Details

analyze462.0ms (12.6%)

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

sample42.0ms (1.1%)

Algorithm

1×

intervals

Results

10.0ms	181×	body	80	valid
7.0ms	28×	body	1280	valid
7.0ms	23×	body	2560	valid
3.0ms	16×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	25×	body	80	nan
1.0ms	17×	body	80	invalid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify200.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (198.0ms)

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: 31.1b

Counts

2 → 1

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms (0.7%)

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:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series64.0ms (1.8%)

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

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune187.0ms (5.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.5b

Counts

83 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms (0.8%)

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:

11.0ms	(/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series85.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(- (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)))

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5012	1600

prune191.0ms (5.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	91	10	101

Merged error: 6.4b

Counts

101 → 10

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
20.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms (0.8%)

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×	`add-exp-log` `sqrt-prod` `add-log-exp`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 85

Calls

4 calls:

10.0ms	(/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series56.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
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)))

simplify40.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4954	1625
1	4954	1625

prune202.0ms (5.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	99	8	107

Merged error: 6.4b

Counts

107 → 8

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(* (* a (/ -1/2 b)) 2.0)
0.2b	(* a (/ -1/2 b))
0.5b	(/ 1 (* (* a (/ -1/2 b)) 2.0))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log`
31×	`add-cbrt-cube`
22×	`prod-exp`
19×	`add-sqr-sqrt`
16×	`pow1` `associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`times-frac` `div-exp`
12×	`cbrt-unprod`
7×	`cbrt-undiv` `pow-prod-down`
4×	`rec-exp` `1-exp` `associate-l`
3×	`pow-flip` `associate-r/` `associate-/l` `add-log-exp`
2×	`associate-l/` `-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `inv-pow`

Counts

3 → 91

Calls

3 calls:

7.0ms	(/ 1 (* (* a (/ -1/2 b)) 2.0))
6.0ms	(* a (/ -1/2 b))
6.0ms	(* (* a (/ -1/2 b)) 2.0)

series9.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ 1 (* (* a (/ -1/2 b)) 2.0))
3.0ms	(* (* a (/ -1/2 b)) 2.0)
3.0ms	(* a (/ -1/2 b))

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4930	713
1	4930	713

prune138.0ms (3.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	96	12	108

Merged error: 6.4b

Counts

108 → 12

regimes337.0ms (9.2%)

Accuracy

Total 4.6b remaining (45%)

Threshold costs 0b (0%)

bsearch50.0ms (1.4%)

Steps

Iters	Range		Point
9	1.1186246520695868e-45	3.3139379921630177e-38	8.399917751723213e-42
6	-4.8905778942266995e+118	-6.972514559688472e+117	-4.266218223523121e+118

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	40
1	92	40

end0.0ms (0%)

sample1.3s (35%)

Algorithm

1×

intervals

Results

321.0ms	1063×	body	2560	valid
281.0ms	5126×	body	80	valid
212.0ms	869×	body	1280	valid
96.0ms	488×	body	640	valid
48.0ms	129×	body	5120	valid
34.0ms	235×	body	320	valid
33.0ms	646×	body	80	nan
23.0ms	387×	body	80	invalid
9.0ms	90×	body	160	valid

Details

analyze462.0ms (12.6%)

sample42.0ms (1.1%)

simplify200.0ms (5.5%)

prune8.0ms (0.2%)

localize14.0ms (0.4%)

rewrite27.0ms (0.7%)

series64.0ms (1.8%)

simplify40.0ms (1.1%)

prune187.0ms (5.1%)

localize12.0ms (0.3%)

rewrite28.0ms (0.8%)

series85.0ms (2.3%)

simplify52.0ms (1.4%)

prune191.0ms (5.2%)

localize13.0ms (0.4%)

rewrite29.0ms (0.8%)

series56.0ms (1.5%)

simplify40.0ms (1.1%)

prune202.0ms (5.5%)

localize6.0ms (0.2%)

rewrite24.0ms (0.7%)

series9.0ms (0.3%)

simplify57.0ms (1.6%)

prune138.0ms (3.8%)

regimes337.0ms (9.2%)

bsearch50.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (35%)

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