Details

analyze605.0ms

Algorithm

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

sample44.0ms

Algorithm

intervals

Results

11.0ms	39×	body	2560	valid
9.0ms	165×	body	80	valid
5.0ms	24×	body	1280	valid
3.0ms	19×	body	640	valid
1.0ms	32×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	5×	body	80	invalid
0.0ms	2×	body	160	valid

simplify492.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 34.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

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

Counts

4 → 82

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
15.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5587	1403

prune158.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	11	95

Merged error: 5.1b

Counts

95 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 83

Calls

4 calls:

14.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
9.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5332	1237

prune136.0ms

Filtered

67 candidates to 95 candidates (-41.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	3	6	9
Picked	1	0	1
Done	1	0	1
Total	97	9	106

Merged error: 5.1b

Counts

106 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 160

Calls

4 calls:

17.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4954	3316
1	4954	3316

prune183.0ms

Filtered

101 candidates to 172 candidates (-70.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	170	11	181

Merged error: 5.1b

Counts

181 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 421

Calls

4 calls:

21.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (/ 1 a) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

433 → 433

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4972	11436
1	4972	11436

prune307.0ms

Filtered

172 candidates to 433 candidates (-151.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	432	1	433
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	432	12	444

Merged error: 5.1b

Counts

444 → 12

regimes390.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 34.0b

bsearch46.0ms

Steps

Iters	Range		Point
7	1.1340168675459213e-64	3.1363185241140265e-63	4.4378498285549336e-64
8	-4.4889919297129856e+86	-1.1704797071595471e+83	-4.4313081382407695e+86

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	135	42
1	135	42

end0.0ms

sample1.1s

Algorithm

intervals

Results

259.0ms	1013×	body	2560	valid
249.0ms	5179×	body	80	valid
188.0ms	884×	body	1280	valid
79.0ms	480×	body	640	valid
36.0ms	823×	body	80	nan
35.0ms	112×	body	5120	valid
26.0ms	213×	body	320	valid
13.0ms	276×	body	80	invalid
10.0ms	119×	body	160	valid

Details

analyze605.0ms

sample44.0ms

simplify492.0ms

prune12.0ms

localize11.0ms

rewrite30.0ms

series72.0ms

simplify61.0ms

prune158.0ms

localize10.0ms

rewrite32.0ms

series57.0ms

simplify60.0ms

prune136.0ms

localize10.0ms

rewrite40.0ms

series66.0ms

simplify73.0ms

prune183.0ms

localize11.0ms

rewrite68.0ms

series68.0ms

simplify117.0ms

prune307.0ms

regimes390.0ms

bsearch46.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling