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)

sample38.0ms (1.3%)

Algorithm

1×

intervals

Results

20.0ms	72×	body	2048	valid
5.0ms	123×	body	128	valid
4.0ms	28×	body	1024	valid
2.0ms	23×	body	512	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify174.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 16.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

1.5b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
3×	`add-log-exp_binary64_1494` `cancel-sign-sub-inv_binary64_1421`
2×	`add-cube-cbrt_binary64_1490`
1×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516` `difference-of-squares_binary64_1424` `add-cbrt-cube_binary64_1491` `flip--_binary64_1430` `diff-atan_binary64_1612` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459` `add-exp-log_binary64_1493`

Counts

1 → 17

Calls

1 calls:

5.0ms

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

series33.0ms (1.1%)

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4965	306
1	4965	306

prune17.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	1	21

Merged error: 0.4b

Counts

21 → 1

Compiler

Compiled 266 to 175 computations (34.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`add-sqr-sqrt_binary64_1477` `pow1_binary64_1516` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455` `add-exp-log_binary64_1493`

Counts

1 → 7

Calls

1 calls:

1.0ms

(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series14.0ms (0.5%)

Counts

1 → 3

Calls

1 calls:

14.0ms

(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify156.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	5189	162

prune25.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	4	11

Merged error: 0.4b

Counts

11 → 4

Compiler

Compiled 349 to 296 computations (15.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(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))))))
15.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1477`
24×	`sqrt-prod_binary64_1471`
21×	`pow1_binary64_1516`
14×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
10×	`sqrt-pow1_binary64_1473` `pow1/2_binary64_1535`
8×	`swap-sqr_binary64_1422`
6×	`associate-r_binary64_1395` `add-cbrt-cube_binary64_1491` `associate-l_binary64_1396` `add-exp-log_binary64_1493`
5×	`pow-prod-up_binary64_1525`
4×	`rem-sqrt-square_binary64_1468` `add-log-exp_binary64_1494` `unswap-sqr_binary64_1423`
3×	`pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`
1×	`prod-exp_binary64_1504` `pow-plus_binary64_1518` `*-commutative_binary64_1386` `sqrt-unprod_binary64_1475` `pow2_binary64_1536` `sqr-abs_binary64_1470` `cbrt-unprod_binary64_1488` `rem-square-sqrt_binary64_1467`

Counts

4 → 83

Calls

4 calls:

8.0ms	(.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))))

series123.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(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)))))
17.0ms	(.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))))

simplify80.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5111	1475

prune192.0ms (6.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	92	7	99

Merged error: 0.4b

Counts

99 → 7

Compiler

Compiled 3249 to 2729 computations (16% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))))
15.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.8b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1477`
21×	`cbrt-prod_binary64_1486`
12×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
11×	`sqrt-prod_binary64_1471`
9×	`associate-r_binary64_1395`
8×	`pow1_binary64_1516`
6×	`associate-l_binary64_1396` `unswap-sqr_binary64_1423` `add-exp-log_binary64_1493`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
3×	`pow1/3_binary64_1537`
2×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `pow1/2_binary64_1535` `pow-prod-down_binary64_1526`
1×	`prod-exp_binary64_1504` `rem-3cbrt-lft_binary64_1480` `pow3_binary64_1538` `*-commutative_binary64_1386` `cbrt-unprod_binary64_1488`

Counts

4 → 72

Calls

4 calls:

9.0ms	(.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (cbrt.f64 (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	(cbrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series386.0ms (13.3%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
47.0ms	(.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))))
42.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
42.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify93.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4971	1892
1	4971	1892

prune204.0ms (7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	84	7	91

Merged error: 0.4b

Counts

91 → 7

Compiler

Compiled 3581 to 2977 computations (16.9% saved)

regimes19.0ms (0.7%)

Compiler: Compiled 185 to 160 computations (13.5% 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%)

sample1.2s (41.4%)

Algorithm

1×

intervals

Results

451.0ms	2195×	body	2048	valid
176.0ms	4074×	body	128	valid
144.0ms	999×	body	1024	valid
56.0ms	487×	body	512	valid
19.0ms	245×	body	256	valid

Compiler

Compiled 210 to 183 computations (12.9% saved)

Details

analyze1.0ms (0%)

sample38.0ms (1.3%)

simplify174.0ms (6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite6.0ms (0.2%)

series33.0ms (1.1%)

simplify66.0ms (2.3%)

prune17.0ms (0.6%)

localize5.0ms (0.2%)

rewrite1.0ms (0%)

series14.0ms (0.5%)

simplify156.0ms (5.4%)

prune25.0ms (0.9%)

localize8.0ms (0.3%)

rewrite19.0ms (0.7%)

series123.0ms (4.2%)

simplify80.0ms (2.7%)

prune192.0ms (6.6%)

localize12.0ms (0.4%)

rewrite23.0ms (0.8%)

series386.0ms (13.3%)

simplify93.0ms (3.2%)

prune204.0ms (7%)

regimes19.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (41.4%)

Profiling