Details

analyze269.0ms (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample44.0ms (1.2%)

Algorithm

1×

intervals

Results

15.0ms	160×	body	160	valid
8.0ms	280×	pre	80	true
6.0ms	44×	body	320	valid
5.0ms	52×	body	80	valid
1.0ms	24×	body	80	nan

simplify202.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 43.8b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
0.1b	(- (* b b) (* 4.0 (* a c)))
0.2b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
38.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms	(- (* b b) (* 4.0 (* a c)))

simplify39.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune207.0ms (5.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	13	83

Merged error: 5.1b

Counts

83 → 13

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune46.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	12	12
Picked	1	1
Done	0	0
Total	13	13

Merged error: 5.1b

Counts

13 → 13

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))
0.2b	(* (/ a b) c)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
15×	`add-sqr-sqrt`
13×	`associate-l`
11×	`cbrt-undiv` `times-frac` `div-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1`
3×	`associate-r`
2×	`associate-*l/` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `associate-/l`

Counts

2 → 62

Calls

2 calls:

9.0ms	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))
6.0ms	(* (/ a b) c)

series10.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(* (/ a b) c)
5.0ms	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))

simplify44.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4991	490
1	4991	490

prune181.0ms (5%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	54	14	68
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	55	26	81

Merged error: 5.0b

Counts

81 → 26

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(* c (/ (sqrt a) (sqrt b)))
0.3b	(* (/ (sqrt a) (sqrt b)) (* c (/ (sqrt a) (sqrt b))))
0.4b	(/ (sqrt a) (sqrt b))
0.4b	(/ (sqrt a) (sqrt b))

rewrite52.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

160×	`sqrt-prod`
148×	`times-frac`
125×	`add-sqr-sqrt`
111×	`add-cube-cbrt` `*-un-lft-identity`
43×	`associate-l`
41×	`associate-r`
34×	`add-exp-log` `add-cbrt-cube`
12×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
11×	`pow1`
8×	`cbrt-undiv` `div-exp`
5×	`unswap-sqr`
4×	`associate-*r/` `pow-prod-down` `div-inv` `add-log-exp`
2×	`sqrt-undiv` `frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 250

Calls

4 calls:

16.0ms	(* (/ (sqrt a) (sqrt b)) (* c (/ (sqrt a) (sqrt b))))
13.0ms	(* c (/ (sqrt a) (sqrt b)))
5.0ms	(/ (sqrt a) (sqrt b))
5.0ms	(/ (sqrt a) (sqrt b))

series40.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (/ (sqrt a) (sqrt b)) (* c (/ (sqrt a) (sqrt b))))
10.0ms	(/ (sqrt a) (sqrt b))
10.0ms	(* c (/ (sqrt a) (sqrt b)))
9.0ms	(/ (sqrt a) (sqrt b))

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	2494
1	4954	2494

prune293.0ms (8.1%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	250	12	262
Fresh	4	20	24
Picked	1	0	1
Done	0	1	1
Total	255	33	288

Merged error: 5.0b

Counts

288 → 33

regimes695.0ms (19.3%)

Accuracy

Total 6.0b remaining (54.1%)

Threshold costs 0b (0%)

bsearch2.0ms (0.1%)

Steps

Iters	Range		Point
0	0.05157698258216537	0.05325266511284204	0.052414823847503705

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	39
1	96	39

end0.0ms (0%)

sample1.2s (34.6%)

Algorithm

1×

intervals

Results

465.0ms	4913×	body	160	valid
253.0ms	8936×	pre	80	true
186.0ms	1329×	body	320	valid
86.0ms	1758×	body	80	valid
50.0ms	936×	body	80	nan

Details

analyze269.0ms (7.5%)

sample44.0ms (1.2%)

simplify202.0ms (5.6%)

prune8.0ms (0.2%)

localize10.0ms (0.3%)

rewrite28.0ms (0.8%)

series64.0ms (1.8%)

simplify39.0ms (1.1%)

prune207.0ms (5.8%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify2.0ms (0.1%)

prune46.0ms (1.3%)

localize7.0ms (0.2%)

rewrite18.0ms (0.5%)

series10.0ms (0.3%)

simplify44.0ms (1.2%)

prune181.0ms (5%)

localize11.0ms (0.3%)

rewrite52.0ms (1.4%)

series40.0ms (1.1%)

simplify75.0ms (2.1%)

prune293.0ms (8.1%)

regimes695.0ms (19.3%)

bsearch2.0ms (0.1%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (34.6%)

Profiling