Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample32.0ms (1%)

Algorithm

1×

intervals

Results

15.0ms	75×	body	2048	valid
5.0ms	126×	body	128	valid
4.0ms	28×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify170.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (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: 14.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

1.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt_binary64_1446` `add-log-exp_binary64_1461` `*-un-lft-identity_binary64_1425`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `add-cube-cbrt_binary64_1457` `distribute-lft-out--_binary64_1379` `sub-neg_binary64_1418` `diff-atan_binary64_1579` `add-cbrt-cube_binary64_1458` `difference-of-squares_binary64_1394` `pow1_binary64_1483` `flip3--_binary64_1429` `add-exp-log_binary64_1460`

Counts

1 → 14

Calls

1 calls:

4.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series24.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

24.0ms

(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify90.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5599	291

prune15.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	2	18

Merged error: 0.3b

Counts

18 → 2

Compiler

Compiled 226 to 149 computations (34.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
4×	`add-cube-cbrt_binary64_1457` `associate-r_binary64_1367` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460`
3×	`associate-l_binary64_1368`
2×	`associate-*r/_binary64_1369` `add-log-exp_binary64_1461`
1×	`distribute-lft-in_binary64_1376` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `flip3-+_binary64_1428` `cbrt-unprod_binary64_1455` `distribute-lft-out_binary64_1378` `distribute-rgt-in_binary64_1377` `flip-+_binary64_1399` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

2 → 30

Calls

2 calls:

10.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series68.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

53.0ms	(*.f64 N (+.f64 N 1))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify93.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4880	383
1	4880	383

prune40.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	31	5	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	31	7	38

Merged error: 0.2b

Counts

38 → 7

Compiler

Compiled 541 to 424 computations (21.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1453`
23×	`add-sqr-sqrt_binary64_1446`
15×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
11×	`pow1_binary64_1483`
9×	`pow1/3_binary64_1504`
6×	`associate-l_binary64_1368` `associate-r_binary64_1367` `swap-sqr_binary64_1392` `add-exp-log_binary64_1460`
4×	`unswap-sqr_binary64_1393` `add-cbrt-cube_binary64_1458` `add-log-exp_binary64_1461`
2×	`pow-sqr_binary64_1398` `pow-prod-up_binary64_1492` `pow-prod-down_binary64_1493`
1×	`prod-exp_binary64_1471` `pow-plus_binary64_1485` `cbrt-unprod_binary64_1455` `pow2_binary64_1503` `*-commutative_binary64_1358`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series621.0ms (20.4%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
151.0ms	(cbrt.f64 N)
148.0ms	(cbrt.f64 N)
147.0ms	(cbrt.f64 N)

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4957	563
1	4957	563

prune85.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	85	7	92

Merged error: 0.2b

Counts

92 → 7

Compiler

Compiled 1657 to 973 computations (41.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cbrt.f64 (.f64 N N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))
0.3b	(atan2.f64 1 (+.f64 1 (.f64 (cbrt.f64 (.f64 N N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))
0.6b	(cbrt.f64 N)
30.3b	(cbrt.f64 (*.f64 N N))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64_1483` `add-exp-log_binary64_1460`
6×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446` `add-cbrt-cube_binary64_1458` `*-un-lft-identity_binary64_1425`
5×	`cbrt-prod_binary64_1453`
4×	`associate-l_binary64_1368` `add-log-exp_binary64_1461`
3×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `pow-prod-down_binary64_1493`
2×	`associate-r/_binary64_1369` `pow1/3_binary64_1504` `associate-l/_binary64_1370`
1×	`flip3-+_binary64_1428` `associate-r_binary64_1367` `flip-+_binary64_1399` `*-commutative_binary64_1358`

Counts

4 → 48

Calls

4 calls:

10.0ms	(.f64 (cbrt.f64 (.f64 N N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))
3.0ms	(cbrt.f64 (*.f64 N N))
1.0ms	(cbrt.f64 N)
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (cbrt.f64 (.f64 N N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

series400.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt.f64 (*.f64 N N))
147.0ms	(cbrt.f64 N)
76.0ms	(.f64 (cbrt.f64 (.f64 N N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))
16.0ms	(atan2.f64 1 (+.f64 1 (.f64 (cbrt.f64 (.f64 N N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

simplify60.0ms (2%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5094	792

prune54.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	60	7	67

Merged error: 0.2b

Counts

67 → 7

Compiler

Compiled 1094 to 627 computations (42.7% saved)

regimes27.0ms (0.9%)

Compiler: Compiled 194 to 168 computations (13.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.1s (36.4%)

Algorithm

1×

intervals

Results

437.0ms	2174×	body	2048	valid
180.0ms	4090×	body	128	valid
142.0ms	958×	body	1024	valid
55.0ms	520×	body	512	valid
20.0ms	258×	body	256	valid

Compiler

Compiled 116 to 102 computations (12.1% saved)

Details

analyze1.0ms (0%)

sample32.0ms (1%)

simplify170.0ms (5.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite5.0ms (0.2%)

series24.0ms (0.8%)

simplify90.0ms (2.9%)

prune15.0ms (0.5%)

localize6.0ms (0.2%)

rewrite13.0ms (0.4%)

series68.0ms (2.2%)

simplify93.0ms (3.1%)

prune40.0ms (1.3%)

localize10.0ms (0.3%)

rewrite16.0ms (0.5%)

series621.0ms (20.4%)

simplify67.0ms (2.2%)

prune85.0ms (2.8%)

localize13.0ms (0.4%)

rewrite18.0ms (0.6%)

series400.0ms (13.1%)

simplify60.0ms (2%)

prune54.0ms (1.8%)

regimes27.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (36.4%)

Profiling