Details

analyze25.0ms (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)

sample38.0ms (1.5%)

Algorithm

1×

intervals

Results

18.0ms	71×	body	2048	valid
5.0ms	123×	body	128	valid
5.0ms	32×	body	1024	valid
2.0ms	21×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify15.0ms (0.6%)

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

16.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.4b	(-.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
✓	0.7b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 31

Calls

1 calls:

3.0ms

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

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

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

simplify77.0ms (3.1%)

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

31 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	753
1	125	472
2	351	418
3	1250	415
4	2898	415
5	4629	415
6	4801	415

prune23.0ms (0.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	1	51

Error

0.9b

Counts

51 → 1

Alt Table

Status	Error	Program
▶	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 776 to 406 computations (47.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.9b	(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)))

series1.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

1.0ms

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

simplify153.0ms (6%)

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 (0.4%)

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

0.9b

Counts

11 → 3

Alt Table

Status	Error	Program
▶	1.5b	(*.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)))))
	2.2b	(.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)))))
✓	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 256 to 158 computations (38.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
✓	15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

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

series7.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

7.0ms

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

simplify164.0ms (6.5%)

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

15 → 19

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	238
1	31	228
2	40	228
3	51	228
4	64	228
5	71	228
6	103	228
7	167	228
8	345	228
9	651	228
10	653	228
11	783	228
12	937	228
13	1105	228
14	1334	228
15	1635	228
16	1983	228
17	2458	228
18	3076	228
19	3272	228
20	3446	228
21	3560	228
22	3607	228
23	3659	228
24	4537	228
25	4840	228

prune66.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	65	6	71

Error

0.9b

Counts

71 → 6

Alt Table

Status	Error	Program
▶	1.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (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)))))
	2.3b	(.f64 (.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)))))) (cbrt.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)))))
	2.2b	(.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)))))
	6.1b	(.f64 (cbrt.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)))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	1.9b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (.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)))))))
✓	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 1730 to 1074 computations (37.9% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
	15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
	15.6b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune92.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	306	6	312

Error

0.9b

Counts

312 → 6

Alt Table

Status	Error	Program
✓	0.9b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	5.7b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))
✓	1.1b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (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)))))
	2.3b	(.f64 (.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)))))) (cbrt.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)))))
	2.2b	(.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)))))
	1.9b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (.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 2394 to 1517 computations (36.6% saved)

regimes100.0ms (4%)

Accuracy

Total 0.0b remaining (9.5%)

Threshold costs 0.0b (9.5%)

Compiler

Compiled 2398 to 1562 computations (34.9% 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)

sample1.7s (67.3%)

Algorithm

1×

intervals

Results

704.0ms	2125×	body	2048	valid
269.0ms	4176×	body	128	valid
226.0ms	984×	body	1024	valid
80.0ms	475×	body	512	valid
30.0ms	240×	body	256	valid

Compiler

Compiled 209 to 138 computations (34% 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

analyze25.0ms (1%)

sample38.0ms (1.5%)

simplify15.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite6.0ms (0.2%)

series3.0ms (0.1%)

simplify77.0ms (3.1%)

prune23.0ms (0.9%)

localize5.0ms (0.2%)

rewrite1.0ms (0%)

series1.0ms (0.1%)

simplify153.0ms (6%)

prune10.0ms (0.4%)

localize9.0ms (0.3%)

rewrite2.0ms (0.1%)

series7.0ms (0.3%)

simplify164.0ms (6.5%)

prune66.0ms (2.6%)

localize10.0ms (0.4%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify11.0ms (0.4%)

prune92.0ms (3.6%)

regimes100.0ms (4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (67.3%)

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