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)

sample2.2s (55.7%)

Results

1.0s	2164×	body	2048	valid
525.0ms	4222×	body	128	valid
376.0ms	1068×	body	1024	valid
139.0ms	543×	body	512	valid
51.0ms	259×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (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

prune2.0ms (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

17.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.3b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series3.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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))

simplify72.0ms (1.9%)

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

40 → 48

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	72	836
1	128	555
2	354	501
3	1262	498
4	2924	498
5	4651	491
6	4824	491

prune34.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	2	49

Error

0.1b

Counts

49 → 2

Alt Table

Status	Error	Program
▶	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	17.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 916 to 505 computations (44.9% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series2.0ms (0%)

Counts

1 → 0

Calls

1 calls:

1.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 9

Calls

1 calls:

0.0ms

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

simplify132.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

9 → 10

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	156
1	21	133
2	29	133
3	41	133
4	54	133
5	61	133
6	93	133
7	157	133
8	335	133
9	641	133
10	645	133
11	775	133
12	929	133
13	1097	133
14	1326	133
15	1627	133
16	1975	133
17	2450	133
18	3068	133
19	3264	133
20	3438	133
21	3552	133
22	3599	133
23	3651	133
24	4529	133
25	4833	133

prune10.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	9	1	10
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	10	2	12

Error

0.1b

Counts

12 → 2

Alt Table

Status	Error	Program
✓	0.1b	(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)))))

Compiler

Compiled 196 to 120 computations (38.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.6b	(*.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)))))
✓	14.9b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series6.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
3.0ms	(*.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)))))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(*.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)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify113.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

498×	`log-prod_binary64`
465×	`*-commutative_binary64`
441×	`unswap-sqr_binary64`
425×	`log-div_binary64`
306×	`sqr-pow_binary64`

Counts

80 → 75

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	52	1385
1	75	1281
2	181	1233
3	389	1149
4	720	1054
5	1324	1054
6	2519	1040
7	4285	1040
8	4994	1040
9	4835	1040

prune116.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	109	4	113

Error

0.0b

Counts

113 → 4

Alt Table

Status	Error	Program
✓	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	1.0b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
▶	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (sqrt.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))))))
✓	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)))))

Compiler

Compiled 2936 to 1827 computations (37.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.1b	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (sqrt.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))))))
✓	0.2b	(*.f64 (sqrt.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)))))
	14.9b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series496.0ms (12.8%)

Counts

2 → 24

Calls

2 calls:

491.0ms

(*.f64 (sqrt.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)))))

4.0ms

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

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-pow1_binary64`
48×	`pow1_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`sqrt-prod_binary64`
36×	`pow-prod-up_binary64`

Counts

2 → 100

Calls

2 calls:

16.0ms

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

7.0ms

(*.f64 (sqrt.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)))))

simplify149.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

429×	`unswap-sqr_binary64`
359×	`log-div_binary64`
358×	`cube-div_binary64`
273×	`associate-*r/_binary64`
260×	`log-prod_binary64`

Counts

124 → 118

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	81	2735
1	137	2079
2	289	1866
3	393	1866
4	720	1832
5	1102	1828
6	2665	1828
7	3886	1705
8	4933	1705
9	4882	1705

prune224.0ms (5.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	194	6	200

Error

0.0b

Counts

200 → 6

Alt Table

Status	Error	Program
	0.3b	(pow.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 4)
✓	0.1b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	1.0b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (sqrt.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))))))
✓	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)))))
	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) 7/2))

Compiler

Compiled 6999 to 4490 computations (35.8% saved)

regimes151.0ms (3.9%)

Accuracy

Total 0.0b remaining (10.1%)

Threshold costs 0.0b (10.1%)

Counts

66 → 1

Compiler

Compiled 3502 to 2358 computations (32.7% saved)

simplify2.0ms (0%)

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

end117.0ms (3%)

Compiler: Compiled 159 to 107 computations (32.7% 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%)

sample2.2s (55.7%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify72.0ms (1.9%)

prune34.0ms (0.9%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify132.0ms (3.4%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series6.0ms (0.2%)

rewrite11.0ms (0.3%)

simplify113.0ms (2.9%)

prune116.0ms (3%)

localize9.0ms (0.2%)

series496.0ms (12.8%)

rewrite34.0ms (0.9%)

simplify149.0ms (3.9%)

prune224.0ms (5.8%)

regimes151.0ms (3.9%)

simplify2.0ms (0%)

end117.0ms (3%)

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