Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample53.0ms (2.7%)

Algorithm

1×

intervals

Results

14.0ms	67×	body	2048	valid
6.0ms	40×	body	1024	valid
5.0ms	131×	body	128	valid
1.0ms	11×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify10.0ms (0.5%)

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 (0.1%)

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

15.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	15.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(-.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))

rewrite7.0ms (0.3%)

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))

simplify72.0ms (3.6%)

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 → 37

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

prune31.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	2	38

Error

0.4b

Counts

38 → 2

Alt Table

Status	Error	Program
	16.1b	(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
▶	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 796 to 422 computations (47% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 N N N))
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series4.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

2.0ms	(+.f64 1 (fma.f64 N N N))
1.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 1 (fma.f64 N N N))
0.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

simplify72.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

832×	`sub-neg_binary64`
634×	`distribute-rgt-in_binary64`
538×	`distribute-lft-in_binary64`
319×	`associate-l_binary64`
301×	`associate-r_binary64`

Counts

39 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	435
1	98	377
2	243	377
3	899	377
4	2950	377
5	4669	377
6	5438	377

prune41.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Error

0.4b

Counts

55 → 4

Alt Table

Status	Error	Program
▶	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
	16.1b	(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
	24.5b	(atan2.f64 1 (/.f64 (-.f64 1 (*.f64 (fma.f64 N N N) (fma.f64 N N N))) (-.f64 1 (fma.f64 N N N))))
	11.0b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))

Compiler

Compiled 786 to 476 computations (39.4% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 N (fma.f64 N N 1))
✓	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

series4.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

2.0ms	(+.f64 N (fma.f64 N N 1))
1.0ms	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 N (fma.f64 N N 1))
0.0ms	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))

simplify86.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

360×	`associate--r+_binary64`
356×	`associate-l_binary64`
276×	`associate-+l-_binary64`
256×	`associate-r_binary64`
239×	`associate--l+_binary64`

Counts

39 → 41

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	435
1	103	389
2	264	386
3	994	386
4	2167	381
5	4689	381
6	4925	381
7	4923	381

prune29.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Error

0.4b

Counts

45 → 4

Alt Table

Status	Error	Program
✓	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
	16.1b	(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
	24.5b	(atan2.f64 1 (/.f64 (-.f64 1 (*.f64 (fma.f64 N N N) (fma.f64 N N N))) (-.f64 1 (fma.f64 N N N))))
▶	11.0b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))

Compiler

Compiled 609 to 397 computations (34.8% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 N (fma.f64 N N 1))
	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
✓	0.6b	(pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3)
✓	11.0b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))

series13.0ms (0.7%)

Counts

2 → 12

Calls

2 calls:

11.0ms	(pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3)
2.0ms	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3))
2.0ms	(pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3)

simplify106.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-def_binary64`
494×	`log-prod_binary64`
433×	`exp-prod_binary64`
424×	`*-commutative_binary64`
389×	`pow-sqr_binary64`

Counts

60 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	1084
1	88	961
2	250	945
3	1121	945
4	2140	942
5	4066	942
6	4480	942
7	4908	942
8	4865	942

prune96.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	95	5	100

Error

0.4b

Counts

100 → 5

Alt Table

Status	Error	Program
	6.3b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1)))) 3)))
✓	0.4b	(atan2.f64 1 (+.f64 N (fma.f64 N N 1)))
	11.0b	(cbrt.f64 (*.f64 (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3/2) (pow.f64 (atan2.f64 1 (+.f64 N (fma.f64 N N 1))) 3/2)))
	16.1b	(expm1.f64 (log1p.f64 (-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))))
	24.5b	(atan2.f64 1 (/.f64 (-.f64 1 (*.f64 (fma.f64 N N N) (fma.f64 N N N))) (-.f64 1 (fma.f64 N N N))))

Compiler

Compiled 1775 to 1300 computations (26.8% saved)

regimes118.0ms (6%)

Accuracy

Total 0.0b remaining (5.4%)

Threshold costs 0.0b (5.4%)

Counts

65 → 1

Compiler

Compiled 2219 to 1521 computations (31.5% 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)

sample1.2s (60.4%)

Algorithm

1×

intervals

Results

476.0ms	2093×	body	2048	valid
184.0ms	4173×	body	128	valid
166.0ms	1004×	body	1024	valid
61.0ms	496×	body	512	valid
19.0ms	234×	body	256	valid

Compiler

Compiled 108 to 75 computations (30.6% 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 (0.1%)

sample53.0ms (2.7%)

simplify10.0ms (0.5%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series2.0ms (0.1%)

rewrite7.0ms (0.3%)

simplify72.0ms (3.6%)

prune31.0ms (1.6%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify72.0ms (3.7%)

prune41.0ms (2.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify86.0ms (4.3%)

prune29.0ms (1.5%)

localize7.0ms (0.4%)

series13.0ms (0.7%)

rewrite6.0ms (0.3%)

simplify106.0ms (5.4%)

prune96.0ms (4.9%)

regimes118.0ms (6%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (60.4%)

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