Details

analyze603.0ms

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

sample41.0ms

Algorithm

intervals

Results

8.0ms	169×	body	80	valid
7.0ms	29×	body	2560	valid
6.0ms	31×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	32×	body	80	nan
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	9×	body	80	invalid
0.0ms	3×	body	160	valid

simplify477.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms

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: 33.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5743	1403

prune138.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 6.3b

Counts

95 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b	(- (* b_2 b_2) (* a c))
4.8b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 91

Calls

4 calls:

6.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
4.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4888	1599
1	4888	1599

prune118.0ms

Filtered

79 candidates to 103 candidates (-30.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	104	9	113

Merged error: 6.3b

Counts

113 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4972	3316
1	4972	3316

prune157.0ms

Filtered

102 candidates to 172 candidates (-68.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	171	10	181

Merged error: 6.2b

Counts

181 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))))
10.2b	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
23.9b	(cbrt (- (* b_2 b_2) (* a c)))
23.9b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3--` `flip--`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

8.0ms	(* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))))
8.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))))
28.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))) b_2)
22.0ms	(cbrt (- (* b_2 b_2) (* a c)))
26.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4958	1442
1	4958	1442

prune87.0ms

Filtered

65 candidates to 77 candidates (-18.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	77	10	87

Merged error: 6.2b

Counts

87 → 10

regimes295.0ms

Accuracy

83.2% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 34.0b

bsearch46.0ms

Steps

Iters	Range		Point
7	3.328013945231586e-28	1.831192788137643e-26	3.555555513404012e-28
8	-3.534683422262958e+95	-7.410923708434795e+91	-3.471130737477603e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	38
1	65	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

261.0ms	1033×	body	2560	valid
226.0ms	5200×	body	80	valid
174.0ms	866×	body	1280	valid
74.0ms	472×	body	640	valid
34.0ms	776×	body	80	nan
30.0ms	102×	body	5120	valid
27.0ms	217×	body	320	valid
10.0ms	229×	body	80	invalid
9.0ms	110×	body	160	valid

Details

analyze603.0ms

sample41.0ms

simplify477.0ms

prune11.0ms

localize10.0ms

rewrite29.0ms

series69.0ms

simplify54.0ms

prune138.0ms

localize9.0ms

rewrite38.0ms

series67.0ms

simplify49.0ms

prune118.0ms

localize10.0ms

rewrite37.0ms

series65.0ms

simplify70.0ms

prune157.0ms

localize12.0ms

rewrite26.0ms

series115.0ms

simplify51.0ms

prune87.0ms

regimes295.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling