Details

analyze23.0ms (1%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample35.0ms (1.4%)

Algorithm

1×

intervals

Results

16.0ms	67×	body	2048	valid
6.0ms	138×	body	128	valid
5.0ms	33×	body	1024	valid
2.0ms	13×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify13.0ms (0.5%)

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 (0.1%)

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

13.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	13.6b	(-.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))
1.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite68.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

12.8b

Rules

21×	`add-cube-cbrt_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 75

Calls

2 calls:

15.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
8.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 1380 to 747 computations (45.9% saved)

series8.0ms (0.3%)

Error

13.6b

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)

simplify115.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

684×	`fma-neg_binary64`
533×	`cancel-sign-sub-inv_binary64`
248×	`div-sub_binary64`
243×	`associate-l_binary64`
230×	`distribute-rgt-neg-in_binary64`

Counts

81 → 24

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	1009
1	186	1003
2	544	966
3	1743	951
4	3777	945
5	4988	945
6	4743	945

prune14.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	1	25

Error

0.3b

Counts

25 → 1

Alt Table

Status	Error	Program
▶	0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 409 to 267 computations (34.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`log1p-expm1-u_binary64`

Counts

1 → 28

Calls

1 calls:

8.0ms

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

Compiler

Compiled 330 to 199 computations (39.7% saved)

series4.0ms (0.2%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

4.0ms

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

Compiler

Compiled 63 to 42 computations (33.3% saved)

simplify179.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1233×	`sqr-pow_binary64`
574×	`cube-prod_binary64`
530×	`pow-sqr_binary64`
518×	`fabs-mul_binary64`
374×	`unswap-sqr_binary64`

Counts

31 → 3

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	350
1	35	327
2	49	327
3	69	327
4	102	327
5	162	327
6	368	327
7	704	327
8	720	327
9	869	327
10	1046	327
11	1245	327
12	1517	327
13	1859	327
14	2243	327
15	2780	327
16	3068	327
17	3231	327
18	3341	327
19	3388	327
20	3437	327
21	4051	327
22	4697	327
23	4813	327

prune5.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	2	2	4

Error

0.3b

Counts

4 → 2

Alt Table

Status	Error	Program
✓	0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶	0.9b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 90 to 58 computations (35.6% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.7b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
15.1b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
15.1b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite140.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
23×	`pow1/2_binary64`
15×	`rem-sqrt-square_binary64`
14×	`pow1_binary64`

Counts

4 → 149

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
9.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
9.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
9.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 2860 to 1773 computations (38% saved)

series25.0ms (1%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

7.0ms	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
6.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
6.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
4.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 442 to 287 computations (35.1% saved)

simplify162.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
701×	`unswap-sqr_binary64`
689×	`log-prod_binary64`
508×	`exp-prod_binary64`
231×	`associate-l_binary64`

Counts

161 → 60

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	68	1950
1	99	1883
2	238	1863
3	716	1846
4	2193	1549
5	4152	1539
6	4959	1539
7	4976	1539
8	5019	1539

prune36.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	57	5	62

Error

0.2b

Counts

62 → 5

Alt Table

Status	Error	Program
	2.2b	(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 5) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
	1.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
▶	1.6b	(*.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)))))
✓	0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.9b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 1059 to 668 computations (36.9% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
15.6b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
15.6b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite115.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

24×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 116

Calls

4 calls:

11.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
9.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
9.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
8.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 2188 to 1413 computations (35.4% saved)

series48.0ms (2%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
16.0ms	(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)

simplify129.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

478×	`distribute-rgt-in_binary64`
456×	`distribute-lft-in_binary64`
411×	`associate-+l+_binary64`
334×	`associate-+r+_binary64`
312×	`associate-/l/_binary64`

Counts

128 → 36

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	40	1474
1	60	1284
2	132	1260
3	434	1260
4	1097	1260
5	3433	1256
6	4615	1256
7	4983	1256
8	4798	1256

prune21.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	36	5	41

Error

0.2b

Counts

41 → 5

Alt Table

Status	Error	Program
	2.2b	(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 5) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
	1.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
	1.6b	(*.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)))))
	0.3b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	0.9b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 743 to 485 computations (34.7% saved)

regimes114.0ms (4.6%)

Accuracy

Total 0.0b remaining (7.6%)

Threshold costs 0.0b (7.6%)

Compiler

Compiled 2438 to 1718 computations (29.5% 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)

sample1.2s (46.9%)

Algorithm

1×

intervals

Results

462.0ms	2215×	body	2048	valid
165.0ms	4050×	body	128	valid
149.0ms	982×	body	1024	valid
61.0ms	496×	body	512	valid
24.0ms	257×	body	256	valid

Compiler

Compiled 128 to 88 computations (31.3% 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

analyze23.0ms (1%)

sample35.0ms (1.4%)

simplify13.0ms (0.5%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

rewrite68.0ms (2.8%)

series8.0ms (0.3%)

simplify115.0ms (4.7%)

prune14.0ms (0.6%)

localize5.0ms (0.2%)

rewrite19.0ms (0.8%)

series4.0ms (0.2%)

simplify179.0ms (7.3%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

rewrite140.0ms (5.7%)

series25.0ms (1%)

simplify162.0ms (6.6%)

prune36.0ms (1.4%)

localize9.0ms (0.4%)

rewrite115.0ms (4.7%)

series48.0ms (2%)

simplify129.0ms (5.2%)

prune21.0ms (0.9%)

regimes114.0ms (4.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (46.9%)

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