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)

sample1.9s (59.1%)

Results

946.0ms	2269×	body	2048	valid
408.0ms	4184×	body	128	valid
321.0ms	1014×	body	1024	valid
143.0ms	562×	body	512	valid
37.0ms	227×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.3%)

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

prune1.0ms (0%)

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

14.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.8b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.8b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series2.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

2.0ms

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

rewrite49.0ms (1.5%)

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

1 → 51

Calls

1 calls:

48.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	156	11
2	2004	11
3	6328	11
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune48.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Error

13.3b

Counts

52 → 4

Alt Table

Status	Error	Program
▶	13.5b	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
	33.3b	(fma.f64 (sqrt.f64 (atan.f64 (+.f64 N 1))) (sqrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
	32.9b	(fma.f64 (pow.f64 (cbrt.f64 (atan.f64 (+.f64 N 1))) 2) (cbrt.f64 (atan.f64 (+.f64 N 1))) (neg.f64 (atan.f64 N)))
	48.0b	(+.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N)) (fma.f64 (neg.f64 (sqrt.f64 (atan.f64 N))) (sqrt.f64 (atan.f64 N)) (atan.f64 N)))

Compiler

Compiled 1005 to 618 computations (38.5% saved)

localize6.0ms (0.2%)

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))))
✓	2.2b	(-.f64 (+.f64 N 1) N)

series5.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

2.0ms	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
2.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(-.f64 (+.f64 N 1) N)

rewrite92.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 194

Calls

3 calls:

89.0ms	(*.f64 N (+.f64 N 1))
89.0ms	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (*.f64 N (+.f64 N 1))))
89.0ms	(-.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

simplify168.0ms (5.2%)

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

230 → 201

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

prune130.0ms (4.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	201	4	205

Error

0.6b

Counts

205 → 4

Alt Table

Status	Error	Program
	13.5b	(atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (/.f64 (*.f64 (fma.f64 N N -1) N) (-.f64 N 1))))
	14.0b	(pow.f64 (sqrt.f64 (atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (fma.f64 N N N)))) 2)
	14.5b	(pow.f64 (cbrt.f64 (atan2.f64 (-.f64 (+.f64 N 1) N) (+.f64 1 (fma.f64 N N N)))) 3)
▶	0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 4080 to 2563 computations (37.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 N (+.f64 N 1))
✓	0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

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

rewrite47.0ms (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 → 19

Calls

1 calls:

47.0ms

(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

simplify159.0ms (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

31 → 21

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

prune58.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Error

0.5b

Counts

81 → 5

Alt Table

Status	Error	Program
	1.8b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓	0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
	35.3b	(atan2.f64 1 (+.f64 1 (fma.f64 (*.f64 N (sqrt.f64 N)) (sqrt.f64 N) N)))
▶	0.7b	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 N (cbrt.f64 (.f64 N N))) (cbrt.f64 N) N)))
	1.1b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)

Compiler

Compiled 1120 to 674 computations (39.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 N (cbrt.f64 (.f64 N N)))
✓	0.6b	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 N (cbrt.f64 (.f64 N N))) (cbrt.f64 N) N)))
✓	0.6b	(cbrt.f64 N)
✓	30.4b	(cbrt.f64 (*.f64 N N))

series96.0ms (3%)

Counts

4 → 48

Calls

4 calls:

34.0ms	(cbrt.f64 (*.f64 N N))
29.0ms	(cbrt.f64 N)
27.0ms	(.f64 N (cbrt.f64 (.f64 N N)))
6.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 N (cbrt.f64 (.f64 N N))) (cbrt.f64 N) N)))

rewrite53.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

817×	`log1p-expm1-u_binary64`
817×	`expm1-log1p-u_binary64`
569×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Counts

4 → 86

Calls

4 calls:

52.0ms	(.f64 N (cbrt.f64 (.f64 N N)))
52.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 (.f64 N (cbrt.f64 (.f64 N N))) (cbrt.f64 N) N)))
52.0ms	(cbrt.f64 N)
52.0ms	(cbrt.f64 (*.f64 N N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	195	31
2	2123	31
3	6003	31
0	0	0
1	0	0

simplify99.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
484×	`*-commutative_binary64`
362×	`fma-neg_binary64`
299×	`associate-l_binary64`
268×	`neg-sub0_binary64`

Counts

134 → 97

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	500
1	63	484
2	129	484
3	340	484
4	1152	476
5	2095	476
6	3127	476
7	4206	476
8	4784	476
9	4987	476
10	4767	476

prune71.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	97	5	102

Error

0.5b

Counts

102 → 5

Alt Table

Status	Error	Program
	8.0b	(atan2.f64 1 (+.f64 1 (fma.f64 (cbrt.f64 N) (cbrt.f64 (pow.f64 N 5)) N)))
	1.1b	(pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2)
	1.8b	(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)
✓	0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
	0.8b	(atan2.f64 1 (+.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (.f64 N (cbrt.f64 (.f64 N N)))) 3) (cbrt.f64 N) N)))

Compiler

Compiled 1637 to 848 computations (48.2% saved)

regimes98.0ms (3.1%)

Accuracy

Total 0.0b remaining (6.9%)

Threshold costs 0.0b (6.9%)

Counts

46 → 1

Compiler

Compiled 1664 to 1195 computations (28.2% saved)

simplify2.0ms (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

end85.0ms (2.6%)

Compiler: Compiled 83 to 61 computations (26.5% 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%)

sample1.9s (59.1%)

simplify10.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite49.0ms (1.5%)

simplify6.0ms (0.2%)

prune48.0ms (1.5%)

localize6.0ms (0.2%)

series5.0ms (0.2%)

rewrite92.0ms (2.9%)

simplify168.0ms (5.2%)

prune130.0ms (4.1%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite47.0ms (1.5%)

simplify159.0ms (5%)

prune58.0ms (1.8%)

localize9.0ms (0.3%)

series96.0ms (3%)

rewrite53.0ms (1.7%)

simplify99.0ms (3.1%)

prune71.0ms (2.2%)

regimes98.0ms (3.1%)

simplify2.0ms (0.1%)

end85.0ms (2.6%)

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