Details

analyze21.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample43.0ms (1.6%)

Algorithm

1×

intervals

Results

19.0ms	58×	body	2048	valid
6.0ms	36×	body	1024	valid
6.0ms	135×	body	128	valid
5.0ms	20×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify19.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

17.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	17.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite43.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

15.6b

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 746 to 394 computations (47.2% saved)

series8.0ms (0.3%)

Error

17.2b

Counts

2 → 6

Calls

2 calls:

5.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
3.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 104 to 78 computations (25% saved)

simplify93.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
392×	`unsub-neg_binary64`
319×	`distribute-rgt-in_binary64`
308×	`unswap-sqr_binary64`
275×	`times-frac_binary64`

Counts

46 → 20

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	72	667
1	128	606
2	354	552
3	1262	549
4	2924	549
5	4651	542
6	4824	542

prune12.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	2	21

Error

0.5b

Counts

21 → 2

Alt Table

Status	Error	Program
▶	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	17.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 166 to 110 computations (33.7% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite71.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

18.0ms	(+.f64 1 (fma.f64 N N N))
1.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 378 to 215 computations (43.1% saved)

series31.0ms (1.1%)

Error

0.5b

Counts

2 → 12

Calls

2 calls:

17.0ms	(+.f64 1 (fma.f64 N N N))
6.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 190 to 144 computations (24.2% saved)

simplify126.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

832×	`sub-neg_binary64`
634×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
319×	`associate-l_binary64`
301×	`associate-r_binary64`

Counts

39 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	438
1	98	386
2	241	386
3	899	386
4	2950	386
5	4669	386
6	5438	386

prune23.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	14	4	18

Error

0.5b

Counts

18 → 4

Alt Table

Status	Error	Program
	11.1b	(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3)))
▶	10.9b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	17.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 192 to 118 computations (38.5% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (fma.f64 N N N))
0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.6b	(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
10.8b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))

rewrite178.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

4 → 75

Calls

4 calls:

5.0ms	(+.f64 1 (fma.f64 N N N))
3.0ms	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
3.0ms	(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
1.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 1236 to 813 computations (34.2% saved)

series63.0ms (2.3%)

Error

0.5b

Counts

4 → 18

Calls

4 calls:

20.0ms	(+.f64 1 (fma.f64 N N N))
19.0ms	(pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3)
8.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
7.0ms	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))

Compiler

Compiled 396 to 310 computations (21.7% saved)

simplify216.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-neg_binary64`
354×	`associate-l_binary64`
348×	`log-prod_binary64`
338×	`exp-prod_binary64`
282×	`associate-r_binary64`

Counts

93 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	1440
1	160	1278
2	453	1262
3	1965	1262
4	3721	1259
5	4907	1259
6	4993	1259
7	4923	1259

prune49.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	52	5	57

Error

0.5b

Counts

57 → 5

Alt Table

Status	Error	Program
	11.1b	(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3)))
	10.9b	(cbrt.f64 (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
▶	1.8b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	17.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 525 to 341 computations (35% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
13.3b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
13.3b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite52.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

4 → 44

Calls

4 calls:

4.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
1.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 1179 to 756 computations (35.9% saved)

series65.0ms (2.4%)

Error

0.5b

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
22.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
5.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
5.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 606 to 415 computations (31.5% saved)

simplify136.0ms (5%)

Algorithm

1×	egg-herbie

Rules

552×	`associate-l_binary64`
370×	`distribute-rgt-in_binary64`
364×	`*-commutative_binary64`
343×	`distribute-lft-in_binary64`
297×	`associate-/l*_binary64`

Counts

56 → 20

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	930
1	40	828
2	98	828
3	312	828
4	1154	820
5	3092	820
6	4510	820
7	4962	820
8	4767	820

prune15.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	19	6	25

Error

0.5b

Counts

25 → 6

Alt Table

Status	Error	Program
	11.1b	(atan2.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 N N N)) 3)))
	10.9b	(cbrt.f64 (*.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	1.8b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	2.4b	(.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2/3)) (cbrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	17.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 423 to 279 computations (34% saved)

regimes174.0ms (6.3%)

Accuracy

Total 0.0b remaining (5.1%)

Threshold costs 0.0b (5.1%)

Compiler

Compiled 2991 to 2091 computations (30.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	9	11
2	8	11

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample1.3s (45.7%)

Algorithm

1×

intervals

Results

511.0ms	2117×	body	2048	valid
186.0ms	1065×	body	1024	valid
182.0ms	4065×	body	128	valid
61.0ms	526×	body	512	valid
20.0ms	227×	body	256	valid

Compiler

Compiled 126 to 88 computations (30.2% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze21.0ms (0.8%)

sample43.0ms (1.6%)

simplify19.0ms (0.7%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite43.0ms (1.6%)

series8.0ms (0.3%)

simplify93.0ms (3.4%)

prune12.0ms (0.4%)

localize8.0ms (0.3%)

rewrite71.0ms (2.6%)

series31.0ms (1.1%)

simplify126.0ms (4.6%)

prune23.0ms (0.8%)

localize14.0ms (0.5%)

rewrite178.0ms (6.5%)

series63.0ms (2.3%)

simplify216.0ms (7.9%)

prune49.0ms (1.8%)

localize15.0ms (0.6%)

rewrite52.0ms (1.9%)

series65.0ms (2.4%)

simplify136.0ms (5%)

prune15.0ms (0.6%)

regimes174.0ms (6.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (45.7%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11