a, 2.0)))))) + ((double) (((double) (((double) (2.0 * l3)) * p3)) / ((double) pow(b, 2.0)))))) <= -inf.0) || !(((double) (((double) (((double) (((double) (((double) (2.0 * l1)) * p1)) / ((double) pow(a, 2.0)))) + ((double) (((double) (((double) (2.0 * l2)) * p2)) / ((double) pow(a, 2.0)))))) + ((double) (((double) (((double) (2.0 * l3)) * p3)) / ((double) pow(b, 2.0)))))) <= 1.9947630136070847e+295))) {
		VAR = ((double) (2.0 * ((double) (((double) (l1 / ((double) (((double) pow(a, 2.0)) / p1)))) + ((double) (((double) (l3 / ((double) (((double) pow(b, 2.0)) / p3)))) + ((double) (l2 / ((double) (((double) pow(a, 2.0)) / p2))))))))));
	} else {
		VAR = ((double) (((double) (((double) (((double) (((double) (2.0 * l1)) * p1)) / ((double) pow(a, 2.0)))) + ((double) (((double) (((double) (2.0 * l2)) * p2)) / ((double) pow(a, 2.0)))))) + ((double) (((double) (((double) (2.0 * l3)) * p3)) / ((double) pow(b, 2.0))))));
	}
	return VAR;
}

Error

Bits error versus l1

Bits error versus p1

Bits error versus a

Bits error versus l2

Bits error versus p2

Bits error versus l3

Bits error versus p3

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (+ (+ (/ (* (* 2.0 l1) p1) (pow a 2.0)) (/ (* (* 2.0 l2) p2) (pow a 2.0))) (/ (* (* 2.0 l3) p3) (pow b 2.0))) < -inf.0 or 1.99476301360708469e295 < (+ (+ (/ (* (* 2.0 l1) p1) (pow a 2.0)) (/ (* (* 2.0 l2) p2) (pow a 2.0))) (/ (* (* 2.0 l3) p3) (pow b 2.0)))

    1. Initial program 63.0

      \[\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}\]

    2. Simplified42.0

      \[\leadsto \color{blue}{2 \cdot \left(\frac{l1}{\frac{{a}^{2}}{p1}} + \left(\frac{l3}{\frac{{b}^{2}}{p3}} + \frac{l2}{\frac{{a}^{2}}{p2}}\right)\right)}\]

    if -inf.0 < (+ (+ (/ (* (* 2.0 l1) p1) (pow a 2.0)) (/ (* (* 2.0 l2) p2) (pow a 2.0))) (/ (* (* 2.0 l3) p3) (pow b 2.0))) < 1.99476301360708469e295

    1. Initial program 7.5

      \[\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification18.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}} = -inf.0 \lor \neg \left(\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}} \le 1.99476301360708469 \cdot 10^{295}\right):\\ \;\;\;\;2 \cdot \left(\frac{l1}{\frac{{a}^{2}}{p1}} + \left(\frac{l3}{\frac{{b}^{2}}{p3}} + \frac{l2}{\frac{{a}^{2}}{p2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\left(2 \cdot l1\right) \cdot p1}{{a}^{2}} + \frac{\left(2 \cdot l2\right) \cdot p2}{{a}^{2}}\right) + \frac{\left(2 \cdot l3\right) \cdot p3}{{b}^{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (l1 p1 a l2 p2 l3 p3 b)
  :name "(+ (+ (/ (* (* 2 l1) p1) (pow a 2)) (/ (* (* 2 l2) p2) (pow a 2))) (/ (* (* 2 l3) p3) (pow b 2)))"
  :precision binary64
  (+ (+ (/ (* (* 2.0 l1) p1) (pow a 2.0)) (/ (* (* 2.0 l2) p2) (pow a 2.0))) (/ (* (* 2.0 l3) p3) (pow b 2.0))))