Details

analyze1.0ms (0.1%)

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 (1.3%)

Algorithm

1×

intervals

Results

16.0ms	75×	body	2048	valid
6.0ms	137×	body	128	valid
4.0ms	25×	body	1024	valid
1.0ms	12×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify170.0ms (6.9%)

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: 12.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 21

Calls

2 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

series30.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

23.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
7.0ms	(atan.f64 (+.f64 N 1))

simplify89.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5609	376

prune21.0ms (0.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	1	28

Merged error: 0.5b

Counts

28 → 1

Compiler

Compiled 327 to 217 computations (33.6% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.0b	(+.f64 1 (*.f64 N (+.f64 N 1)))
0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
5×	`add-cube-cbrt_binary64_1457` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
4×	`associate-r_binary64_1367`
3×	`associate-l_binary64_1368`
2×	`distribute-lft-in_binary64_1376` `flip3-+_binary64_1428` `associate-*r/_binary64_1369` `distribute-rgt-in_binary64_1377` `flip-+_binary64_1399` `associate-+r+_binary64_1359`
1×	`unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `distribute-lft-out_binary64_1378` `sum-log_binary64_1513` `+-commutative_binary64_1357` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

3 → 43

Calls

3 calls:

7.0ms	(*.f64 N (+.f64 N 1))
4.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series89.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(*.f64 N (+.f64 N 1))
17.0ms	(+.f64 1 (*.f64 N (+.f64 N 1)))
13.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify90.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4899	599
1	4899	599

prune48.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	4	53

Merged error: 0.5b

Counts

53 → 4

Compiler

Compiled 742 to 578 computations (22.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
16.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
16.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1446`
24×	`sqrt-prod_binary64_1440`
21×	`pow1_binary64_1483`
14×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
10×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442`
8×	`swap-sqr_binary64_1392`
6×	`associate-l_binary64_1368` `associate-r_binary64_1367` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
5×	`pow-prod-up_binary64_1492`
4×	`unswap-sqr_binary64_1393` `add-log-exp_binary64_1461`
3×	`pow-sqr_binary64_1398` `pow-prod-down_binary64_1493`
2×	`rem-sqrt-square_binary64_1438`
1×	`prod-exp_binary64_1471` `pow-plus_binary64_1485` `cbrt-unprod_binary64_1455` `rem-square-sqrt_binary64_1437` `pow2_binary64_1503` `sqrt-unprod_binary64_1444` `*-commutative_binary64_1358`

Counts

4 → 82

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

series121.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
44.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
16.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
13.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify64.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5063	1485

prune113.0ms (4.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Merged error: 0.5b

Counts

98 → 4

Compiler

Compiled 2009 to 1654 computations (17.7% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
16.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
16.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_1446`
6×	`add-cube-cbrt_binary64_1457` `sqrt-prod_binary64_1440` `pow1_binary64_1483` `*-un-lft-identity_binary64_1425`
4×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
2×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `rem-sqrt-square_binary64_1438`

Counts

4 → 40

Calls

4 calls:

2.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

series106.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
41.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
11.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
10.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify58.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4937	862
1	4937	862

prune81.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	51	5	56

Merged error: 0.5b

Counts

56 → 5

Compiler

Compiled 1552 to 1313 computations (15.4% saved)

regimes40.0ms (1.6%)

Compiler: Compiled 390 to 328 computations (15.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.2s (50%)

Algorithm

1×

intervals

Results

461.0ms	2167×	body	2048	valid
174.0ms	4061×	body	128	valid
152.0ms	1011×	body	1024	valid
59.0ms	492×	body	512	valid
25.0ms	269×	body	256	valid

Compiler

Compiled 214 to 182 computations (15% saved)

Details

analyze1.0ms (0.1%)

sample32.0ms (1.3%)

simplify170.0ms (6.9%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite6.0ms (0.3%)

series30.0ms (1.2%)

simplify89.0ms (3.6%)

prune21.0ms (0.8%)

localize9.0ms (0.4%)

rewrite14.0ms (0.6%)

series89.0ms (3.6%)

simplify90.0ms (3.6%)

prune48.0ms (1.9%)

localize8.0ms (0.3%)

rewrite18.0ms (0.7%)

series121.0ms (4.9%)

simplify64.0ms (2.6%)

prune113.0ms (4.5%)

localize11.0ms (0.4%)

rewrite8.0ms (0.3%)

series106.0ms (4.3%)

simplify58.0ms (2.3%)

prune81.0ms (3.3%)

regimes40.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (50%)

Profiling