Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.1s (58.7%)

Results

1.5s	2143×	body	2048	valid
646.0ms	4286×	body	128	valid
608.0ms	1033×	body	1024	valid
216.0ms	527×	body	512	valid
73.0ms	267×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify20.0ms (0.4%)

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 → 1

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

prune3.0ms (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

17.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.4b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series5.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
2.0ms	(atan.f64 (+.f64 N 1))

rewrite72.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
688×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
75×	`add-log-exp_binary64`

Counts

2 → 68

Calls

2 calls:

68.0ms	(atan.f64 (+.f64 N 1))
68.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	17
2	2004	17
3	6328	17
0	0	0
1	0	0

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune100.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Error

16.5b

Counts

69 → 3

Alt Table

Status	Error	Program
▶	16.8b	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
	34.4b	(-.f64 (cbrt.f64 (pow.f64 (atan.f64 (+.f64 N 1)) 3)) (atan.f64 N))
	35.3b	(-.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 3) (atan.f64 N))

Compiler

Compiled 1133 to 714 computations (37% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 N (+.f64 N 1))
✓	0.0b	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
✓	4.1b	(-.f64 (+.f64 N 1) N)

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
4.0ms	(*.f64 N (+.f64 N 1))
2.0ms	(-.f64 (+.f64 N 1) N)

rewrite147.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

544×	`fma-def_binary64`
410×	`log-prod_binary64`
270×	`fma-neg_binary64`
192×	`egg-rr`
160×	`log1p-udef_binary64`

Counts

3 → 192

Calls

3 calls:

140.0ms	(*.f64 N (+.f64 N 1))
140.0ms	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
140.0ms	(-.f64 (+.f64 N 1) N)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	183	29
2	2391	29
3	4988	29
4	4991	29
0	0	0
1	0	0

simplify202.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
903×	`fma-def_binary64`
579×	`fabs-mul_binary64`
572×	`cube-prod_binary64`
536×	`pow-sqr_binary64`

Counts

228 → 199

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	240
1	20	198
2	31	198
3	50	198
4	99	198
5	221	198
6	599	198
7	1229	198
8	1384	198
9	1541	198
10	1726	198
11	1934	198
12	2129	198
13	2410	198
14	2837	198
15	3433	198
16	4128	198
17	4348	198
18	4592	198
19	4677	198
20	4710	198
21	4731	198
22	5297	198

prune224.0ms (4.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	200	2	202

Error

0.5b

Counts

202 → 2

Alt Table

Status	Error	Program
	0.5b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
▶	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 3971 to 2490 computations (37.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 N (+.f64 N 1))
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite77.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
565×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
70×	`add-log-exp_binary64`

Counts

1 → 18

Calls

1 calls:

76.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	152	11
2	1863	11
3	5646	11
0	0	0
1	0	0

simplify183.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
1103×	`fma-def_binary64`
573×	`fabs-mul_binary64`
572×	`cube-prod_binary64`
536×	`pow-sqr_binary64`

Counts

30 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	156
1	18	132
2	29	132
3	46	132
4	85	132
5	196	132
6	554	132
7	1162	132
8	1341	132
9	1522	132
10	1723	132
11	1928	132
12	2125	132
13	2410	132
14	2837	132
15	3433	132
16	4128	132
17	4348	132
18	4592	132
19	4677	132
20	4710	132
21	4731	132
22	5297	132

prune122.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Error

0.5b

Counts

78 → 6

Alt Table

Status	Error	Program
	0.9b	(atan2.f64 1 (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))
▶	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 (.f64 N N)) (.f64 (cbrt.f64 N) N) N)))
	25.5b	(atan2.f64 1 (+.f64 1 (fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))
	34.0b	(atan2.f64 1 (+.f64 1 (fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))
	1.0b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 1158 to 702 computations (39.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 N) N)
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 (.f64 N N)) (.f64 (cbrt.f64 N) N) N)))
✓	0.5b	(cbrt.f64 N)
✓	29.6b	(cbrt.f64 (*.f64 N N))

series198.0ms (3.8%)

Counts

4 → 48

Calls

4 calls:

70.0ms	(*.f64 (cbrt.f64 N) N)
61.0ms	(cbrt.f64 N)
59.0ms	(cbrt.f64 (*.f64 N N))
8.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 (.f64 N N)) (.f64 (cbrt.f64 N) N) N)))

rewrite96.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

791×	`log1p-expm1-u_binary64`
791×	`expm1-log1p-u_binary64`
565×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

93.0ms	(*.f64 (cbrt.f64 N) N)
93.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 (.f64 N N)) (.f64 (cbrt.f64 N) N) N)))
93.0ms	(cbrt.f64 N)
93.0ms	(cbrt.f64 (*.f64 N N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	195	24
2	2039	24
3	5845	24
0	0	0
1	0	0

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

939×	`unswap-sqr_binary64`
704×	`fma-def_binary64`
428×	`*-commutative_binary64`
380×	`distribute-lft-neg-in_binary64`
369×	`distribute-rgt-neg-in_binary64`

Counts

132 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	520
1	59	516
2	127	516
3	340	516
4	1141	508
5	2223	508
6	4904	508
7	4906	508

prune150.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	95	6	101

Error

0.5b

Counts

101 → 6

Alt Table

Status	Error	Program
	0.9b	(atan2.f64 1 (+.f64 1 (pow.f64 (cbrt.f64 (fma.f64 N N N)) 3)))
✓	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 (.f64 N N)) (.f64 (cbrt.f64 N) N) N)))
	25.5b	(atan2.f64 1 (+.f64 1 (fma.f64 (-.f64 1 (pow.f64 (fma.f64 N N N) 2)) (/.f64 1 (-.f64 1 (fma.f64 N N N))) -1)))
	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 (.f64 N N)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 N)) 3) N) N)))
	1.0b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
✓	0.5b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 1610 to 944 computations (41.4% saved)

regimes206.0ms (3.9%)

Accuracy

Total 0.0b remaining (9.9%)

Threshold costs 0.0b (9.9%)

Counts

67 → 1

Compiler

Compiled 1888 to 1404 computations (25.6% 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

end186.0ms (3.6%)

Compiler: Compiled 108 to 77 computations (28.7% 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

analyze1.0ms (0%)

sample3.1s (58.7%)

simplify20.0ms (0.4%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series5.0ms (0.1%)

rewrite72.0ms (1.4%)

simplify12.0ms (0.2%)

prune100.0ms (1.9%)

localize15.0ms (0.3%)

series9.0ms (0.2%)

rewrite147.0ms (2.8%)

simplify202.0ms (3.9%)

prune224.0ms (4.3%)

localize9.0ms (0.2%)

series4.0ms (0.1%)

rewrite77.0ms (1.5%)

simplify183.0ms (3.5%)

prune122.0ms (2.3%)

localize16.0ms (0.3%)

series198.0ms (3.8%)

rewrite96.0ms (1.8%)

simplify95.0ms (1.8%)

prune150.0ms (2.9%)

regimes206.0ms (3.9%)

simplify3.0ms (0.1%)

end186.0ms (3.6%)

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