Details

analyze3.0ms (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)

sample45.0ms (1.5%)

Algorithm

1×

intervals

Results

19.0ms	62×	body	2048	valid
7.0ms	131×	body	128	valid
7.0ms	31×	body	1024	valid
4.0ms	25×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify140.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (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

Error

16.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize10.0ms (0.3%)

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))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
4×	`add-log-exp_binary64_1140`
3×	`add-cube-cbrt_binary64_1136` `cancel-sign-sub-inv_binary64_1067`
2×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
1×	`diff-log_binary64_1193` `diff-atan_binary64_1258` `difference-of-squares_binary64_1070` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105`

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
2.0ms	(atan.f64 (+.f64 N 1))

series32.0ms (1%)

Counts

2 → 6

Calls

2 calls:

27.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(atan.f64 (+.f64 N 1))

simplify71.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune27.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	2	31

Error

0.3b

Counts

31 → 2

Compiler

Compiled 381 to 250 computations (34.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
3×	`associate-l_binary64_1042`
2×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `distribute-lft-in_binary64_1050` `flip3-+_binary64_1104` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`

Counts

2 → 30

Calls

2 calls:

11.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series62.0ms (2%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(*.f64 N (+.f64 N 1))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify137.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4927	383
1	4927	383

prune54.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	31	7	38

Error

0.3b

Counts

38 → 7

Compiler

Compiled 578 to 456 computations (21.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 N N) N)
0.4b	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_1140`
3×	`*-un-lft-identity_binary64_1101`
2×	`add-sqr-sqrt_binary64_1123` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
1×	`distribute-rgt-out_binary64_1054` `sum-log_binary64_1192` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075` `distribute-lft1-in_binary64_1056`

Counts

2 → 20

Calls

2 calls:

6.0ms	(+.f64 (*.f64 N N) N)
0.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

series40.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

26.0ms	(+.f64 (*.f64 N N) N)
14.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

simplify100.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4920	318
1	4920	318

prune27.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	26	7	33

Error

0.3b

Counts

33 → 7

Compiler

Compiled 440 to 265 computations (39.8% 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))))))
14.1b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.1b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1123`
24×	`sqrt-prod_binary64_1117`
21×	`pow1_binary64_1162`
14×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
10×	`sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
8×	`swap-sqr_binary64_1068`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041` `associate-l_binary64_1042`
5×	`pow-prod-up_binary64_1171`
4×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
3×	`pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `rem-square-sqrt_binary64_1113` `sqr-abs_binary64_1116` `sqrt-unprod_binary64_1121` `pow2_binary64_1182`

Counts

4 → 83

Calls

4 calls:

14.0ms	(.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))))

series76.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
24.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
10.0ms	(.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))))))
7.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify129.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5103	1475

prune171.0ms (5.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Error

0.3b

Counts

102 → 9

Compiler

Compiled 1987 to 1634 computations (17.8% saved)

regimes69.0ms (2.2%)

Accuracy

Total 0.0b remaining (11.6%)

Threshold costs 0.0b (11.6%)

Compiler

Compiled 748 to 626 computations (16.3% 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%)

sample1.8s (58.4%)

Algorithm

1×

intervals

Results

486.0ms	2093×	body	2048	valid
188.0ms	4117×	body	128	valid
165.0ms	1020×	body	1024	valid
66.0ms	530×	body	512	valid
25.0ms	240×	body	256	valid

Compiler

Compiled 393 to 331 computations (15.8% saved)

Details

analyze3.0ms (0.1%)

sample45.0ms (1.5%)

simplify140.0ms (4.5%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

rewrite11.0ms (0.4%)

series32.0ms (1%)

simplify71.0ms (2.3%)

prune27.0ms (0.9%)

localize10.0ms (0.3%)

rewrite15.0ms (0.5%)

series62.0ms (2%)

simplify137.0ms (4.4%)

prune54.0ms (1.8%)

localize5.0ms (0.2%)

rewrite9.0ms (0.3%)

series40.0ms (1.3%)

simplify100.0ms (3.2%)

prune27.0ms (0.9%)

localize8.0ms (0.3%)

rewrite25.0ms (0.8%)

series76.0ms (2.5%)

simplify129.0ms (4.2%)

prune171.0ms (5.6%)

regimes69.0ms (2.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.8s (58.4%)

Profiling