Details

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample57.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
9.0ms	120×	body	80	nan
4.0ms	46×	body	80	invalid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	18

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 10.8b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

2.1b	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
4.2b	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
5.0b	(* M (/ D (* 2.0 d)))
8.2b	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
34×	`add-sqr-sqrt`
26×	`associate-r`
25×	`prod-exp`
20×	`add-cbrt-cube`
19×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`div-exp`
11×	`associate-l`
9×	`pow1`
8×	`pow-exp`
7×	`sqrt-prod` `cbrt-unprod` `unswap-sqr`
4×	`sqrt-div` `associate-*r/` `add-log-exp`
3×	`cbrt-undiv` `*-commutative` `sqr-pow`
2×	`pow-to-exp` `flip3--` `pow-prod-down` `flip--` `div-inv`
1×	`unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 111

Calls

4 calls:

7.0ms	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
4.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
7.0ms	(* M (/ D (* 2.0 d)))
8.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

series544.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
147.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
7.0ms	(* M (/ D (* 2.0 d)))
209.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

simplify33.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5600	1864

prune250.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Merged error: 7.1b

Counts

125 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

3.9b	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
4.2b	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
4.9b	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
5.0b	(* M (/ D (* 2.0 d)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
24×	`prod-exp`
20×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`div-exp`
12×	`add-cube-cbrt` `associate-r`
8×	`pow-exp`
7×	`pow1`
6×	`times-frac` `associate-l` `cbrt-unprod`
5×	`sqrt-prod`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-/r*` `unswap-sqr`
2×	`pow-to-exp` `sqrt-div` `*-commutative` `div-inv` `sqr-pow`
1×	`unpow-prod-down` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

5.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
6.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
6.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
7.0ms	(* M (/ D (* 2.0 d)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
121.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
172.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
6.0ms	(* M (/ D (* 2.0 d)))

simplify29.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5084	1475

prune210.0ms

Filtered

73 candidates to 107 candidates (-46.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 6.6b

Counts

115 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
4.9b	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
5.0b	(* M (/ D (* 2.0 d)))
5.0b	(* M (/ D (* 2.0 d)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

251×	`add-exp-log`
138×	`prod-exp`
73×	`div-exp`
52×	`pow-exp`
31×	`add-cbrt-cube`
20×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`associate-r`
13×	`pow-to-exp` `add-cube-cbrt`
11×	`cbrt-unprod`
9×	`pow1` `times-frac`
7×	`cbrt-undiv`
6×	`associate-l`
5×	`sqrt-prod`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`sqrt-div` `associate-r/` `pow-prod-down` `-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 134

Calls

4 calls:

8.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
12.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
7.0ms	(* M (/ D (* 2.0 d)))
7.0ms	(* M (/ D (* 2.0 d)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
171.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))

simplify74.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4975	2192
1	4975	2192

prune237.0ms

Filtered

74 candidates to 146 candidates (-97.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	146	8	154

Merged error: 6.6b

Counts

154 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))))
4.5b	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
5.0b	(* M (/ D (* 2.0 d)))
5.0b	(* M (/ D (* 2.0 d)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
26×	`add-sqr-sqrt`
24×	`add-cbrt-cube`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
12×	`div-exp` `prod-exp`
9×	`pow1`
8×	`cbrt-unprod`
6×	`associate-l`
5×	`cbrt-undiv` `associate-/l*`
4×	`unpow-prod-down` `pow-exp` `add-log-exp` `sqr-pow`
3×	`associate-/r*` `sqrt-prod` `div-inv`
2×	`sqrt-div` `associate-r/` `pow-prod-down` `-commutative` `unswap-sqr`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 109

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))))
5.0ms	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
7.0ms	(* M (/ D (* 2.0 d)))
7.0ms	(* M (/ D (* 2.0 d)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (- 1.0 (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))))
173.0ms	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))

simplify48.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4997	1729
1	4997	1729

prune236.0ms

Filtered

86 candidates to 121 candidates (-40.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	121	8	129

Merged error: 6.6b

Counts

129 → 8

regimes1.0s

Accuracy

21.8% (1.1b remaining)

Error of 8.6b against oracle of 7.5b and baseline of 8.9b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	115	80
1	115	80

end0.0ms

sample1.4s

Algorithm

intervals

Results

610.0ms	8000×	body	80	valid
246.0ms	3098×	body	80	nan
114.0ms	1391×	body	80	invalid

Details

analyze2.2s

sample57.0ms

simplify45.0ms

prune17.0ms

localize14.0ms

rewrite30.0ms

series544.0ms

simplify33.0ms

prune250.0ms

localize14.0ms

rewrite28.0ms

series391.0ms

simplify29.0ms

prune210.0ms

localize17.0ms

rewrite42.0ms

series305.0ms

simplify74.0ms

prune237.0ms

localize17.0ms

rewrite28.0ms

series307.0ms

simplify48.0ms

prune236.0ms

regimes1.0s

bsearch2.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling