Details

analyze765.0ms (8.7%)

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)

sample83.0ms (0.9%)

Algorithm

1×

intervals

Results

22.0ms	64×	body	1024	valid
19.0ms	43×	body	1024	invalid
12.0ms	156×	body	128	valid
6.0ms	26×	body	512	invalid
6.0ms	24×	body	512	valid
2.0ms	24×	body	128	invalid
2.0ms	12×	body	256	valid
1.0ms	9×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify173.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune6.0ms (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: 0.6b

Counts

2 → 2

Compiler

Compiled 77 to 63 computations (18.2% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.4b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_445`
38×	`times-frac_binary64_429`
32×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
22×	`sqrt-prod_binary64_439` `associate-r_binary64_363`
10×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`associate-/r*_binary64_367`
5×	`pow1_binary64_484` `add-log-exp_binary64_462`
3×	`associate-l_binary64_364` `unswap-sqr_binary64_391` `associate-/l*_binary64_368`
2×	`flip-+_binary64_397` `prod-exp_binary64_472` `associate-/l/_binary64_370` `flip3-+_binary64_426` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `+-commutative_binary64_353` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `sum-log_binary64_514`

Counts

3 → 94

Calls

3 calls:

14.0ms	(.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))

series489.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

345.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
106.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
38.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4965	2380
1	4965	2380

prune581.0ms (6.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0.3b

Counts

105 → 10

Compiler

Compiled 11822 to 7056 computations (40.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cos.f64 th) (/.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))))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite187.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64_429`
403×	`sqrt-prod_binary64_439`
312×	`add-sqr-sqrt_binary64_445`
270×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
257×	`associate-r_binary64_363`
18×	`sqrt-div_binary64_440`
15×	`associate-/r/_binary64_369` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
11×	`unswap-sqr_binary64_391`
9×	`flip-+_binary64_397` `flip3-+_binary64_426`
8×	`pow1_binary64_484` `div-inv_binary64_420`
6×	`associate-/l_binary64_368` `associate-/r_binary64_367`
4×	`add-log-exp_binary64_462` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
3×	`associate-l_binary64_364` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
2×	`rem-sqrt-square_binary64_436` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`
1×	`pow-prod-down_binary64_494` `sqrt-undiv_binary64_444` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

4 → 380

Calls

4 calls:

86.0ms	(.f64 (cos.f64 th) (/.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)))

series506.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
87.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
50.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
44.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify173.0ms (2%)

Algorithm

1×	egg-herbie

Counts

392 → 392

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4953	11753
1	4953	11753

prune698.0ms (7.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	388	4	392
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	393	9	402

Merged error: 0.3b

Counts

402 → 9

Compiler

Compiled 18900 to 6297 computations (66.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))))
0.4b	(.f64 (cos.f64 th) (.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)))))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite105.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64_445`
92×	`times-frac_binary64_429`
76×	`sqrt-prod_binary64_439`
59×	`associate-r_binary64_363`
54×	`add-exp-log_binary64_461`
48×	`cbrt-prod_binary64_454`
47×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
40×	`add-cbrt-cube_binary64_459`
23×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
21×	`unswap-sqr_binary64_391`
14×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
13×	`associate-l_binary64_364` `pow1_binary64_484`
5×	`associate-*r/_binary64_365`
4×	`sqrt-div_binary64_440` `pow-prod-down_binary64_494` `add-log-exp_binary64_462`
2×	`frac-times_binary64_433` `flip-+_binary64_397` `rem-sqrt-square_binary64_436` `associate-l/_binary64_366` `-commutative_binary64_354` `flip3-+_binary64_426` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420`

Counts

4 → 174

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))))
28.0ms	(.f64 (cos.f64 th) (.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)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series555.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

348.0ms	(.f64 (cos.f64 th) (.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)))))
113.0ms	(.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))))
50.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
43.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4927	5864
1	4927	5864

prune325.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	186	9	195

Merged error: 0.3b

Counts

195 → 9

Compiler

Compiled 7186 to 3412 computations (52.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
0.5b	(/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.6b	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))

rewrite98.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`times-frac_binary64_429`
169×	`sqrt-prod_binary64_439`
132×	`add-sqr-sqrt_binary64_445`
113×	`associate-r_binary64_363`
106×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
17×	`associate-/r/_binary64_369`
11×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
9×	`flip-+_binary64_397` `flip3-+_binary64_426` `div-inv_binary64_420`
8×	`pow1_binary64_484`
7×	`unswap-sqr_binary64_391`
4×	`sqrt-div_binary64_440` `add-log-exp_binary64_462`
3×	`associate-l_binary64_364` `rem-sqrt-square_binary64_436` `associate-/l_binary64_368` `associate-/r_binary64_367`
2×	`prod-exp_binary64_472` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

4 → 208

Calls

4 calls:

46.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
7.0ms	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
6.0ms	(/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series517.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
95.0ms	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
54.0ms	(/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
42.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5127	6449

prune327.0ms (3.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	220	9	229

Merged error: 0.3b

Counts

229 → 9

Compiler

Compiled 9449 to 3065 computations (67.6% saved)

regimes154.0ms (1.8%)

Compiler: Compiled 1655 to 1111 computations (32.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	36
1	16	36

end0.0ms (0%)

sample2.7s (30.5%)

Algorithm

1×

intervals

Results

628.0ms	1760×	body	1024	valid
523.0ms	1486×	body	1024	invalid
371.0ms	4850×	body	128	valid
222.0ms	927×	body	512	valid
195.0ms	811×	body	512	invalid
72.0ms	462×	body	256	valid
62.0ms	384×	body	256	invalid
62.0ms	685×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 268 to 177 computations (34% saved)

Details

analyze765.0ms (8.7%)

sample83.0ms (0.9%)

simplify173.0ms (2%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

rewrite35.0ms (0.4%)

series489.0ms (5.6%)

simplify70.0ms (0.8%)

prune581.0ms (6.6%)

localize14.0ms (0.2%)

rewrite187.0ms (2.1%)

series506.0ms (5.8%)

simplify173.0ms (2%)

prune698.0ms (7.9%)

localize16.0ms (0.2%)

rewrite105.0ms (1.2%)

series555.0ms (6.3%)

simplify111.0ms (1.3%)

prune325.0ms (3.7%)

localize13.0ms (0.1%)

rewrite98.0ms (1.1%)

series517.0ms (5.9%)

simplify93.0ms (1.1%)

prune327.0ms (3.7%)

regimes154.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (30.5%)

Profiling