Details

analyze2.3s (25.1%)

Algorithm

1×

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

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	80	valid
6.0ms	81×	body	80	nan
4.0ms	46×	body	80	invalid

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	18

prune18.0ms (0.2%)

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: 16.8b

Counts

2 → 2

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
4.0b	(* M (/ D (* 2.0 d)))
5.6b	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
11.3b	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

rewrite33.0ms (0.4%)

Algorithm

1×	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:

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

series540.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))
176.0ms	(* 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))))
6.0ms	(* M (/ D (* 2.0 d)))

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5600	1864

prune337.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Merged error: 9.2b

Counts

125 → 7

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(* M (/ D (* 2.0 d)))
4.5b	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
5.6b	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
6.5b	(* h (pow (* M (/ D (* 2.0 d))) 2.0))

rewrite31.0ms (0.3%)

Algorithm

1×	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:

8.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
7.0ms	(* M (/ D (* 2.0 d)))
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)

series390.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
122.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
95.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
7.0ms	(* M (/ D (* 2.0 d)))

simplify30.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5084	1475

prune279.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Merged error: 8.7b

Counts

114 → 7

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(* M (/ D (* 2.0 d)))
4.5b	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
5.5b	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
5.6b	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

259×	`add-exp-log`
144×	`prod-exp`
73×	`div-exp`
56×	`pow-exp`
24×	`add-cbrt-cube`
20×	`add-sqr-sqrt`
14×	`pow-to-exp` `*-un-lft-identity`
12×	`add-cube-cbrt` `associate-r`
8×	`cbrt-unprod`
7×	`pow1`
6×	`times-frac` `associate-l`
5×	`cbrt-undiv` `sqrt-prod`
4×	`add-log-exp`
3×	`associate-/r*` `unswap-sqr`
2×	`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 → 132

Calls

4 calls:

11.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
9.0ms	(sqrt (- 1.0 (/ (* (* 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)))
5.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

series393.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
124.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
93.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
6.0ms	(* M (/ D (* 2.0 d)))

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5282	2404

prune450.0ms (4.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	144	7	151

Merged error: 8.5b

Counts

151 → 7

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(* M (/ D (* 2.0 d)))
4.6b	(* (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ 1 l))
5.5b	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
5.6b	(sqrt (- 1.0 (* (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ 1 l))))

rewrite291.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

989×	`add-exp-log`
706×	`prod-exp`
212×	`pow-exp`
194×	`div-exp`
53×	`pow-to-exp`
43×	`rec-exp` `1-exp`
36×	`add-cbrt-cube`
25×	`associate-r`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity` `cbrt-unprod`
12×	`times-frac`
9×	`pow1`
7×	`associate-l`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative` `unswap-sqr`
2×	`sqrt-div` `associate-*r/` `pow-prod-down` `div-inv` `sqr-pow`
1×	`unpow-prod-down` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `un-div-inv` `flip--`

Counts

4 → 270

Calls

4 calls:

239.0ms	(sqrt (- 1.0 (* (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ 1 l))))
15.0ms	(* (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ 1 l))
7.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

series394.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(* (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ 1 l))
128.0ms	(sqrt (- 1.0 (* (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ 1 l))))
90.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
6.0ms	(* M (/ D (* 2.0 d)))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5007	4812

prune940.0ms (10.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	282	0	282
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	282	7	289

Merged error: 8.5b

Counts

289 → 7

regimes933.0ms (10.1%)

Accuracy

Total 1.7b remaining (18.9%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	111	34
1	111	34

end0.0ms (0%)

sample1.5s (16.2%)

Algorithm

1×

intervals

Results

644.0ms	8000×	body	80	valid
251.0ms	3001×	body	80	nan
116.0ms	1342×	body	80	invalid

Details

analyze2.3s (25.1%)

sample52.0ms (0.6%)

simplify45.0ms (0.5%)

prune18.0ms (0.2%)

localize16.0ms (0.2%)

rewrite33.0ms (0.4%)

series540.0ms (5.8%)

simplify34.0ms (0.4%)

prune337.0ms (3.6%)

localize16.0ms (0.2%)

rewrite31.0ms (0.3%)

series390.0ms (4.2%)

simplify30.0ms (0.3%)

prune279.0ms (3%)

localize21.0ms (0.2%)

rewrite39.0ms (0.4%)

series393.0ms (4.2%)

simplify45.0ms (0.5%)

prune450.0ms (4.9%)

localize20.0ms (0.2%)

rewrite291.0ms (3.1%)

series394.0ms (4.2%)

simplify100.0ms (1.1%)

prune940.0ms (10.1%)

regimes933.0ms (10.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (16.2%)

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