Details

analyze806.0ms (8.6%)

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)

sample89.0ms (0.9%)

Algorithm

1×

intervals

Results

21.0ms	57×	body	1024	invalid
18.0ms	49×	body	1024	valid
13.0ms	164×	body	128	valid
10.0ms	28×	body	512	valid
6.0ms	24×	body	512	invalid
2.0ms	14×	body	256	valid
2.0ms	14×	body	256	invalid
1.0ms	15×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify182.0ms (1.9%)

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: 0.3b

Counts

2 → 2

Compiler

Compiled 77 to 63 computations (18.2% 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))

rewrite36.0ms (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))

series493.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

344.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
111.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
39.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4965	2380
1	4965	2380

prune476.0ms (5.1%)

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: 0b

Counts

105 → 10

Compiler

Compiled 8995 to 5572 computations (38.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite104.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64_429`
111×	`add-sqr-sqrt_binary64_445`
94×	`cbrt-prod_binary64_454`
91×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
67×	`associate-r_binary64_363`
47×	`sqrt-prod_binary64_439`
32×	`add-exp-log_binary64_461`
22×	`div-inv_binary64_420`
20×	`add-cbrt-cube_binary64_459`
12×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
10×	`associate-/l_binary64_368` `associate-/r_binary64_367`
7×	`prod-exp_binary64_472` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
6×	`pow1_binary64_484` `add-log-exp_binary64_462`
3×	`associate-l_binary64_364` `associate-/l/_binary64_370`
2×	`flip-+_binary64_397` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434`
1×	`pow-prod-down_binary64_494` `+-commutative_binary64_353` `associate-r/_binary64_365` `-commutative_binary64_354` `sum-log_binary64_514`

Counts

4 → 225

Calls

4 calls:

34.0ms	(.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))))
16.0ms	(/.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)))
12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series819.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

347.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
328.0ms	(.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))))
105.0ms	(/.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)))
38.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify127.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4923	8061
1	4923	8061

prune443.0ms (4.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	239	8	247

Merged error: 0b

Counts

247 → 8

Compiler

Compiled 8337 to 4827 computations (42.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cos.f64 th))
0.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))
0.3b	(/.f64 (.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))

rewrite83.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64_429`
87×	`add-sqr-sqrt_binary64_445`
69×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
66×	`unpow-prod-down_binary64_502`
56×	`cbrt-prod_binary64_454`
46×	`associate-l_binary64_364`
35×	`add-exp-log_binary64_461`
28×	`sqrt-prod_binary64_439`
23×	`associate-/r*_binary64_367`
17×	`add-cbrt-cube_binary64_459`
14×	`div-exp_binary64_474`
8×	`prod-exp_binary64_472` `unpow2_binary64_488` `sqr-pow_binary64_395`
7×	`unswap-sqr_binary64_391`
6×	`pow1_binary64_484` `add-log-exp_binary64_462` `cbrt-undiv_binary64_457`
4×	`associate-/l*_binary64_368` `cbrt-unprod_binary64_456`
3×	`pow-to-exp_binary64_492` `pow-exp_binary64_491` `associate-/l/_binary64_370` `associate-r_binary64_363` `div-inv_binary64_420`
2×	`flip-+_binary64_397` `associate-*l/_binary64_366` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434`
1×	`pow-prod-down_binary64_494` `+-commutative_binary64_353` `*-commutative_binary64_354` `sum-log_binary64_514`

Counts

4 → 196

Calls

4 calls:

23.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cos.f64 th))
18.0ms	(/.f64 (.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
11.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.3s (14.2%)

Counts

4 → 12

Calls

4 calls:

520.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))
514.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cos.f64 th))
243.0ms	(/.f64 (.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
45.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5002	6027

prune355.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	208	8	216

Merged error: 0b

Counts

216 → 8

Compiler

Compiled 7016 to 3940 computations (43.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-prod_binary64_439`
72×	`times-frac_binary64_429`
61×	`add-sqr-sqrt_binary64_445`
59×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
40×	`associate-r_binary64_363`
18×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
11×	`pow1_binary64_484`
10×	`sqrt-div_binary64_440`
6×	`prod-exp_binary64_472` `associate-l/_binary64_366` `associate-/l_binary64_368` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`
5×	`flip-+_binary64_397` `flip3-+_binary64_426`
4×	`add-log-exp_binary64_462`
3×	`pow-prod-down_binary64_494` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`frac-times_binary64_433` `rem-sqrt-square_binary64_436` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420`
1×	`associate-l_binary64_364` `sqrt-undiv_binary64_444` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

4 → 157

Calls

4 calls:

22.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
6.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series456.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

248.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
109.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
50.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
49.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5110	4501

prune236.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	169	8	177

Merged error: 0b

Counts

177 → 8

Compiler

Compiled 6258 to 2217 computations (64.6% saved)

regimes109.0ms (1.2%)

Compiler: Compiled 1030 to 816 computations (20.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample2.8s (30.3%)

Algorithm

1×

intervals

Results

686.0ms	1793×	body	1024	valid
566.0ms	1502×	body	1024	invalid
407.0ms	4845×	body	128	valid
231.0ms	904×	body	512	valid
206.0ms	805×	body	512	invalid
81.0ms	455×	body	256	valid
75.0ms	381×	body	256	invalid
61.0ms	650×	body	128	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 210 to 161 computations (23.3% saved)

Details

analyze806.0ms (8.6%)

sample89.0ms (0.9%)

simplify182.0ms (1.9%)

prune6.0ms (0.1%)

localize11.0ms (0.1%)

rewrite36.0ms (0.4%)

series493.0ms (5.3%)

simplify74.0ms (0.8%)

prune476.0ms (5.1%)

localize17.0ms (0.2%)

rewrite104.0ms (1.1%)

series819.0ms (8.8%)

simplify127.0ms (1.4%)

prune443.0ms (4.7%)

localize15.0ms (0.2%)

rewrite83.0ms (0.9%)

series1.3s (14.2%)

simplify96.0ms (1%)

prune355.0ms (3.8%)

localize14.0ms (0.1%)

rewrite63.0ms (0.7%)

series456.0ms (4.9%)

simplify82.0ms (0.9%)

prune236.0ms (2.5%)

regimes109.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (30.3%)

Profiling