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

15.0ms	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)

simplify178.0ms (7.3%)

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: 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))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133`
4×	`add-log-exp_binary64_1150`
3×	`cancel-sign-sub-inv_binary64_1077` `add-cube-cbrt_binary64_1146`
2×	`add-cbrt-cube_binary64_1147` `pow1_binary64_1172` `add-exp-log_binary64_1149`
1×	`diff-atan_binary64_1268` `flip3--_binary64_1115` `diff-log_binary64_1203` `difference-of-squares_binary64_1080` `sub-neg_binary64_1104` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086`

Counts

2 → 24

Calls

2 calls:

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

series31.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

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

simplify70.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4971	391
1	4971	391

prune26.0ms (1.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.5b

Counts

31 → 1

Compiler

Compiled 367 to 243 computations (33.8% saved)

localize6.0ms (0.2%)

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×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133`
5×	`add-cbrt-cube_binary64_1147` `add-cube-cbrt_binary64_1146` `add-log-exp_binary64_1150` `pow1_binary64_1172` `add-exp-log_binary64_1149`
4×	`associate-r_binary64_1051`
3×	`associate-l_binary64_1052`
2×	`flip-+_binary64_1085` `distribute-lft-in_binary64_1060` `flip3-+_binary64_1114` `distribute-rgt-in_binary64_1061` `associate-*r/_binary64_1053` `associate-+r+_binary64_1043`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `+-commutative_binary64_1041` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079` `distribute-lft-out_binary64_1062` `sum-log_binary64_1202`

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))))

series87.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

57.0ms	(*.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))))

simplify95.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4915	599
1	4915	599

prune64.0ms (2.7%)

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 1018 to 808 computations (20.6% 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)))))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1133`
24×	`sqrt-prod_binary64_1127`
21×	`pow1_binary64_1172`
14×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
10×	`pow1/2_binary64_1191` `sqrt-pow1_binary64_1129`
8×	`swap-sqr_binary64_1078`
6×	`add-cbrt-cube_binary64_1147` `associate-r_binary64_1051` `associate-l_binary64_1052` `add-exp-log_binary64_1149`
5×	`pow-prod-up_binary64_1181`
4×	`rem-sqrt-square_binary64_1124` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
3×	`pow-sqr_binary64_1084` `pow-prod-down_binary64_1182`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `rem-square-sqrt_binary64_1123` `pow-plus_binary64_1174` `pow2_binary64_1192` `sqrt-unprod_binary64_1131` `sqr-abs_binary64_1126`

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))))))
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))))

series127.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
46.0ms	(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))))))
12.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify79.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5111	1475

prune123.0ms (5.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	95	4	99

Merged error: 0.5b

Counts

99 → 4

Compiler

Compiled 2190 to 1805 computations (17.6% saved)

localize11.0ms (0.5%)

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_1133`
6×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146` `pow1_binary64_1172` `sqrt-prod_binary64_1127`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
2×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `sqrt-pow1_binary64_1129`

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))))

series102.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
39.0ms	(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))))

simplify61.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4937	862
1	4937	862

prune92.0ms (3.8%)

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 1670 to 1414 computations (15.3% saved)

regimes15.0ms (0.6%)

Compiler: Compiled 120 to 103 computations (14.2% 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 (47.6%)

Algorithm

1×

intervals

Results

452.0ms	2167×	body	2048	valid
180.0ms	4061×	body	128	valid
153.0ms	1011×	body	1024	valid
54.0ms	492×	body	512	valid
21.0ms	269×	body	256	valid

Compiler

Compiled 145 to 126 computations (13.1% saved)

Details

analyze1.0ms (0.1%)

sample32.0ms (1.3%)

simplify178.0ms (7.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite7.0ms (0.3%)

series31.0ms (1.3%)

simplify70.0ms (2.9%)

prune26.0ms (1.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.6%)

series87.0ms (3.6%)

simplify95.0ms (3.9%)

prune64.0ms (2.7%)

localize8.0ms (0.3%)

rewrite20.0ms (0.8%)

series127.0ms (5.2%)

simplify79.0ms (3.3%)

prune123.0ms (5.1%)

localize11.0ms (0.5%)

rewrite8.0ms (0.3%)

series102.0ms (4.2%)

simplify61.0ms (2.5%)

prune92.0ms (3.8%)

regimes15.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (47.6%)

Profiling