Details

analyze2.3s

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

sample49.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
6.0ms	82×	body	80	nan
4.0ms	45×	body	80	invalid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

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: 13.3b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
3.5b	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
4.7b	(* M (/ D (* 2.0 d)))
10.1b	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

rewrite32.0ms

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:

8.0ms	(* 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))))
8.0ms	(* M (/ D (* 2.0 d)))
9.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

series549.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
151.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
6.0ms	(* M (/ D (* 2.0 d)))
213.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

simplify36.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5600	1864

prune227.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	119	6	125

Merged error: 6.3b

Counts

125 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (* (/ h l) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))))))
4.7b	(* M (/ D (* 2.0 d)))
4.7b	(* M (/ D (* 2.0 d)))
10.1b	(* (/ h l) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
32×	`add-sqr-sqrt`
28×	`prod-exp`
27×	`add-cbrt-cube`
19×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
17×	`times-frac`
14×	`div-exp`
10×	`cbrt-unprod`
9×	`pow1`
8×	`pow-exp`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative` `div-inv` `sqr-pow`
2×	`pow-to-exp` `sqrt-div` `associate-*r/` `pow-prod-down`
1×	`unpow-prod-down` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-*l/` `flip--`

Counts

4 → 114

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (* (/ h l) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))))))
7.0ms	(* M (/ D (* 2.0 d)))
7.0ms	(* M (/ D (* 2.0 d)))
9.0ms	(* (/ h l) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (* (/ h l) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))))))
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))
151.0ms	(* (/ h l) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

simplify35.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5168	1747

prune279.0ms

Filtered

84 candidates to 126 candidates (-50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	125	7	132

Merged error: 5.6b

Counts

132 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
4.7b	(* M (/ D (* 2.0 d)))
4.7b	(* M (/ D (* 2.0 d)))
6.7b	(* h (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
41×	`add-sqr-sqrt`
38×	`times-frac`
33×	`associate-r`
30×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-cbrt-cube`
23×	`prod-exp`
20×	`div-exp`
10×	`pow1` `cbrt-unprod`
9×	`associate-l`
8×	`pow-exp` `sqr-pow`
7×	`unpow-prod-down`
6×	`cbrt-undiv`
5×	`associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/r` `*-commutative`
2×	`pow-to-exp`
1×	`frac-2neg` `clear-num`

Counts

4 → 138

Calls

4 calls:

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)))
9.0ms	(* h (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))

series358.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))
172.0ms	(* h (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))

simplify49.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4988	2147
1	4988	2147

prune349.0ms

Filtered

105 candidates to 150 candidates (-42.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	149	8	157

Merged error: 5.6b

Counts

157 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (* (cbrt h) (cbrt h)) (* (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l) (cbrt h)))
4.5b	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
4.7b	(* M (/ D (* 2.0 d)))
4.7b	(* M (/ D (* 2.0 d)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-exp-log`
58×	`prod-exp`
35×	`add-cbrt-cube`
28×	`div-exp`
24×	`add-sqr-sqrt`
21×	`times-frac` `cbrt-unprod`
20×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r`
12×	`pow-exp`
10×	`pow-prod-down`
7×	`cbrt-undiv` `associate-l`
5×	`associate-/l*`
4×	`unpow-prod-down` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `associate-r/` `associate-/r` `*-commutative` `div-inv`
2×	`unswap-sqr`
1×	`frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 131

Calls

4 calls:

13.0ms	(* (* (cbrt h) (cbrt h)) (* (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l) (cbrt h)))
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)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (* (cbrt h) (cbrt h)) (* (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l) (cbrt h)))
175.0ms	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))

simplify36.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5461	2017

prune243.0ms

Filtered

86 candidates to 143 candidates (-66.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	143	8	151

Merged error: 5.6b

Counts

151 → 8

regimes2.1s

Accuracy

52.3% (0.6b remaining)

Error of 7.8b against oracle of 7.2b and baseline of 8.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	113	75
1	113	75

end0.0ms

sample1.6s

Algorithm

intervals

Results

840.0ms	8000×	body	80	valid
253.0ms	3116×	body	80	nan
107.0ms	1300×	body	80	invalid

Details

analyze2.3s

sample49.0ms

simplify46.0ms

prune17.0ms

localize19.0ms

rewrite32.0ms

series549.0ms

simplify36.0ms

prune227.0ms

localize16.0ms

rewrite33.0ms

series312.0ms

simplify35.0ms

prune279.0ms

localize20.0ms

rewrite34.0ms

series358.0ms

simplify49.0ms

prune349.0ms

localize21.0ms

rewrite41.0ms

series365.0ms

simplify36.0ms

prune243.0ms

regimes2.1s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling