Details

analyze755.0ms (12.3%)

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 20 to 16 computations (20% saved)

sample93.0ms (1.5%)

Algorithm

1×

intervals

Results

21.0ms	40×	body	1280	invalid
17.0ms	41×	body	1280	valid
11.0ms	157×	body	80	valid
11.0ms	36×	body	640	valid
10.0ms	32×	body	640	invalid
3.0ms	15×	body	320	invalid
3.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	15×	body	80	invalid
1.0ms	6×	body	160	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune8.0ms (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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

2 → 83

Calls

2 calls:

12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series58.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

42.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
16.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6141	2187

prune95.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 0.0b

Counts

91 → 8

Compiler

Compiled 2208 to 873 computations (60.5% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

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

0.2b

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

rewrite63.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
110×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
90×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
67×	`associate-r_binary64`
47×	`sqrt-prod_binary64`
31×	`add-exp-log_binary64`
22×	`div-inv_binary64`
19×	`add-cbrt-cube_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r_binary64` `associate-/l_binary64`
7×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
3×	`associate-/l/_binary64` `add-log-exp_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

3 → 214

Calls

3 calls:

27.0ms

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

14.0ms

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

11.0ms

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

series98.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

41.0ms

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

39.0ms

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

18.0ms

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

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5391	7868

prune256.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	223	8	231

Merged error: 0b

Counts

231 → 8

Compiler

Compiled 7322 to 4109 computations (43.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(*.f64 (cos.f64 th) (/.f64 (*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

0.2b

(/.f64 (*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))

0.4b

(*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`add-exp-log_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-r_binary64`
12×	`add-cbrt-cube_binary64`
9×	`associate-/r_binary64` `associate-l*_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-*r/_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `div-inv_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64`

Counts

3 → 94

Calls

3 calls:

12.0ms

(*.f64 (cos.f64 th) (/.f64 (*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

10.0ms

(/.f64 (*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))

8.0ms

(*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

series120.0ms (2%)

Counts

3 → 9

Calls

3 calls:

75.0ms

(*.f64 (cos.f64 th) (/.f64 (*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

34.0ms

(/.f64 (*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))

12.0ms

(*.f64 (cbrt.f64 1/2) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4953	2415
1	4953	2415

prune100.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Merged error: 0b

Counts

111 → 8

Compiler

Compiled 2531 to 1378 computations (45.6% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(*.f64 (cos.f64 th) (*.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))))

0.3b

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

0.4b

(*.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
60×	`times-frac_binary64`
53×	`cbrt-prod_binary64`
47×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
32×	`associate-r_binary64`
23×	`sqrt-prod_binary64`
19×	`add-exp-log_binary64`
12×	`add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-/r_binary64` `associate-l*_binary64`
8×	`unswap-sqr_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64`
3×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/l_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

3 → 133

Calls

3 calls:

16.0ms

(*.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))

13.0ms

(*.f64 (cos.f64 th) (*.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))))

9.0ms

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

series141.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

76.0ms

(*.f64 (cos.f64 th) (*.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))))

37.0ms

(*.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))

28.0ms

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

simplify130.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4997	4094
1	4997	4094

prune112.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	142	8	150

Merged error: 0b

Counts

150 → 8

Compiler

Compiled 3857 to 1890 computations (51% saved)

regimes262.0ms (4.3%)

Compiler: Compiled 1078 to 810 computations (24.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms (0%)

sample3.4s (55.2%)

Algorithm

1×

intervals

Results

638.0ms	1437×	body	1280	valid
509.0ms	1146×	body	1280	invalid
359.0ms	1156×	body	640	valid
338.0ms	4562×	body	80	valid
292.0ms	933×	body	640	invalid
130.0ms	572×	body	320	valid
106.0ms	472×	body	320	invalid
41.0ms	273×	body	160	valid
39.0ms	503×	body	80	invalid
36.0ms	236×	body	160	invalid

Compiler

Compiled 213 to 162 computations (23.9% saved)

Details

analyze755.0ms (12.3%)

sample93.0ms (1.5%)

simplify15.0ms (0.3%)

prune8.0ms (0.1%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series58.0ms (0.9%)

simplify65.0ms (1.1%)

prune95.0ms (1.5%)

localize15.0ms (0.2%)

rewrite63.0ms (1%)

series98.0ms (1.6%)

simplify124.0ms (2%)

prune256.0ms (4.2%)

localize13.0ms (0.2%)

rewrite34.0ms (0.5%)

series120.0ms (2%)

simplify107.0ms (1.7%)

prune100.0ms (1.6%)

localize13.0ms (0.2%)

rewrite43.0ms (0.7%)

series141.0ms (2.3%)

simplify130.0ms (2.1%)

prune112.0ms (1.8%)

regimes262.0ms (4.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.4s (55.2%)

Profiling