Details

analyze1.1s (6.8%)

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)

sample92.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	61×	body	1024	invalid
17.0ms	55×	body	1024	valid
12.0ms	158×	body	128	valid
6.0ms	27×	body	512	invalid
6.0ms	26×	body	512	valid
3.0ms	17×	body	256	valid
1.0ms	18×	body	128	invalid
1.0ms	8×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune9.0ms (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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% 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 (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))

rewrite152.0ms (1%)

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:

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 2362 to 862 computations (63.5% saved)

series664.0ms (4.3%)

Error

0.4b

Counts

3 → 40

Calls

3 calls:

363.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
176.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
89.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1429 to 1264 computations (11.5% saved)

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5013	2823

prune154.0ms (1%)

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 2814 to 1125 computations (60% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
6.6b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.6b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite478.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`times-frac_binary64_425`
102×	`sqrt-prod_binary64_435`
86×	`add-sqr-sqrt_binary64_441`
84×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
78×	`cbrt-prod_binary64_450`
58×	`associate-r_binary64_359`
38×	`add-exp-log_binary64_457`
29×	`add-cbrt-cube_binary64_455`
16×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`pow1_binary64_480`
9×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/r*_binary64_363`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow-prod-down_binary64_490` `associate-*r/_binary64_361`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-inv_binary64_416` `associate-/l/_binary64_366`
1×	`frac-times_binary64_429` `associate-l/_binary64_362` `associate-l_binary64_360` `-commutative_binary64_350` `frac-2neg_binary64_430` `clear-num_binary64_418`

Counts

4 → 201

Calls

4 calls:

28.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 9640 to 4180 computations (56.6% saved)

series928.0ms (6%)

Error

Counts

4 → 52

Calls

4 calls:

398.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
282.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
93.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
85.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 4066 to 3241 computations (20.3% saved)

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5217	8006

prune421.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	252	1	253
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	253	8	261

Error

Counts

261 → 8

Compiler

Compiled 9644 to 4467 computations (53.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite217.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 116

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (cbrt.f64 (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))

Compiler

Compiled 3736 to 2030 computations (45.7% saved)

series1.6s (10%)

Error

Counts

4 → 60

Calls

4 calls:

749.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
387.0ms	(/.f64 (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
247.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
96.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 3575 to 3252 computations (9% saved)

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4998	3850
1	4998	3850

prune227.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	176	8	184

Error

Counts

184 → 8

Compiler

Compiled 4354 to 2491 computations (42.8% saved)

localize11.0ms (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))
0.4b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 1) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite814.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

763×	`times-frac_binary64_425`
361×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
138×	`sqrt-prod_binary64_435`
39×	`div-inv_binary64_416`
25×	`associate-/r*_binary64_363`
22×	`add-exp-log_binary64_457`
19×	`associate-/l*_binary64_364`
17×	`add-cbrt-cube_binary64_455`
14×	`div-exp_binary64_470`
9×	`cbrt-undiv_binary64_453`
5×	`add-log-exp_binary64_458`
3×	`pow1_binary64_480`
2×	`1-exp_binary64_463` `frac-2neg_binary64_430` `clear-num_binary64_418`
1×	`associate-/l/_binary64_366` `associate-/r/_binary64_365` `sum-log_binary64_510` `flip3-+_binary64_422` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

3 → 393

Calls

3 calls:

21.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
4.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 13556 to 6295 computations (53.6% saved)

series521.0ms (3.3%)

Error

Counts

3 → 32

Calls

3 calls:

365.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
89.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
41.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

Compiler

Compiled 1279 to 1106 computations (13.5% saved)

simplify198.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5065	16941

prune541.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	424	1	425
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	426	7	433

Error

Counts

433 → 7

Compiler

Compiled 11970 to 4446 computations (62.9% saved)

regimes1.9s (12%)

Accuracy

Total 0.4b remaining (94.9%)

Threshold costs 0.4b (94.9%)

Compiler

Compiled 24019 to 18095 computations (24.7% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	52
1	20	52

Remove

(sort a1 a2)

Compiler

Compiled 64 to 44 computations (31.3% saved)

end0.0ms (0%)

sample5.3s (34.1%)

Algorithm

1×

intervals

Results

706.0ms	1631×	body	1024	invalid
579.0ms	1821×	body	1024	valid
374.0ms	4812×	body	128	valid
215.0ms	933×	body	512	valid
173.0ms	771×	body	512	invalid
67.0ms	388×	body	256	invalid
66.0ms	432×	body	256	valid
51.0ms	646×	body	128	invalid
1.0ms	2×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 3031 to 2278 computations (24.8% saved)

Details

analyze1.1s (6.8%)

sample92.0ms (0.6%)

simplify9.0ms (0.1%)

prune9.0ms (0.1%)

localize10.0ms (0.1%)

rewrite152.0ms (1%)

series664.0ms (4.3%)

simplify88.0ms (0.6%)

prune154.0ms (1%)

localize18.0ms (0.1%)

rewrite478.0ms (3.1%)

series928.0ms (6%)

simplify110.0ms (0.7%)

prune421.0ms (2.7%)

localize14.0ms (0.1%)

rewrite217.0ms (1.4%)

series1.6s (10%)

simplify90.0ms (0.6%)

prune227.0ms (1.5%)

localize11.0ms (0.1%)

rewrite814.0ms (5.2%)

series521.0ms (3.3%)

simplify198.0ms (1.3%)

prune541.0ms (3.5%)

regimes1.9s (12%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample5.3s (34.1%)

Profiling