Details

analyze2.2s (11.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample226.0ms (1.2%)

Algorithm

1×

intervals

Results

51.0ms	54×	body	1024	valid
50.0ms	55×	body	1024	invalid
35.0ms	159×	body	128	valid
17.0ms	30×	body	512	valid
10.0ms	18×	body	512	invalid
6.0ms	16×	body	256	invalid
5.0ms	13×	body	256	valid
4.0ms	17×	body	128	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series152.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

111.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
41.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

2 → 85

Calls

2 calls:

15.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify190.0ms (1%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

145 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3315
1	365	3012
2	1289	2968
3	4359	2968
4	5076	2968

prune294.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	142	9	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	144	9	153

Error

Counts

153 → 9

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	1.4b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1)))) (fabs.f64 (cbrt.f64 2)))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3825 to 1822 computations (52.4% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series112.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

112.0ms

(*.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`associate-l_binary64`
20×	`times-frac_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 44

Calls

1 calls:

14.0ms

(*.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))

simplify130.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

454×	`associate-l_binary64`
393×	`unswap-sqr_binary64`
389×	`associate-r_binary64`
331×	`fma-neg_binary64`
310×	`times-frac_binary64`

Counts

80 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2273
1	324	2099
2	994	1695
3	3622	1695
4	5155	1695

prune285.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	154	9	163

Error

Counts

163 → 9

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	1.4b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (fma.f64 a2 a2 (.f64 a1 a1)))) (fabs.f64 (cbrt.f64 2)))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3895 to 1859 computations (52.3% saved)

localize23.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
✓	0.2b	(/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
✓	0.3b	(/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

series745.0ms (4%)

Counts

3 → 84

Calls

3 calls:

594.0ms

(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

107.0ms

(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

43.0ms

(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite139.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
110×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
90×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`

Counts

3 → 218

Calls

3 calls:

47.0ms

(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

17.0ms

(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

13.0ms

(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

simplify500.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
500×	`associate-/r/_binary64`
260×	`fma-def_binary64`
191×	`associate-/l*_binary64`
181×	`associate-/l/_binary64`

Counts

302 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	9806
1	697	8974
2	2581	8924
3	4583	8924
4	5353	8924

prune734.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	363	2	365
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	366	8	374

Error

Counts

374 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
✓	0.4b	(.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))

Compiler

Compiled 12799 to 8109 computations (36.6% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a2 a2 (*.f64 a1 a1))
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
✓	0.3b	(/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
✓	0.4b	(.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))

series1.3s (6.7%)

Counts

4 → 108

Calls

4 calls:

833.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
370.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
34.0ms	(.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
12.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
18×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`

Counts

4 → 106

Calls

4 calls:

17.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
7.0ms	(.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
1.0ms	(fma.f64 a2 a2 (*.f64 a1 a1))

simplify287.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-def_binary64`
452×	`fma-neg_binary64`
290×	`cancel-sign-sub-inv_binary64`
284×	`associate-l_binary64`
258×	`distribute-rgt-in_binary64`

Counts

214 → 204

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	5022
1	472	4392
2	1984	4275
3	4663	4273
4	4983	4273

prune402.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	206	6	212

Error

Counts

212 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (cos.f64 th) (/.f64 (cbrt.f64 1/2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))))
	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.4b	(.f64 (.f64 (cos.f64 th) (.f64 (cbrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))) (/.f64 1 (cbrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.4b	(.f64 (.f64 (cbrt.f64 1/2) (cos.f64 th)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2))))
	0.4b	(/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 2))

Compiler

Compiled 5042 to 2980 computations (40.9% saved)

regimes3.7s (19.6%)

Accuracy

Total 0.4b remaining (88.2%)

Threshold costs 0.4b (88.2%)

Counts

212 → 1

Compiler

Compiled 38940 to 27838 computations (28.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	17	25
2	17	25

end15.0ms (0.1%)

Compiler: Compiled 57 to 42 computations (26.3% saved)

sample7.1s (38.1%)

Algorithm

1×

intervals

Results

1.7s	1799×	body	1024	valid
1.6s	1585×	body	1024	invalid
895.0ms	4856×	body	128	valid
532.0ms	903×	body	512	valid
477.0ms	785×	body	512	invalid
169.0ms	438×	body	256	valid
161.0ms	420×	body	256	invalid
131.0ms	648×	body	128	invalid
10.0ms	4×	body	2048	valid

Compiler

Compiled 161 to 117 computations (27.3% saved)

Details

analyze2.2s (11.9%)

sample226.0ms (1.2%)

simplify20.0ms (0.1%)

prune7.0ms (0%)

localize17.0ms (0.1%)

series152.0ms (0.8%)

rewrite39.0ms (0.2%)

simplify190.0ms (1%)

prune294.0ms (1.6%)

localize17.0ms (0.1%)

series112.0ms (0.6%)

rewrite22.0ms (0.1%)

simplify130.0ms (0.7%)

prune285.0ms (1.5%)

localize23.0ms (0.1%)

series745.0ms (4%)

rewrite139.0ms (0.7%)

simplify500.0ms (2.7%)

prune734.0ms (3.9%)

localize27.0ms (0.1%)

series1.3s (6.7%)

rewrite47.0ms (0.3%)

simplify287.0ms (1.5%)

prune402.0ms (2.2%)

regimes3.7s (19.6%)

simplify4.0ms (0%)

end15.0ms (0.1%)

sample7.1s (38.1%)

Profiling