Details

analyze610.0ms (14.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample42.0ms (1%)

Algorithm

1×

intervals

Results

10.0ms	37×	body	2560	valid
7.0ms	161×	body	80	valid
5.0ms	23×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	32×	body	80	nan
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid
0.0ms	3×	body	80	invalid

simplify508.0ms (12.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune9.0ms (0.2%)

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: 36.2b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 89

Calls

4 calls:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series61.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune168.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Merged error: 6.3b

Counts

102 → 7

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
5.2b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

15.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series118.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
44.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4961	2488
1	4961	2488

prune178.0ms (4.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Merged error: 6.2b

Counts

142 → 8

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

12.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms (2%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune137.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 6.2b

Counts

101 → 9

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

22.6b	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
23.3b	(cbrt (- (* b_2 b_2) (* a c)))
23.3b	(cbrt (- (* b_2 b_2) (* a c)))
23.3b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

17.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series87.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (- (* b_2 b_2) (* a c)))
23.0ms	(cbrt (- (* b_2 b_2) (* a c)))
23.0ms	(cbrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (* (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c)))) (cbrt (- (* b_2 b_2) (* a c)))))

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4898	2055
1	4898	2055

prune189.0ms (4.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	101	9	110

Merged error: 6.2b

Counts

110 → 9

regimes321.0ms (7.7%)

Accuracy

Total 1.3b remaining (18.6%)

Threshold costs 0b (0%)

bsearch75.0ms (1.8%)

Steps

Iters	Range	Point
6	7.621631647479164e+54	1.1620003065684158e+56	8.146902378104984e+55
9	-7.69721194200277e-282	-3.897062007467286e-287	-3.9422997567625006e-287
7	-6.383117637049118e+125	-1.5564611129376612e+124	-5.882030433389928e+125

Iters

Range

Point

7.621631647479164e+54

1.1620003065684158e+56

8.146902378104984e+55

-7.69721194200277e-282

-3.897062007467286e-287

-3.9422997567625006e-287

-6.383117637049118e+125

-1.5564611129376612e+124

-5.882030433389928e+125

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	145	54
1	145	54

end0.0ms (0%)

sample1.1s (26.7%)

Algorithm

1×

intervals

Results

281.0ms	1114×	body	2560	valid
228.0ms	5045×	body	80	valid
195.0ms	903×	body	1280	valid
77.0ms	479×	body	640	valid
34.0ms	831×	body	80	nan
33.0ms	108×	body	5120	valid
30.0ms	242×	body	320	valid
13.0ms	308×	body	80	invalid
9.0ms	109×	body	160	valid

Details

analyze610.0ms (14.7%)

sample42.0ms (1%)

simplify508.0ms (12.2%)

prune9.0ms (0.2%)

localize12.0ms (0.3%)

rewrite51.0ms (1.2%)

series61.0ms (1.5%)

simplify62.0ms (1.5%)

prune168.0ms (4.1%)

localize10.0ms (0.2%)

rewrite38.0ms (0.9%)

series118.0ms (2.8%)

simplify66.0ms (1.6%)

prune178.0ms (4.3%)

localize10.0ms (0.2%)

rewrite31.0ms (0.7%)

series82.0ms (2%)

simplify63.0ms (1.5%)

prune137.0ms (3.3%)

localize15.0ms (0.4%)

rewrite34.0ms (0.8%)

series87.0ms (2.1%)

simplify65.0ms (1.6%)

prune189.0ms (4.5%)

regimes321.0ms (7.7%)

bsearch75.0ms (1.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (26.7%)

Profiling