Details

analyze1.0s (5.5%)

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

Symmetry

(sort a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample97.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	59×	body	1024	valid
15.0ms	48×	body	1024	invalid
11.0ms	151×	body	128	valid
6.0ms	28×	body	512	invalid
6.0ms	28×	body	512	valid
3.0ms	18×	body	256	valid
2.0ms	14×	body	256	invalid
2.0ms	27×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify10.0ms (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%)

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

0.4b

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))

rewrite153.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

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))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series660.0ms (3.5%)

Error

0.3b

Counts

3 → 40

Calls

3 calls:

357.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
174.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
94.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1429 to 1264 computations (11.5% saved)

simplify93.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5013	2823

prune154.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Error

Counts

136 → 8

Compiler

Compiled 2825 to 1134 computations (59.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite586.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

195×	`times-frac_binary64_425`
111×	`add-sqr-sqrt_binary64_441`
94×	`cbrt-prod_binary64_450`
91×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
67×	`associate-r_binary64_359`
47×	`sqrt-prod_binary64_435`
32×	`add-exp-log_binary64_457`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455`
12×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
10×	`associate-/l_binary64_364` `associate-/r_binary64_363`
7×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l/_binary64_366` `associate-l_binary64_360`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 225

Calls

4 calls:

30.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
15.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
11.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 8603 to 5119 computations (40.5% saved)

series1.3s (7.2%)

Error

Counts

4 → 52

Calls

4 calls:

620.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
381.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
185.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
97.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2503 to 2302 computations (8% saved)

simplify182.0ms (1%)

Algorithm

1×	egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4938	8603
1	4938	8603

prune450.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	276	1	277
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	277	8	285

Error

Counts

285 → 8

Compiler

Compiled 8251 to 4628 computations (43.9% saved)

localize15.0ms (0.1%)

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 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.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)))

rewrite169.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-sqr-sqrt_binary64_441`
22×	`cbrt-prod_binary64_450`
20×	`add-exp-log_binary64_457`
18×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419` `times-frac_binary64_425`
16×	`associate-r_binary64_359`
13×	`add-cbrt-cube_binary64_455`
9×	`associate-l_binary64_360` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
8×	`pow1_binary64_480`
6×	`prod-exp_binary64_468` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452`
5×	`associate-*r/_binary64_361`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`unswap-sqr_binary64_387` `flip3-+_binary64_422` `flip-+_binary64_393`
2×	`pow-prod-down_binary64_490` `*-commutative_binary64_350` `div-inv_binary64_416` `associate-/l/_binary64_366`
1×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l*_binary64_364` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 105

Calls

4 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))))
9.0ms	(/.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)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2769 to 1381 computations (50.1% saved)

series1.7s (9.2%)

Error

Counts

4 → 52

Calls

4 calls:

842.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
558.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
158.0ms	(.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
99.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2891 to 2690 computations (7% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5127	3349

prune174.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	157	8	165

Error

Counts

165 → 8

Compiler

Compiled 3463 to 1871 computations (46% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite2.2s (11.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1137×	`sqrt-prod_binary64_435`
1119×	`times-frac_binary64_425`
625×	`add-sqr-sqrt_binary64_441`
578×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
283×	`associate-r_binary64_359`
34×	`associate-/l*_binary64_364`
22×	`div-inv_binary64_416`
20×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
18×	`associate-/r*_binary64_363`
13×	`unswap-sqr_binary64_387`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l/_binary64_366` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 713

Calls

4 calls:

85.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
19.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 27448 to 15232 computations (44.5% saved)

series904.0ms (4.8%)

Error

Counts

4 → 52

Calls

4 calls:

350.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
234.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
170.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
94.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2239 to 2038 computations (9% saved)

simplify287.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

765 → 765

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5062	26753

prune1.5s (7.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	765	0	765
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	765	8	773

Error

Counts

773 → 8

Compiler

Compiled 24418 to 12063 computations (50.6% saved)

regimes1.8s (9.5%)

Accuracy

Total 0.4b remaining (93.2%)

Threshold costs 0.4b (93.2%)

Compiler

Compiled 21991 to 16519 computations (24.9% saved)

bsearch0.0ms (0%)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	36
1	17	36

Remove

(sort a1 a2)

Compiler

Compiled 44 to 40 computations (9.1% saved)

end0.0ms (0%)

sample5.1s (27.3%)

Algorithm

1×

intervals

Results

562.0ms	1763×	body	1024	valid
465.0ms	1509×	body	1024	invalid
386.0ms	4835×	body	128	valid
216.0ms	944×	body	512	valid
191.0ms	820×	body	512	invalid
72.0ms	455×	body	256	valid
57.0ms	382×	body	256	invalid
52.0ms	655×	body	128	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 2776 to 2087 computations (24.8% saved)

Details

analyze1.0s (5.5%)

sample97.0ms (0.5%)

simplify10.0ms (0.1%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite153.0ms (0.8%)

series660.0ms (3.5%)

simplify93.0ms (0.5%)

prune154.0ms (0.8%)

localize15.0ms (0.1%)

rewrite586.0ms (3.1%)

series1.3s (7.2%)

simplify182.0ms (1%)

prune450.0ms (2.4%)

localize15.0ms (0.1%)

rewrite169.0ms (0.9%)

series1.7s (9.2%)

simplify64.0ms (0.3%)

prune174.0ms (0.9%)

localize16.0ms (0.1%)

rewrite2.2s (11.7%)

series904.0ms (4.8%)

simplify287.0ms (1.5%)

prune1.5s (7.8%)

regimes1.8s (9.5%)

bsearch0.0ms (0%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample5.1s (27.3%)

Profiling