Details

analyze938.0ms (11.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	279	80
1	279	80
0	3	3
1	3	3

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)

sample88.0ms (1.1%)

Algorithm

1×

intervals

Results

20.0ms	61×	body	1024	valid
20.0ms	49×	body	1024	invalid
13.0ms	160×	body	128	valid
8.0ms	31×	body	512	invalid
5.0ms	21×	body	512	valid
2.0ms	14×	body	256	valid
2.0ms	19×	body	128	invalid
1.0ms	9×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.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))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_100`
38×	`times-frac_binary64_84`
32×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
22×	`sqrt-prod_binary64_94` `associate-r_binary64_18`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-/r*_binary64_22`
5×	`add-log-exp_binary64_117` `pow1_binary64_139`
3×	`associate-l_binary64_19` `associate-/l*_binary64_23` `unswap-sqr_binary64_46`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `flip-+_binary64_52` `div-inv_binary64_75` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `frac-2neg_binary64_89` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

3 → 94

Calls

3 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))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series236.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

160.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
55.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
21.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4977	2380
1	4977	2380

prune126.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Error

0.0b

Counts

105 → 7

Compiler

Compiled 2425 to 945 computations (61% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite88.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_100`
146×	`times-frac_binary64_84`
127×	`sqrt-prod_binary64_94`
90×	`cbrt-prod_binary64_109`
87×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
58×	`associate-r_binary64_18`
27×	`add-exp-log_binary64_116`
21×	`unswap-sqr_binary64_46`
19×	`add-cbrt-cube_binary64_114`
10×	`associate-l_binary64_19`
9×	`associate-/r*_binary64_22`
8×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `pow1_binary64_139`
6×	`associate-/l*_binary64_23` `sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117`
3×	`flip-+_binary64_52` `div-inv_binary64_75` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-/l/_binary64_25` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 226

Calls

4 calls:

38.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series228.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
59.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
24.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5181	8434

prune473.0ms (5.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	238	7	245

Error

0.0b

Counts

245 → 7

Compiler

Compiled 9735 to 4502 computations (53.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_100`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`add-log-exp_binary64_117` `pow1_binary64_139`
4×	`associate-*l/_binary64_21`
3×	`associate-l_binary64_19` `flip-+_binary64_52` `associate-r_binary64_18` `flip3-+_binary64_81`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

3 → 60

Calls

3 calls:

8.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series217.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

127.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
70.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
20.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4932	1303
1	4932	1303

prune70.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Error

Counts

76 → 7

Compiler

Compiled 1399 to 541 computations (61.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))

rewrite62.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64_100`
70×	`times-frac_binary64_84`
49×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
46×	`cbrt-prod_binary64_109`
32×	`add-exp-log_binary64_116`
31×	`associate-r_binary64_18`
23×	`sqrt-prod_binary64_94`
22×	`add-cbrt-cube_binary64_114`
10×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/r*_binary64_22`
9×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
8×	`unswap-sqr_binary64_46`
7×	`associate-l_binary64_19`
6×	`add-log-exp_binary64_117` `associate-/l*_binary64_23` `pow1_binary64_139`
4×	`div-inv_binary64_75`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `sum-log_binary64_169`

Counts

4 → 155

Calls

4 calls:

22.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
10.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
5.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series419.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
121.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
118.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
21.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify114.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4942	4311
1	4942	4311

prune254.0ms (3.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	167	7	174

Error

Counts

174 → 7

Compiler

Compiled 4649 to 2630 computations (43.4% saved)

regimes748.0ms (9.2%)

Accuracy

Total 0.4b remaining (94.6%)

Threshold costs 0.4b (94.6%)

Compiler

Compiled 8514 to 6271 computations (26.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	13	20

Compiler

Compiled 26 to 22 computations (15.4% saved)

end0.0ms (0%)

sample3.7s (45.3%)

Algorithm

1×

intervals

Results

626.0ms	1835×	body	1024	valid
505.0ms	1462×	body	1024	invalid
420.0ms	4857×	body	128	valid
221.0ms	911×	body	512	valid
190.0ms	775×	body	512	invalid
65.0ms	392×	body	256	valid
58.0ms	347×	body	256	invalid
51.0ms	579×	body	128	invalid
3.0ms	5×	body	2048	valid

Compiler

Compiled 1082 to 797 computations (26.3% saved)

Details

analyze938.0ms (11.5%)

sample88.0ms (1.1%)

simplify8.0ms (0.1%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite31.0ms (0.4%)

series236.0ms (2.9%)

simplify74.0ms (0.9%)

prune126.0ms (1.5%)

localize18.0ms (0.2%)

rewrite88.0ms (1.1%)

series228.0ms (2.8%)

simplify116.0ms (1.4%)

prune473.0ms (5.8%)

localize11.0ms (0.1%)

rewrite23.0ms (0.3%)

series217.0ms (2.7%)

simplify85.0ms (1%)

prune70.0ms (0.9%)

localize15.0ms (0.2%)

rewrite62.0ms (0.8%)

series419.0ms (5.1%)

simplify114.0ms (1.4%)

prune254.0ms (3.1%)

regimes748.0ms (9.2%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.7s (45.3%)

Profiling