Details

analyze844.0ms (7.1%)

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

Compiler

Compiled 20 to 16 computations (20% saved)

sample86.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	49×	body	1024	invalid
15.0ms	50×	body	1024	valid
11.0ms	160×	body	128	valid
6.0ms	27×	body	512	valid
5.0ms	23×	body	512	invalid
3.0ms	19×	body	256	valid
2.0ms	11×	body	256	invalid
1.0ms	17×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms (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

0.3b

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))
0.1b	(.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))

rewrite136.0ms (1.1%)

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 2362 to 862 computations (63.5% saved)

series690.0ms (5.8%)

Error

0.3b

Counts

3 → 40

Calls

3 calls:

383.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
175.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
96.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1429 to 1264 computations (11.5% saved)

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5013	2823

prune141.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	125	9	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Error

0.0b

Counts

136 → 9

Compiler

Compiled 2833 to 1136 computations (59.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.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 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
5.3b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.3b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite544.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

149×	`add-sqr-sqrt_binary64_441`
146×	`times-frac_binary64_425`
127×	`sqrt-prod_binary64_435`
90×	`cbrt-prod_binary64_450`
87×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
58×	`associate-r_binary64_359`
27×	`add-exp-log_binary64_457`
21×	`unswap-sqr_binary64_387`
19×	`add-cbrt-cube_binary64_455`
10×	`associate-l_binary64_360`
9×	`associate-/r*_binary64_363`
8×	`pow1_binary64_480` `div-exp_binary64_470` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cbrt-undiv_binary64_453`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `div-inv_binary64_416`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `frac-times_binary64_429` `associate-l/_binary64_362` `associate-r/_binary64_361` `*-commutative_binary64_350` `frac-2neg_binary64_430` `clear-num_binary64_418`

Counts

4 → 226

Calls

4 calls:

35.0ms	(.f64 (/.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 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
6.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 11015 to 4717 computations (57.2% saved)

series750.0ms (6.3%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

276.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
200.0ms	(.f64 (/.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 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
96.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
93.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4137 to 3269 computations (21% saved)

simplify187.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4936	8932
1	4936	8932

prune468.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	279	1	280
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	280	9	289

Error

Counts

289 → 9

Compiler

Compiled 10939 to 5127 computations (53.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
5.3b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.3b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite241.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

100×	`sqrt-prod_binary64_435`
91×	`add-sqr-sqrt_binary64_441`
80×	`times-frac_binary64_425`
61×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
40×	`associate-r_binary64_359`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`sqrt-div_binary64_436` `unswap-sqr_binary64_387`
8×	`pow1_binary64_480`
6×	`associate-/l_binary64_364` `associate-/r_binary64_363` `associate-l_binary64_360`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`add-log-exp_binary64_458`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `sqrt-undiv_binary64_440` `div-inv_binary64_416` `associate-/l/_binary64_366` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `associate-*l/_binary64_362`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `sqrt-unprod_binary64_439` `associate-r/_binary64_361` `-commutative_binary64_350`

Counts

4 → 168

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 6288 to 1682 computations (73.3% saved)

series569.0ms (4.8%)

Error

Counts

4 → 54

Calls

4 calls:

190.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
147.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
87.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
86.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3033 to 2165 computations (28.6% saved)

simplify103.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4977	5435
1	4977	5435

prune248.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	222	9	231

Error

Counts

231 → 9

Compiler

Compiled 6711 to 2266 computations (66.2% saved)

localize10.0ms (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))

rewrite83.0ms (0.7%)

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:

11.0ms	(/.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 1347 to 424 computations (68.5% saved)

series729.0ms (6.1%)

Error

Counts

3 → 44

Calls

3 calls:

370.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
234.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
89.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1637 to 1411 computations (13.8% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5001	1788

prune76.0ms (0.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	104	9	113

Error

Counts

113 → 9

Compiler

Compiled 1686 to 610 computations (63.8% saved)

regimes1.3s (11%)

Accuracy

Total 0.4b remaining (96.2%)

Threshold costs 0.4b (96.2%)

Compiler

Compiled 16699 to 12245 computations (26.7% 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

Compiler

Compiled 64 to 44 computations (31.3% saved)

end0.0ms (0%)

sample4.5s (37.5%)

Algorithm

1×

intervals

Results

554.0ms	1757×	body	1024	valid
489.0ms	1616×	body	1024	invalid
365.0ms	4850×	body	128	valid
202.0ms	911×	body	512	valid
174.0ms	772×	body	512	invalid
73.0ms	477×	body	256	valid
56.0ms	380×	body	256	invalid
50.0ms	648×	body	128	invalid
2.0ms	5×	body	2048	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 2119 to 1550 computations (26.9% saved)

Details

analyze844.0ms (7.1%)

sample86.0ms (0.7%)

simplify8.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite136.0ms (1.1%)

series690.0ms (5.8%)

simplify82.0ms (0.7%)

prune141.0ms (1.2%)

localize15.0ms (0.1%)

rewrite544.0ms (4.6%)

series750.0ms (6.3%)

simplify187.0ms (1.6%)

prune468.0ms (3.9%)

localize12.0ms (0.1%)

rewrite241.0ms (2%)

series569.0ms (4.8%)

simplify103.0ms (0.9%)

prune248.0ms (2.1%)

localize10.0ms (0.1%)

rewrite83.0ms (0.7%)

series729.0ms (6.1%)

simplify76.0ms (0.6%)

prune76.0ms (0.6%)

regimes1.3s (11%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample4.5s (37.5%)

Profiling