Details

analyze1.1s (4.8%)

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)

sample91.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	62×	body	1024	invalid
18.0ms	60×	body	1024	valid
11.0ms	159×	body	128	valid
5.0ms	25×	body	512	valid
5.0ms	23×	body	512	invalid
2.0ms	12×	body	256	valid
2.0ms	20×	body	128	invalid
1.0ms	10×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune9.0ms (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)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.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))

rewrite189.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

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))

Compiler

Compiled 2096 to 762 computations (63.6% saved)

series1.1s (5%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

662.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
296.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
133.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1297 to 1213 computations (6.5% saved)

simplify65.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5044	2993

prune162.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Error

0.0b

Counts

138 → 7

Compiler

Compiled 1966 to 813 computations (58.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
0.5b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
7.6b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.6b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite1.0s (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

522×	`times-frac_binary64_425`
403×	`sqrt-prod_binary64_435`
312×	`add-sqr-sqrt_binary64_441`
270×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
257×	`associate-r_binary64_359`
18×	`sqrt-div_binary64_436`
15×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `associate-/r/_binary64_365`
11×	`unswap-sqr_binary64_387`
9×	`flip3-+_binary64_422` `flip-+_binary64_393`
8×	`pow1_binary64_480` `div-inv_binary64_416`
6×	`associate-/l_binary64_364` `associate-/r_binary64_363`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
1×	`sqrt-undiv_binary64_440` `frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350`

Counts

4 → 380

Calls

4 calls:

79.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
8.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 11623 to 3054 computations (73.7% saved)

series1.3s (5.7%)

Error

0.0b

Counts

4 → 64

Calls

4 calls:

664.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
280.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
120.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
119.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3282 to 2508 computations (23.6% saved)

simplify177.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

444 → 444

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4953	13195
1	4953	13195

prune466.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	442	2	444
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	443	8	451

Error

Counts

451 → 8

Compiler

Compiled 7720 to 2342 computations (69.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.2b	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

rewrite130.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`add-sqr-sqrt_binary64_441`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
6×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
4×	`associate-*l/_binary64_362`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-l_binary64_360` `associate-r_binary64_359`
2×	`prod-exp_binary64_468` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452` `associate-/l/_binary64_366`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 60

Calls

3 calls:

9.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1281 to 397 computations (69% saved)

series1.2s (5.5%)

Error

Counts

3 → 48

Calls

3 calls:

651.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
416.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
127.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1644 to 1488 computations (9.5% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4967	2050
1	4967	2050

prune122.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	109	7	116

Error

Counts

116 → 7

Compiler

Compiled 1411 to 599 computations (57.5% saved)

localize13.0ms (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) (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))))
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))))

rewrite450.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

71×	`add-sqr-sqrt_binary64_441`
70×	`times-frac_binary64_425`
49×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
46×	`cbrt-prod_binary64_450`
32×	`add-exp-log_binary64_457`
31×	`associate-r_binary64_359`
23×	`sqrt-prod_binary64_435`
22×	`add-cbrt-cube_binary64_455`
10×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/r*_binary64_363`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`unswap-sqr_binary64_387`
7×	`associate-l_binary64_360`
6×	`pow1_binary64_480` `add-log-exp_binary64_458` `associate-/l*_binary64_364`
4×	`div-inv_binary64_416`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `frac-times_binary64_429` `associate-l/_binary64_362` `associate-r/_binary64_361` `*-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

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))

Compiler

Compiled 4812 to 2804 computations (41.7% saved)

series2.2s (9.9%)

Error

Counts

4 → 48

Calls

4 calls:

1.1s	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
670.0ms	(.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))))
226.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
153.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2249 to 2101 computations (6.6% saved)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4984	5234
1	4984	5234

prune337.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	203	7	210

Error

Counts

210 → 7

Compiler

Compiled 3983 to 2321 computations (41.7% saved)

regimes9.3s (41.5%)

Accuracy

Total 0.4b remaining (93.5%)

Threshold costs 0.4b (93.5%)

Compiler

Compiled 95792 to 74069 computations (22.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end9.0ms (0%)

Remove: (sort a1 a2)
Compiler: Compiled 51 to 45 computations (11.8% saved)

sample2.7s (12%)

Algorithm

1×

intervals

Results

581.0ms	1845×	body	1024	valid
467.0ms	1510×	body	1024	invalid
375.0ms	4791×	body	128	valid
202.0ms	916×	body	512	valid
191.0ms	854×	body	512	invalid
66.0ms	442×	body	256	valid
65.0ms	394×	body	256	invalid
52.0ms	653×	body	128	invalid
3.0ms	6×	body	2048	valid

Compiler

Compiled 212 to 164 computations (22.6% saved)

Details

analyze1.1s (4.8%)

sample91.0ms (0.4%)

simplify8.0ms (0%)

prune9.0ms (0%)

localize10.0ms (0%)

rewrite189.0ms (0.8%)

series1.1s (5%)

simplify65.0ms (0.3%)

prune162.0ms (0.7%)

localize17.0ms (0.1%)

rewrite1.0s (4.7%)

series1.3s (5.7%)

simplify177.0ms (0.8%)

prune466.0ms (2.1%)

localize12.0ms (0.1%)

rewrite130.0ms (0.6%)

series1.2s (5.5%)

simplify79.0ms (0.4%)

prune122.0ms (0.5%)

localize13.0ms (0.1%)

rewrite450.0ms (2%)

series2.2s (9.9%)

simplify91.0ms (0.4%)

prune337.0ms (1.5%)

regimes9.3s (41.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end9.0ms (0%)

sample2.7s (12%)

Profiling