Details

analyze514.0ms (10.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

valid

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	452	21
1	452	21

prune10.0ms (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: 14.6b

Counts

2 → 2

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
0.0b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.1b	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
14.2b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`associate-r/` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log`

Counts

4 → 98

Calls

4 calls:

19.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
3.0ms	(+ x (* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))

series106.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ x (* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
24.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
5.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify36.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5729	2166

prune244.0ms (5.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* y (/ (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
13.6b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
13.6b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
13.6b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

rewrite95.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

280×	`times-frac`
175×	`add-sqr-sqrt`
150×	`associate-r`
149×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
20×	`sqrt-div`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
11×	`flip3-+` `flip-+`
8×	`pow1` `div-inv`
7×	`unswap-sqr`
6×	`associate-/r*`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 249

Calls

4 calls:

54.0ms	(* y (/ (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
15.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series45.0ms (1%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(* y (/ (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
13.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
4.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
3.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4978	6528
1	4978	6528

prune1.2s (25.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	261	5	266

Merged error: 0.0b

Counts

266 → 5

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.1b	(* y (/ 1 (/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))))
0.5b	(/ 1 (/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)))
14.2b	(/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))

rewrite72.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`times-frac`
112×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
96×	`add-cube-cbrt`
53×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`associate-/r*` `associate-/r/`
15×	`div-exp`
10×	`flip3-+` `flip-+` `div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-*r/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `associate-/l/`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `un-div-inv` `inv-pow`

Counts

4 → 216

Calls

4 calls:

24.0ms	(* y (/ 1 (/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))))
16.0ms	(/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
15.0ms	(/ 1 (/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))

series44.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(* y (/ 1 (/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))))
5.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
5.0ms	(/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525))
5.0ms	(/ 1 (/ (+ (* z (+ z 6.012459259764103)) 3.350343815022304) (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525)))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5008	5326

prune647.0ms (13.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	228	5	233

Merged error: 0.0b

Counts

233 → 5

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

13.6b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
13.6b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
13.6b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
13.6b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series17.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
4.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
3.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
3.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify40.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4977	840
1	4977	840

prune296.0ms (6.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	72	5	77

Merged error: 0.0b

Counts

77 → 5

regimes320.0ms (6.8%)

Accuracy

Total 0.1b remaining (78.7%)

Threshold costs 0.1b (78.7%)

bsearch39.0ms (0.8%)

Steps

Iters	Range		Point
11	0.006277777667856217	5.3675831592446266e+17	179323532.70281792
8	-1492748711985618.0	-136566175011.07425	-203723538555.02405

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	41
1	46	41

end0.0ms (0%)

sample617.0ms (13.2%)

Algorithm

1×

intervals

Results

435.0ms

8000×

body

valid

Details

analyze514.0ms (10.9%)

sample23.0ms (0.5%)

simplify10.0ms (0.2%)

prune10.0ms (0.2%)

localize13.0ms (0.3%)

rewrite45.0ms (1%)

series106.0ms (2.3%)

simplify36.0ms (0.8%)

prune244.0ms (5.2%)

localize16.0ms (0.3%)

rewrite95.0ms (2%)

series45.0ms (1%)

simplify79.0ms (1.7%)

prune1.2s (25.9%)

localize14.0ms (0.3%)

rewrite72.0ms (1.5%)

series44.0ms (0.9%)

simplify87.0ms (1.9%)

prune647.0ms (13.8%)

localize21.0ms (0.5%)

rewrite26.0ms (0.6%)

series17.0ms (0.4%)

simplify40.0ms (0.8%)

prune296.0ms (6.3%)

regimes320.0ms (6.8%)

bsearch39.0ms (0.8%)

simplify1.0ms (0%)

end0.0ms (0%)

sample617.0ms (13.2%)

Profiling