Details

analyze21.0ms (0.8%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample34.0ms (1.3%)

Algorithm

1×

intervals

Results

14.0ms	66×	body	2048	valid
6.0ms	42×	body	1024	valid
5.0ms	135×	body	128	valid
1.0ms	9×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify14.0ms (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

14.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.1b	(-.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))
✓	1.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (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))

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))

simplify83.0ms (3.4%)

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 → 61

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 (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Error

0.5b

Counts

62 → 2

Alt Table

Status	Error	Program
	14.1b	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
▶	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 926 to 513 computations (44.6% 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))
✓	0.5b	(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)))

series5.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(+.f64 1 (fma.f64 N N N))
1.0ms	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

simplify78.0ms (3.1%)

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 → 69

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

prune47.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Error

0.5b

Counts

71 → 5

Alt Table

Status	Error	Program
▶	0.9b	(atan2.f64 1 (.f64 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
	14.1b	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
	1.9b	(.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)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	11.0b	(cbrt.f64 (.f64 (.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 877 to 532 computations (39.3% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(atan2.f64 1 (.f64 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
	16.0b	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
	16.0b	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
✓	16.0b	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`cbrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`cbrt-div_binary64`

Counts

2 → 25

Calls

2 calls:

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

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(cbrt.f64 (+.f64 1 (fma.f64 N N N)))
2.0ms	(atan2.f64 1 (.f64 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))

simplify101.0ms (4%)

Algorithm

1×	egg-herbie

Rules

949×	`fma-neg_binary64`
380×	`distribute-rgt-in_binary64`
264×	`distribute-lft-in_binary64`
212×	`sub-neg_binary64`
202×	`distribute-rgt-out_binary64`

Counts

49 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	781
1	165	748
2	381	734
3	1058	734
4	2267	734
5	4749	734
6	4950	734
7	4888	734

prune116.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	204	5	209

Error

0.5b

Counts

209 → 5

Alt Table

Status	Error	Program
✓	0.9b	(atan2.f64 1 (.f64 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
	14.1b	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
▶	1.9b	(.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)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	11.0b	(cbrt.f64 (.f64 (.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 3819 to 2208 computations (42.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	15.7b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
	15.7b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
✓	15.7b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

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

series540.0ms (21.7%)

Counts

1 → 12

Calls

1 calls:

540.0ms

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

simplify81.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-/r/_binary64`
618×	`log-prod_binary64`
449×	`associate-l_binary64`
350×	`distribute-rgt-out_binary64`
295×	`associate-r_binary64`

Counts

25 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	393
1	33	379
2	66	379
3	131	379
4	376	375
5	1656	375
6	2947	375
7	3840	375
8	5315	375

prune70.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	182	7	189

Error

0.5b

Counts

189 → 7

Alt Table

Status	Error	Program
✓	1.9b	(.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)))))
	2.1b	(.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 (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 (.f64 (cbrt.f64 (+.f64 1 (fma.f64 N N N))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (+.f64 1 (fma.f64 N N N)))))
	14.1b	(+.f64 (atan.f64 (+.f64 N 1)) (neg.f64 (atan.f64 N)))
	2.1b	(.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 (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)))))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	11.0b	(cbrt.f64 (.f64 (.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 2434 to 1501 computations (38.3% saved)

regimes64.0ms (2.6%)

Accuracy

Total 0.0b remaining (8.4%)

Threshold costs 0.0b (8.4%)

Compiler

Compiled 1312 to 830 computations (36.7% 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)

sample1.1s (45.9%)

Algorithm

1×

intervals

Results

422.0ms	2039×	body	2048	valid
179.0ms	4172×	body	128	valid
151.0ms	1080×	body	1024	valid
49.0ms	460×	body	512	valid
20.0ms	249×	body	256	valid

Compiler

Compiled 205 to 132 computations (35.6% 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

analyze21.0ms (0.8%)

sample34.0ms (1.3%)

simplify14.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite6.0ms (0.2%)

series3.0ms (0.1%)

simplify83.0ms (3.4%)

prune34.0ms (1.4%)

localize5.0ms (0.2%)

rewrite4.0ms (0.2%)

series5.0ms (0.2%)

simplify78.0ms (3.1%)

prune47.0ms (1.9%)

localize9.0ms (0.4%)

rewrite4.0ms (0.2%)

series7.0ms (0.3%)

simplify101.0ms (4%)

prune116.0ms (4.7%)

localize10.0ms (0.4%)

rewrite1.0ms (0.1%)

series540.0ms (21.7%)

simplify81.0ms (3.3%)

prune70.0ms (2.8%)

regimes64.0ms (2.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (45.9%)

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