Details

analyze2.6s (12.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

sample108.0ms (0.5%)

Algorithm

1×

intervals

Results

45.0ms	432×	body	80	nan
26.0ms	256×	body	80	valid
5.0ms	52×	body	80	invalid

simplify40.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5186	28

prune17.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.1b

Counts

2 → 2

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
7.4b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
8.4b	(/ (* l l) Om)
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`pow1`
23×	`add-cbrt-cube`
22×	`associate-*r/`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`add-sqr-sqrt` `*-un-lft-identity` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`sqrt-pow1` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-l` `pow-exp` `associate--l+` `*-commutative`
1×	`pow-to-exp` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 97

Calls

4 calls:

13.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
13.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0ms	(/ (* l l) Om)

series2.5s (12.2%)

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
373.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
131.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
3.0ms	(/ (* l l) Om)

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5140	2554

prune356.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	96	13	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 19.3b

Counts

111 → 13

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b	(* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U)))))
7.3b	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U))))) (cbrt (- U U*)))))
8.4b	(/ (* l l) Om)
20.1b	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U))))) (cbrt (- U U*))))))

rewrite97.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

350×	`associate-*r/`
228×	`cbrt-div`
168×	`flip3--` `flip--`
116×	`frac-times`
104×	`frac-sub`
58×	`associate-*l/`
54×	`sqrt-div`
48×	`add-exp-log`
28×	`prod-exp`
25×	`pow1` `add-cbrt-cube`
13×	`pow-prod-down` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`sub-neg` `sqrt-pow1` `div-exp` `associate-r` `associate-l` `pow-exp` `add-log-exp`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `associate--l+` `*-commutative`
1×	`frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `div-inv` `associate-/l*`

Counts

4 → 200

Calls

4 calls:

25.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U))))) (cbrt (- U U*)))))
24.0ms	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U))))) (cbrt (- U U*))))))
18.0ms	(* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U)))))
4.0ms	(/ (* l l) Om)

series2.4s (12%)

Counts

4 → 12

Calls

4 calls:

2.0s	(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U))))) (cbrt (- U U*))))))
371.0ms	(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U))))) (cbrt (- U U*)))))
102.0ms	(* n (* (pow (/ l Om) 2.0) (* (cbrt (- U U)) (cbrt (- U U)))))
3.0ms	(/ (* l l) Om)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5216	12980

prune887.0ms (4.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	210	15	225

Merged error: 19.2b

Counts

225 → 15

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(* (pow (/ l Om) 2.0) (- U U*))
6.8b	(* n (* (pow (/ l Om) 2.0) (- U U*)))
7.6b	(* (* 2.0 n) (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
20.1b	(sqrt (* (* 2.0 n) (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-exp-log`
31×	`pow1`
24×	`add-sqr-sqrt`
23×	`add-cbrt-cube`
21×	`associate-l` `prod-exp`
17×	`pow-prod-down`
16×	`*-un-lft-identity`
15×	`unpow-prod-down`
14×	`add-cube-cbrt` `associate-*r/`
12×	`cbrt-unprod`
10×	`sub-neg` `times-frac`
9×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-r`
5×	`sqrt-pow1`
4×	`flip3--` `pow-exp` `flip--` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow-to-exp` `sqrt-div` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 113

Calls

4 calls:

14.0ms	(* (* 2.0 n) (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
12.0ms	(sqrt (* (* 2.0 n) (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
11.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
11.0ms	(* (pow (/ l Om) 2.0) (- U U*))

series2.6s (12.6%)

Counts

4 → 12

Calls

4 calls:

1.9s	(sqrt (* (* 2.0 n) (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*))))))))
357.0ms	(* (* 2.0 n) (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))
132.0ms	(* n (* (pow (/ l Om) 2.0) (- U U*)))
126.0ms	(* (pow (/ l Om) 2.0) (- U U*))

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4980	2456
1	4980	2456

prune391.0ms (1.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	123	17	140

Merged error: 17.9b

Counts

140 → 17

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

20.1b	(sqrt (* (* (cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U))))))))) (cbrt ( 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U)))))))))) (cbrt ( 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))))
21.9b	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))
21.9b	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))
21.9b	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

188×	`associate-*r/`
60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`pow-prod-up`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 83

Calls

4 calls:

13.0ms	(sqrt (* (* (cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U))))))))) (cbrt ( 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U)))))))))) (cbrt ( 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))))
13.0ms	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))
13.0ms	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))
12.0ms	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))

series3.0s (14.6%)

Counts

4 → 12

Calls

4 calls:

1.6s	(sqrt (* (* (cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U))))))))) (cbrt ( 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U)))))))))) (cbrt ( 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))))
459.0ms	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))
458.0ms	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))
458.0ms	(cbrt (* 2.0 (* n (* U (- t (+ (* 2.0 (* (/ l Om) l)) (* n (* (pow (/ l Om) 2.0) (- U U*)))))))))

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5371	6280

prune523.0ms (2.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	95	17	112

Merged error: 17.9b

Counts

112 → 17

regimes1.1s (5.4%)

Accuracy

Total 12.1b remaining (39.1%)

Threshold costs 0b (0%)

bsearch209.0ms (1%)

Steps

Iters	Range	Point
7	1.7611260343986184e+72	1.7841436293156583e+74	7.158335102890174e+73
7	1.3516915780628772e-196	2.335818691228601e-194	1.3152323392947841e-194
8	-5.122315113553601e-302	-9.052826171263548e-307	-9.27291794463707e-307

Iters

Range

Point

1.7611260343986184e+72

1.7841436293156583e+74

7.158335102890174e+73

1.3516915780628772e-196

2.335818691228601e-194

1.3152323392947841e-194

-5.122315113553601e-302

-9.052826171263548e-307

-9.27291794463707e-307

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	684	81
1	684	81

end0.0ms (0%)

sample3.0s (14.7%)

Algorithm

1×

intervals

Results

1.3s	12833×	body	80	nan
801.0ms	8000×	body	80	valid
129.0ms	1244×	body	80	invalid

Details

analyze2.6s (12.9%)

sample108.0ms (0.5%)

simplify40.0ms (0.2%)

prune17.0ms (0.1%)

localize20.0ms (0.1%)

rewrite45.0ms (0.2%)

series2.5s (12.2%)

simplify44.0ms (0.2%)

prune356.0ms (1.8%)

localize27.0ms (0.1%)

rewrite97.0ms (0.5%)

series2.4s (12%)

simplify91.0ms (0.4%)

prune887.0ms (4.4%)

localize21.0ms (0.1%)

rewrite52.0ms (0.3%)

series2.6s (12.6%)

simplify67.0ms (0.3%)

prune391.0ms (1.9%)

localize29.0ms (0.1%)

rewrite58.0ms (0.3%)

series3.0s (14.6%)

simplify56.0ms (0.3%)

prune523.0ms (2.6%)

regimes1.1s (5.4%)

bsearch209.0ms (1%)

simplify20.0ms (0.1%)

end0.0ms (0%)

sample3.0s (14.7%)

Profiling