Details

analyze468.0ms (12.3%)

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

sample48.0ms (1.3%)

Algorithm

1×

intervals

Results

15.0ms	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

simplify265.0ms (7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (263.0ms)

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: 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)))

rewrite28.0ms (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:

11.0ms	(/ (- (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 (1.7%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
16.0ms	(- (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))

simplify56.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune197.0ms (5.2%)

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

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
3.7b	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
10.5b	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac`
77×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
36×	`associate-/l*`
19×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`div-inv`
3×	`flip3-+` `div-sub` `distribute-frac-neg` `sqrt-prod` `flip-+`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 158

Calls

4 calls:

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

series125.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	3981
1	4977	3981

prune429.0ms (11.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	172	8	180

Merged error: 6.5b

Counts

180 → 8

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 71

Calls

4 calls:

8.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series83.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify73.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune161.0ms (4.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	83	8	91

Merged error: 6.5b

Counts

91 → 8

localize6.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	3	3
Total	8	8

Merged error: 6.5b

Counts

8 → 8

regimes280.0ms (7.4%)

Accuracy

Total 1.0b remaining (16.3%)

Threshold costs 0b (0%)

bsearch75.0ms (2%)

Steps

Iters	Range	Point
7	2.225872940459687e+100	2.9814383966772936e+102	2.425599302719474e+102
6	-1.0676346551229214e-298	-1.1179846591094473e-299	-8.299193755122384e-299
8	-6.217592569728448e+112	-1.141697663647829e+110	-2.0801679587946785e+111

Iters

Range

Point

2.225872940459687e+100

2.9814383966772936e+102

2.425599302719474e+102

-1.0676346551229214e-298

-1.1179846591094473e-299

-8.299193755122384e-299

-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	123	61
1	123	61

end0.0ms (0%)

sample1.3s (33.4%)

Algorithm

1×

intervals

Results

334.0ms	1087×	body	2560	valid
270.0ms	5080×	body	80	valid
223.0ms	898×	body	1280	valid
94.0ms	491×	body	640	valid
41.0ms	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

analyze468.0ms (12.3%)

sample48.0ms (1.3%)

simplify265.0ms (7%)

prune8.0ms (0.2%)

localize11.0ms (0.3%)

rewrite28.0ms (0.7%)

series64.0ms (1.7%)

simplify56.0ms (1.5%)

prune197.0ms (5.2%)

localize13.0ms (0.3%)

rewrite37.0ms (1%)

series125.0ms (3.3%)

simplify66.0ms (1.7%)

prune429.0ms (11.3%)

localize13.0ms (0.3%)

rewrite24.0ms (0.6%)

series83.0ms (2.2%)

simplify73.0ms (1.9%)

prune161.0ms (4.2%)

localize6.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify3.0ms (0.1%)

prune1.0ms (0%)

regimes280.0ms (7.4%)

bsearch75.0ms (2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (33.4%)

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