Details

analyze731.0ms (10.8%)

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)

sample86.0ms (1.3%)

Algorithm

1×

intervals

Results

22.0ms	62×	body	1024	invalid
15.0ms	43×	body	1024	valid
13.0ms	172×	body	128	valid
7.0ms	32×	body	512	invalid
7.0ms	28×	body	512	valid
5.0ms	30×	body	128	invalid
2.0ms	13×	body	256	valid
2.0ms	10×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms (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: 0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize13.0ms (0.2%)

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))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series465.0ms (6.8%)

Counts

3 → 9

Calls

3 calls:

326.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
99.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
40.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	6033	2380

prune125.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0b

Counts

105 → 9

Compiler

Compiled 2449 to 965 computations (60.6% saved)

localize10.0ms (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))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

12.0ms	(/.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))

series409.0ms (6%)

Counts

3 → 9

Calls

3 calls:

235.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
133.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
41.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4932	1293
1	4932	1293

prune70.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Merged error: 0b

Counts

78 → 9

Compiler

Compiled 1442 to 576 computations (60.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`sqrt-prod_binary64`
25×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
6×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 158

Calls

3 calls:

13.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
5.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series337.0ms (5%)

Counts

3 → 9

Calls

3 calls:

240.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
56.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
42.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5102	5041

prune179.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	169	7	176

Merged error: 0b

Counts

176 → 7

Compiler

Compiled 4150 to 1532 computations (63.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
8.0b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.0b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite118.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

540×	`times-frac_binary64`
429×	`sqrt-prod_binary64`
297×	`add-sqr-sqrt_binary64`
295×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`associate-/r*_binary64`
22×	`sqrt-div_binary64`
17×	`associate-/r/_binary64`
12×	`associate-/l*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`sqrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 411

Calls

4 calls:

23.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
8.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series291.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
83.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
51.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
48.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify213.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4938	16776
1	4938	16776

prune564.0ms (8.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	423	7	430

Merged error: 0b

Counts

430 → 7

Compiler

Compiled 14178 to 4388 computations (69.1% saved)

regimes102.0ms (1.5%)

Compiler: Compiled 868 to 744 computations (14.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	20
1	14	20

end0.0ms (0%)

sample2.7s (39.9%)

Algorithm

1×

intervals

Results

644.0ms	1801×	body	1024	valid
586.0ms	1640×	body	1024	invalid
376.0ms	4849×	body	128	valid
221.0ms	908×	body	512	valid
196.0ms	800×	body	512	invalid
69.0ms	436×	body	256	valid
61.0ms	391×	body	256	invalid
57.0ms	651×	body	128	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 174 to 147 computations (15.5% saved)

Details

analyze731.0ms (10.8%)

sample86.0ms (1.3%)

simplify10.0ms (0.2%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

rewrite34.0ms (0.5%)

series465.0ms (6.8%)

simplify55.0ms (0.8%)

prune125.0ms (1.8%)

localize10.0ms (0.1%)

rewrite28.0ms (0.4%)

series409.0ms (6%)

simplify98.0ms (1.4%)

prune70.0ms (1%)

localize10.0ms (0.1%)

rewrite40.0ms (0.6%)

series337.0ms (5%)

simplify81.0ms (1.2%)

prune179.0ms (2.6%)

localize12.0ms (0.2%)

rewrite118.0ms (1.7%)

series291.0ms (4.3%)

simplify213.0ms (3.1%)

prune564.0ms (8.3%)

regimes102.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (39.9%)

Profiling