Details

analyze2.4s (25.5%)

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

sample55.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	80	valid
11.0ms	92×	body	80	nan
3.0ms	44×	body	80	invalid

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	18

prune11.0ms (0.1%)

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: 15.6b

Counts

2 → 1

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.9b	(* 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))))
5.0b	(/ (* M D) (* 2.0 d))
12.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite34.0ms (0.4%)

Algorithm

1×	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:

10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))
8.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))

series538.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))
174.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
146.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5373	1965

prune338.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 8.2b

Counts

126 → 7

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))))
4.8b	(* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))
5.0b	(/ (* M D) (* 2.0 d))
5.4b	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
22×	`associate-r`
21×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`associate-l` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

11.0ms	(* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))
7.0ms	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
6.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))))
6.0ms	(/ (* M D) (* 2.0 d))

series405.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))
122.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))))
106.0ms	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
9.0ms	(/ (* M D) (* 2.0 d))

simplify64.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4986	1940
1	4986	1940

prune372.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	139	8	147

Merged error: 7.7b

Counts

147 → 8

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
4.8b	(* (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ 1 l))
5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))

rewrite78.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

1402×	`add-exp-log`
907×	`prod-exp`
366×	`div-exp`
305×	`pow-exp`
61×	`pow-to-exp`
57×	`rec-exp` `1-exp`
51×	`add-cbrt-cube`
22×	`associate-r`
21×	`cbrt-unprod`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`cbrt-undiv`
6×	`pow1` `unpow-prod-down`
4×	`associate-l` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 332

Calls

4 calls:

19.0ms	(* (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ 1 l))
7.0ms	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series272.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (/ 1 l))
92.0ms	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5074	5677

prune1.1s (11.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	344	8	352

Merged error: 7.5b

Counts

352 → 8

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))
6.5b	(/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) l)

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-exp-log`
34×	`times-frac`
32×	`add-cbrt-cube`
30×	`add-sqr-sqrt`
26×	`unpow-prod-down`
25×	`add-cube-cbrt` `*-un-lft-identity`
23×	`div-exp` `prod-exp`
11×	`associate-/l*`
10×	`pow-exp`
9×	`cbrt-undiv` `associate-r` `cbrt-unprod`
8×	`div-inv`
6×	`sqr-pow`
5×	`associate-/r*`
4×	`pow1` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `unswap-sqr`
2×	`pow-to-exp`
1×	`*-commutative`

Counts

4 → 130

Calls

4 calls:

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

series279.0ms (3%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (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))
6.0ms	(/ (* M D) (* 2.0 d))

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5318	2156

prune434.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	142	8	150

Merged error: 7.5b

Counts

150 → 8

regimes1.3s (13.7%)

Accuracy

Total 1.2b remaining (14.4%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	32
1	68	32

end0.0ms (0%)

sample1.5s (15.5%)

Algorithm

1×

intervals

Results

613.0ms	8000×	body	80	valid
261.0ms	3180×	body	80	nan
117.0ms	1359×	body	80	invalid

Details

analyze2.4s (25.5%)

sample55.0ms (0.6%)

simplify53.0ms (0.6%)

prune11.0ms (0.1%)

localize15.0ms (0.2%)

rewrite34.0ms (0.4%)

series538.0ms (5.7%)

simplify32.0ms (0.3%)

prune338.0ms (3.6%)

localize16.0ms (0.2%)

rewrite36.0ms (0.4%)

series405.0ms (4.3%)

simplify64.0ms (0.7%)

prune372.0ms (3.9%)

localize21.0ms (0.2%)

rewrite78.0ms (0.8%)

series272.0ms (2.9%)

simplify67.0ms (0.7%)

prune1.1s (11.2%)

localize17.0ms (0.2%)

rewrite33.0ms (0.3%)

series279.0ms (3%)

simplify37.0ms (0.4%)

prune434.0ms (4.6%)

regimes1.3s (13.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (15.5%)

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