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)

sample33.0ms (1.3%)

Algorithm

1×

intervals

Results

14.0ms	70×	body	2048	valid
6.0ms	133×	body	128	valid
4.0ms	29×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify171.0ms (6.7%)

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: 14.3b

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))
2.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_2120` `add-log-exp_binary64_2135` `*-un-lft-identity_binary64_2099`
2×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-exp-log_binary64_2134`
1×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `flip3--_binary64_2103` `flip--_binary64_2074` `diff-atan_binary64_2253` `distribute-lft-out--_binary64_2053` `diff-log_binary64_2188`

Counts

2 → 21

Calls

2 calls:

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

series32.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

24.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
8.0ms	(atan.f64 (+.f64 N 1))

simplify89.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5609	376

prune24.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Merged error: 0.5b

Counts

28 → 3

Compiler

Compiled 336 to 225 computations (33% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_2120` `*-un-lft-identity_binary64_2099`
4×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `associate-r_binary64_2041` `add-exp-log_binary64_2134`
3×	`associate-l_binary64_2042`
2×	`associate-*r/_binary64_2043` `add-log-exp_binary64_2135`
1×	`distribute-lft-out_binary64_2052` `flip3-+_binary64_2102` `distribute-rgt-in_binary64_2051` `*-commutative_binary64_2032` `distribute-lft-in_binary64_2050` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `flip-+_binary64_2073` `cbrt-unprod_binary64_2129`

Counts

2 → 30

Calls

2 calls:

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

series67.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

54.0ms	(*.f64 N (+.f64 N 1))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify90.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4880	383
1	4880	383

prune38.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	34	5	39

Merged error: 0.4b

Counts

39 → 5

Compiler

Compiled 521 to 408 computations (21.7% 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))))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.6b	(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_2120`
24×	`sqrt-prod_binary64_2114`
21×	`pow1_binary64_2157`
14×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
10×	`pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
8×	`swap-sqr_binary64_2066`
6×	`associate-l_binary64_2042` `add-cbrt-cube_binary64_2132` `associate-r_binary64_2041` `add-exp-log_binary64_2134`
5×	`pow-prod-up_binary64_2166`
4×	`add-log-exp_binary64_2135` `unswap-sqr_binary64_2067`
3×	`pow-prod-down_binary64_2167` `pow-sqr_binary64_2072`
2×	`rem-sqrt-square_binary64_2112`
1×	`sqrt-unprod_binary64_2118` `rem-square-sqrt_binary64_2111` `*-commutative_binary64_2032` `prod-exp_binary64_2145` `pow2_binary64_2177` `pow-plus_binary64_2159` `cbrt-unprod_binary64_2129`

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))))))
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))))

series115.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5063	1485

prune118.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	92	7	99

Merged error: 0.4b

Counts

99 → 7

Compiler

Compiled 2083 to 1717 computations (17.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite35.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-pow1_binary64_2116`
45×	`pow1_binary64_2157`
30×	`pow1/2_binary64_2176` `pow-prod-up_binary64_2166`
16×	`add-sqr-sqrt_binary64_2120`
14×	`sqrt-prod_binary64_2114`
9×	`add-cube-cbrt_binary64_2131` `add-cbrt-cube_binary64_2132` `*-un-lft-identity_binary64_2099` `add-exp-log_binary64_2134`
7×	`pow-prod-down_binary64_2167`
6×	`associate-l_binary64_2042` `pow-sqr_binary64_2072`
4×	`add-log-exp_binary64_2135`
3×	`prod-exp_binary64_2145` `rem-sqrt-square_binary64_2112` `cbrt-unprod_binary64_2129`
2×	`sqrt-unprod_binary64_2118` `unswap-sqr_binary64_2067` `swap-sqr_binary64_2066`
1×	`-commutative_binary64_2032` `associate-r*_binary64_2041`

Counts

4 → 85

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.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	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series151.0ms (5.9%)

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)))))
41.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
24.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))

simplify81.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4759	1397
1	4759	1397

prune150.0ms (5.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	97	7	104

Merged error: 0.4b

Counts

104 → 7

Compiler

Compiled 2677 to 2218 computations (17.1% saved)

regimes34.0ms (1.3%)

Compiler: Compiled 314 to 268 computations (14.6% 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 (46.7%)

Algorithm

1×

intervals

Results

450.0ms	2134×	body	2048	valid
192.0ms	4189×	body	128	valid
146.0ms	923×	body	1024	valid
56.0ms	495×	body	512	valid
22.0ms	259×	body	256	valid

Compiler

Compiled 176 to 152 computations (13.6% saved)

Details

analyze1.0ms (0.1%)

sample33.0ms (1.3%)

simplify171.0ms (6.7%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite6.0ms (0.2%)

series32.0ms (1.2%)

simplify89.0ms (3.5%)

prune24.0ms (1%)

localize6.0ms (0.2%)

rewrite9.0ms (0.4%)

series67.0ms (2.6%)

simplify90.0ms (3.5%)

prune38.0ms (1.5%)

localize8.0ms (0.3%)

rewrite18.0ms (0.7%)

series115.0ms (4.5%)

simplify61.0ms (2.4%)

prune118.0ms (4.6%)

localize11.0ms (0.4%)

rewrite35.0ms (1.4%)

series151.0ms (5.9%)

simplify81.0ms (3.2%)

prune150.0ms (5.9%)

regimes34.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (46.7%)

Profiling