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)

sample60.0ms (1.9%)

Algorithm

1×

intervals

Results

16.0ms	63×	body	2048	valid
6.0ms	36×	body	1024	valid
5.0ms	130×	body	128	valid
2.0ms	14×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% 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

prune2.0ms (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

16.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	2.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series4.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

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

rewrite5.0ms (0.2%)

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 (2.2%)

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

prune29.0ms (0.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

49 → 1

Alt Table

Status	Error	Program
▶	0.2b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 908 to 499 computations (45% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series2.0ms (0%)

Counts

1 → 0

Calls

1 calls:

2.0ms

(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)))

simplify133.0ms (4.1%)

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

prune9.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	8	2	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	3	11

Error

0.2b

Counts

11 → 3

Alt Table

Status	Error	Program
✓	0.2b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶	0.8b	(*.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)))))
	1.5b	(.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))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 256 to 158 computations (38.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(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)))))
✓	13.9b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series8.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

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

simplify108.0ms (3.3%)

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 (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

0.1b

Counts

114 → 7

Alt Table

Status	Error	Program
	1.5b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 5/2) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓	0.2b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	1.7b	(.f64 (.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.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))))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
▶	1.1b	(.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))))))
✓	0.8b	(*.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)))))
	11.2b	(cbrt.f64 (.f64 (.f64 (.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))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (*.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))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	1.5b	(*.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)))))

Compiler

Compiled 3170 to 1979 computations (37.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.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)))))
✓	7.7b	(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))))))
	13.9b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
✓	14.5b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series1.2s (35.9%)

Counts

3 → 36

Calls

3 calls:

443.0ms

(*.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)))))

364.0ms

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

350.0ms

(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))))))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
18×	`pow1_binary64`
13×	`pow1/3_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 76

Calls

3 calls:

4.0ms

(*.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)))))

3.0ms

(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))))))

1.0ms

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

simplify111.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

820×	`log-prod_binary64`
571×	`distribute-rgt-in_binary64`
532×	`distribute-lft-in_binary64`
455×	`unswap-sqr_binary64`
364×	`fma-def_binary64`

Counts

112 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	69	2013
1	100	1827
2	259	1769
3	583	1735
4	1457	1483
5	3368	1483
6	4299	1483
7	4805	1483

prune170.0ms (5.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	138	7	145

Error

0.1b

Counts

145 → 7

Alt Table

Status	Error	Program
	1.5b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 5/2) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
	8.0b	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 2))) (.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))))))
✓	0.2b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	1.7b	(.f64 (.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (*.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))))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓	1.1b	(.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))))))
✓	0.8b	(*.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)))))
	1.5b	(*.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)))))

Compiler

Compiled 6843 to 4303 computations (37.1% saved)

regimes88.0ms (2.7%)

Accuracy

Total 0.0b remaining (9.1%)

Threshold costs 0.0b (9.1%)

Counts

45 → 1

Compiler

Compiled 2676 to 1714 computations (35.9% 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

end0.0ms (0%)

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

sample1.1s (33.7%)

Algorithm

1×

intervals

Results

429.0ms	2163×	body	2048	valid
158.0ms	4135×	body	128	valid
134.0ms	957×	body	1024	valid
55.0ms	492×	body	512	valid
19.0ms	253×	body	256	valid

Compiler

Compiled 212 to 142 computations (33% 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%)

sample60.0ms (1.9%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify72.0ms (2.2%)

prune29.0ms (0.9%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify133.0ms (4.1%)

prune9.0ms (0.3%)

localize6.0ms (0.2%)

series8.0ms (0.2%)

rewrite11.0ms (0.3%)

simplify108.0ms (3.3%)

prune116.0ms (3.6%)

localize11.0ms (0.4%)

series1.2s (35.9%)

rewrite13.0ms (0.4%)

simplify111.0ms (3.4%)

prune170.0ms (5.3%)

regimes88.0ms (2.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (33.7%)

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