Details

analyze461.0ms (12%)

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample46.0ms (1.2%)

Algorithm

1×

intervals

Results

13.0ms	43×	body	2560	valid
8.0ms	34×	body	1280	valid
8.0ms	152×	body	80	valid
3.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	15×	body	80	nan
0.0ms	7×	body	80	invalid
0.0ms	3×	body	160	valid

simplify246.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (244.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune9.0ms (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: 36.5b

Counts

2 → 1

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms (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))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series64.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms	(- (* b b) (* 4.0 (* a c)))

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5340	1316

prune190.0ms (5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 6.5b

Counts

83 → 10

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (* b b) (* 4.0 (* a c)))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 52

Calls

4 calls:

6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series45.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (* b b) (* 4.0 (* a c)))

simplify39.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5246	824

prune172.0ms (4.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	64	10	74

Merged error: 6.5b

Counts

74 → 10

localize5.0ms (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

prune24.0ms (0.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Merged error: 6.5b

Counts

10 → 10

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

23.5b	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
24.3b	(cbrt (- (* b b) (* 4.0 (* a c))))
24.3b	(cbrt (- (* b b) (* 4.0 (* a c))))
24.3b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms (0.9%)

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 b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series92.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
18.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5384	2531

prune289.0ms (7.5%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	101	10	111

Merged error: 6.5b

Counts

111 → 10

regimes552.0ms (14.4%)

Accuracy

Total 4.7b remaining (46.3%)

Threshold costs 0b (0%)

bsearch117.0ms (3.1%)

Steps

Iters	Range		Point
8	19632.042828082296	11222340.51519018	477515.78107987816
9	6.191562960307448e-31	3.849886770774018e-24	4.162966466628992e-26
8	1.8735819436265453e-63	7.090452779956445e-59	1.4820993962288012e-59
8	-6.217592569728448e+112	-1.141697663647829e+110	-2.0801679587946785e+111

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	47
1	106	47

end0.0ms (0%)

sample1.3s (32.8%)

Algorithm

1×

intervals

Results

329.0ms	1087×	body	2560	valid
270.0ms	5080×	body	80	valid
221.0ms	898×	body	1280	valid
93.0ms	491×	body	640	valid
39.0ms	108×	body	5120	valid
37.0ms	244×	body	320	valid
31.0ms	637×	body	80	nan
20.0ms	383×	body	80	invalid
9.0ms	92×	body	160	valid

Details

analyze461.0ms (12%)

sample46.0ms (1.2%)

simplify246.0ms (6.4%)

prune9.0ms (0.2%)

localize11.0ms (0.3%)

rewrite31.0ms (0.8%)

series64.0ms (1.7%)

simplify42.0ms (1.1%)

prune190.0ms (5%)

localize14.0ms (0.4%)

rewrite20.0ms (0.5%)

series45.0ms (1.2%)

simplify39.0ms (1%)

prune172.0ms (4.5%)

localize5.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify2.0ms (0.1%)

prune24.0ms (0.6%)

localize15.0ms (0.4%)

rewrite36.0ms (0.9%)

series92.0ms (2.4%)

simplify51.0ms (1.3%)

prune289.0ms (7.5%)

regimes552.0ms (14.4%)

bsearch117.0ms (3.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (32.8%)

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