Details

analyze2.9s

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
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

sample71.0ms

Algorithm

intervals

Results

17.0ms	185×	body	80	valid
16.0ms	31×	body	2560	valid
10.0ms	23×	body	1280	valid
3.0ms	11×	body	320	valid
2.0ms	20×	body	80	nan
2.0ms	5×	body	640	valid
2.0ms	17×	body	80	invalid
0.0ms	1×	body	160	valid

simplify1.6s

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.6s)

Iter	Nodes	Cost
0	1932	24
1	1932	24

prune31.0ms

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: 30.0b

Counts

2 → 1

localize91.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

Algorithm

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:

26.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
14.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
29.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
76.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
45.0ms	(- (* b b) (* (* 4.0 a) c))
40.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify419.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (288.0ms)

Iter	Nodes	Cost
0	4922	1982
1	4922	1982

prune839.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 5.1b

Counts

83 → 9

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

92.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0))
29.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

375.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0))
89.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
46.0ms	(- (* b b) (* (* 4.0 a) c))
94.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify397.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (241.0ms)

Iter	Nodes	Cost
0	5011	2978

prune1.7s

Filtered

81 candidates to 117 candidates (-44.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	116	10	126

Merged error: 5.0b

Counts

126 → 10

localize128.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 a))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b	(- (* b b) (* (* 4.0 a) c))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`cbrt-prod`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv` `distribute-lft-out--`

Counts

4 → 62

Calls

4 calls:

16.0ms	(cbrt (/ 1 a))
69.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
49.0ms	(- (* b b) (* (* 4.0 a) c))
32.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series630.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (/ 1 a))
157.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify508.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (383.0ms)

Iter	Nodes	Cost
0	4925	1277
1	4925	1277

prune1.4s

Filtered

53 candidates to 74 candidates (-39.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	74	10	84

Merged error: 5.0b

Counts

84 → 10

localize111.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (* b b) (* (* 4.0 a) c))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 52

Calls

4 calls:

20.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify215.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	5018	1236

prune794.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	64	10	74

Merged error: 5.0b

Counts

74 → 10

regimes1.2s

Accuracy

88.3% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 34.3b

bsearch521.0ms

Steps

Iters	Range		Point
7	5.077603163681316e+86	3.0675607530650454e+88	1.0076800180697053e+87
8	1.1967310277021378e-191	8.34259427963184e-189	2.43077786380867e-190
6	-5.59945793777678e+90	-4.402997549349525e+89	-4.787296627726359e+90

simplify51.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	112	97
1	112	97

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.0s	1051×	body	2560	valid
1.5s	5147×	body	80	valid
1.2s	883×	body	1280	valid
429.0ms	123×	body	5120	valid
425.0ms	443×	body	640	valid
178.0ms	231×	body	320	valid
139.0ms	641×	body	80	nan
68.0ms	418×	body	80	invalid
56.0ms	122×	body	160	valid

Details

analyze2.9s

sample71.0ms

simplify1.6s

prune31.0ms

localize91.0ms

rewrite99.0ms

series419.0ms

simplify419.0ms

prune839.0ms

localize62.0ms

rewrite185.0ms

series603.0ms

simplify397.0ms

prune1.7s

localize128.0ms

rewrite210.0ms

series630.0ms

simplify508.0ms

prune1.4s

localize111.0ms

rewrite80.0ms

series261.0ms

simplify215.0ms

prune794.0ms

regimes1.2s

bsearch521.0ms

simplify51.0ms

end0.0ms

sample7.2s

Profiling