Details

analyze480.0ms (11.1%)

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

sample44.0ms (1%)

Algorithm

1×

intervals

Results

11.0ms	29×	body	2560	valid
9.0ms	178×	body	80	valid
6.0ms	25×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	17×	body	80	nan
1.0ms	14×	body	80	invalid
1.0ms	4×	body	320	valid

simplify267.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (265.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 30.0b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (neg 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)))

series64.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
11.0ms	(- (* b b) (* 4.0 (* a c)))

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5946	1448

prune211.0ms (4.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 4.3b

Counts

88 → 11

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.1b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
7.9b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

16.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
13.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series142.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
50.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5232	2497

prune264.0ms (6.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Merged error: 4.2b

Counts

135 → 10

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.8b	(- (* b b) (* 4.0 (* a c)))
2.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.3b	(sqrt (- (* b b) (* 4.0 (* 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 b) (* 4.0 (* a c)))) b))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series96.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
9.0ms	(- (* b b) (* 4.0 (* a c)))

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune202.0ms (4.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 4.2b

Counts

103 → 10

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.1b	(/ (* (* 4.0 (* a c)) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
7.9b	(* (* 4.0 (* a c)) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`add-exp-log`
90×	`add-cbrt-cube`
85×	`prod-exp`
44×	`div-exp`
43×	`cbrt-unprod`
32×	`add-sqr-sqrt`
24×	`associate-r`
23×	`cbrt-undiv` `*-un-lft-identity`
19×	`times-frac`
15×	`add-cube-cbrt`
14×	`pow1`
9×	`rec-exp` `1-exp`
8×	`difference-of-squares`
7×	`sqrt-prod`
6×	`pow-prod-down` `add-log-exp`
4×	`distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 140

Calls

4 calls:

19.0ms	(/ (* (* 4.0 (* a c)) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
17.0ms	(* (* 4.0 (* a c)) (/ 1 (- (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))))

series144.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* 4.0 (* a c)) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
49.0ms	(/ (* (* 4.0 (* a c)) (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))) (* 2.0 a))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4980	2867
1	4980	2867

prune279.0ms (6.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Merged error: 4.2b

Counts

162 → 10

regimes329.0ms (7.6%)

Accuracy

Total 1.2b remaining (18.4%)

Threshold costs 0b (0%)

bsearch72.0ms (1.7%)

Steps

Iters	Range	Point
8	6.935890742706509e+60	2.2816268548923162e+64	1.304608330782827e+64
5	2.7573175966824064e-279	7.936480566151615e-279	7.420373164236022e-279
6	-2.0168463992321823e+147	-1.7280299014924793e+146	-1.9209858444379851e+146

Iters

Range

Point

6.935890742706509e+60

2.2816268548923162e+64

1.304608330782827e+64

2.7573175966824064e-279

7.936480566151615e-279

7.420373164236022e-279

-2.0168463992321823e+147

-1.7280299014924793e+146

-1.9209858444379851e+146

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	122	61
1	122	61

end0.0ms (0%)

sample1.3s (29.9%)

Algorithm

1×

intervals

Results

335.0ms	1083×	body	2560	valid
287.0ms	5145×	body	80	valid
222.0ms	869×	body	1280	valid
92.0ms	445×	body	640	valid
47.0ms	126×	body	5120	valid
37.0ms	732×	body	80	nan
32.0ms	217×	body	320	valid
21.0ms	387×	body	80	invalid
12.0ms	115×	body	160	valid

Details

analyze480.0ms (11.1%)

sample44.0ms (1%)

simplify267.0ms (6.1%)

prune7.0ms (0.2%)

localize12.0ms (0.3%)

rewrite31.0ms (0.7%)

series64.0ms (1.5%)

simplify45.0ms (1%)

prune211.0ms (4.9%)

localize12.0ms (0.3%)

rewrite46.0ms (1.1%)

series142.0ms (3.3%)

simplify38.0ms (0.9%)

prune264.0ms (6.1%)

localize13.0ms (0.3%)

rewrite31.0ms (0.7%)

series96.0ms (2.2%)

simplify72.0ms (1.6%)

prune202.0ms (4.6%)

localize16.0ms (0.4%)

rewrite55.0ms (1.3%)

series144.0ms (3.3%)

simplify70.0ms (1.6%)

prune279.0ms (6.4%)

regimes329.0ms (7.6%)

bsearch72.0ms (1.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (29.9%)

Profiling