Details

analyze2.1s

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

sample53.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
7.0ms	95×	body	80	nan
2.0ms	27×	body	80	invalid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4790	18
1	4790	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: 12.7b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

2.4b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.4b	(/ (* M D) (* 2.0 d))
11.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

9.0ms	(* 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))))
5.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series524.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
142.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
205.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify64.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4972	1950
1	4972	1950

prune266.0ms

Filtered

84 candidates to 125 candidates (-48.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 8.5b

Counts

127 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
4.0b	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
4.8b	(* M (/ D (* 2.0 d)))
6.9b	(* h (pow (* M (/ D (* 2.0 d))) 2.0))

rewrite27.0ms

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:

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)))
5.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))

series377.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
161.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
6.0ms	(* M (/ D (* 2.0 d)))
91.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5076	1467

prune218.0ms

Filtered

71 candidates to 107 candidates (-50.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 7.7b

Counts

115 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (* 1/2 2.0))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
4.8b	(* M (/ D (* 2.0 d)))
4.8b	(* M (/ D (* 2.0 d)))
5.1b	(* h (pow (* M (/ D (* 2.0 d))) (* 1/2 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

268×	`add-exp-log`
148×	`prod-exp`
75×	`div-exp`
56×	`pow-exp`
33×	`add-cbrt-cube`
21×	`add-sqr-sqrt`
19×	`associate-r`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-unprod`
9×	`times-frac` `associate-l`
8×	`pow1`
7×	`cbrt-undiv`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/r` `-commutative` `div-inv`
2×	`associate-*r/` `pow-prod-down` `sqr-pow`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 142

Calls

4 calls:

12.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (* 1/2 2.0))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
7.0ms	(* M (/ D (* 2.0 d)))
7.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* h (pow (* M (/ D (* 2.0 d))) (* 1/2 2.0)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (* 1/2 2.0))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
7.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))
93.0ms	(* h (pow (* M (/ D (* 2.0 d))) (* 1/2 2.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4932	1923
1	4932	1923

prune263.0ms

Filtered

75 candidates to 154 candidates (-105.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	151	3	154
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	154	8	162

Merged error: 7.2b

Counts

162 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (pow (* M (/ D (* 2.0 d))) (* 2.0 1/2)) l)
4.8b	(* M (/ D (* 2.0 d)))
4.8b	(* M (/ D (* 2.0 d)))
5.1b	(* h (pow (* M (/ D (* 2.0 d))) (* 2.0 1/2)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

5.0ms	(/ (pow (* M (/ D (* 2.0 d))) (* 2.0 1/2)) l)
7.0ms	(* M (/ D (* 2.0 d)))
7.0ms	(* M (/ D (* 2.0 d)))
8.0ms	(* h (pow (* M (/ D (* 2.0 d))) (* 2.0 1/2)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (pow (* M (/ D (* 2.0 d))) (* 2.0 1/2)) l)
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))
92.0ms	(* h (pow (* M (/ D (* 2.0 d))) (* 2.0 1/2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4978	1744
1	4978	1744

prune275.0ms

Filtered

90 candidates to 131 candidates (-45.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	131	8	139

Merged error: 7.2b

Counts

139 → 8

regimes1.1s

Accuracy

0% (1.5b remaining)

Error of 9.0b against oracle of 7.5b and baseline of 9.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	128	32
1	128	32

end0.0ms

sample1.5s

Algorithm

intervals

Results

632.0ms	8000×	body	80	valid
251.0ms	3189×	body	80	nan
117.0ms	1343×	body	80	invalid

Details

analyze2.1s

sample53.0ms

simplify67.0ms

prune17.0ms

localize13.0ms

rewrite33.0ms

series524.0ms

simplify64.0ms

prune266.0ms

localize16.0ms

rewrite27.0ms

series377.0ms

simplify36.0ms

prune218.0ms

localize18.0ms

rewrite39.0ms

series270.0ms

simplify95.0ms

prune263.0ms

localize15.0ms

rewrite30.0ms

series273.0ms

simplify68.0ms

prune275.0ms

regimes1.1s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling