Details

analyze745.0ms (0.2%)

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)

sample85.0ms (0%)

Algorithm

1×

intervals

Results

20.0ms	65×	body	1024	valid
15.0ms	152×	body	128	valid
13.0ms	44×	body	1024	invalid
7.0ms	31×	body	512	invalid
6.0ms	26×	body	512	valid
2.0ms	25×	body	128	invalid
2.0ms	13×	body	256	valid
1.0ms	6×	body	256	invalid

Compiler

Compiled 42 to 40 computations (4.8% saved)

simplify95.0ms (0%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	109	23
1	109	23

prune5.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

0.4b

Counts

8 → 5

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

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

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

6 calls:

16.0ms	(.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))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))

series693.0ms (0.2%)

Counts

3 → 42

Calls

3 calls:

413.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
195.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
85.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 995 to 969 computations (2.6% saved)

simplify77.0ms (0%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5044	2993

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64_425`
70×	`add-sqr-sqrt_binary64_441`
60×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
44×	`associate-l_binary64_360` `sqrt-prod_binary64_435`
32×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`pow1_binary64_480`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r*_binary64_363`
6×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `div-exp_binary64_470` `associate-/l*_binary64_364` `cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416`
2×	`associate-l/_binary64_362` `clear-num_binary64_418` `associate-r_binary64_359` `-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

4 → 168

Calls

8 calls:

10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

series426.0ms (0.1%)

Counts

4 → 28

Calls

4 calls:

165.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
153.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
55.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
52.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1068 to 916 computations (14.2% saved)

simplify96.0ms (0%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4946	3315
1	4946	3315

prune1.9s (0.6%)

Pruning

162 alts after pruning (161 fresh and 1 done)

	Pruned	Kept	Total
New	174	158	332
Fresh	0	3	3
Picked	0	0	0
Done	1	1	2
Total	175	162	337

Error

Counts

337 → 162

Compiler

Compiled 9563 to 5707 computations (40.3% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite261.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 713

Calls

8 calls:

87.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
20.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series953.0ms (0.3%)

Counts

4 → 54

Calls

4 calls:

423.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
243.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
196.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
88.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1493 to 1473 computations (1.3% saved)

simplify302.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

767 → 767

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4970	26923
1	4970	26923

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64_425`
17×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
12×	`sqrt-prod_binary64_435`
6×	`associate-/r*_binary64_363`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `sum-log_binary64_510` `frac-2neg_binary64_430` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

2 → 52

Calls

4 calls:

7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series281.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

195.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
86.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 348 to 396 computations (-13.8% saved)

simplify81.0ms (0%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4987	1476
1	4987	1476

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

2.4b	(log.f64 (pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
2.4b	(log.f64 (pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th)))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
23×	`pow-pow_binary64_491`
22×	`exp-prod_binary64_471`
21×	`sqrt-prod_binary64_435`
7×	`log-prod_binary64_505` `add-exp-log_binary64_457`
6×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `associate-/r*_binary64_363`
5×	`pow1_binary64_480`
3×	`rem-log-exp_binary64_460` `pow-unpow_binary64_496` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `flip-+_binary64_393` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sum-log_binary64_510` `log-pow_binary64_508` `frac-2neg_binary64_430` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 109

Calls

8 calls:

11.0ms	(pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th))
8.0ms	(log.f64 (pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th))

series2.0s (0.6%)

Counts

4 → 50

Calls

4 calls:

1.2s	(log.f64 (pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th)))
580.0ms	(pow.f64 (exp.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cos.f64 th))
176.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
94.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1562 to 1500 computations (4% saved)

simplify65.0ms (0%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5021	3860

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.3b	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))
0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.5b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.6b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite118.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

616×	`sqrt-prod_binary64_435`
614×	`times-frac_binary64_425`
345×	`add-sqr-sqrt_binary64_441`
340×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
37×	`associate-/l*_binary64_364`
25×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
24×	`associate-/r*_binary64_363`
22×	`associate-l_binary64_360`
14×	`div-inv_binary64_416`
9×	`pow1_binary64_480`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `unswap-sqr_binary64_387` `frac-2neg_binary64_430`
1×	`associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350` `associate-/l/_binary64_366`

Counts

4 → 469

Calls

8 calls:

18.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2)))

series348.0ms (0.1%)

Counts

4 → 25

Calls

4 calls:

163.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
68.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
62.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
55.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 1114 to 978 computations (12.2% saved)

simplify176.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5060	13474

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th)))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a1 a1)))
0.0b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
0.3b	(cbrt.f64 (cos.f64 th))
0.3b	(cbrt.f64 (cos.f64 th))
0.7b	(/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_425`
49×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
33×	`sqrt-prod_binary64_435`
27×	`cbrt-prod_binary64_450`
12×	`associate-/r*_binary64_363`
9×	`associate-/l*_binary64_364`
8×	`add-exp-log_binary64_457`
7×	`add-cbrt-cube_binary64_455`
4×	`add-log-exp_binary64_458` `pow1_binary64_480`
2×	`clear-num_binary64_418` `pow1/3_binary64_501` `div-inv_binary64_416` `frac-2neg_binary64_430` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 121

Calls

8 calls:

6.0ms	(/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
1.0ms	(cbrt.f64 (cos.f64 th))
1.0ms	(cbrt.f64 (cos.f64 th))
0.0ms	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

series343.0ms (0.1%)

Counts

4 → 23

Calls

4 calls:

124.0ms	(/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2))
81.0ms	(cbrt.f64 (cos.f64 th))
78.0ms	(cbrt.f64 (cos.f64 th))
59.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1132 to 844 computations (25.4% saved)

simplify101.0ms (0%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4921	2299
1	4921	2299

prune27.0s (8.3%)

Pruning

550 alts after pruning (545 fresh and 5 done)

	Pruned	Kept	Total
New	1232	408	1640
Fresh	19	137	156
Picked	0	0	0
Done	1	5	6
Total	1252	550	1802

Error

Counts

1802 → 550

Compiler

Compiled 39964 to 24800 computations (37.9% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2))))
0.3b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
0.2b	(.f64 (cos.f64 th) (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.3b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2))))
1.0b	(/.f64 1 (sqrt.f64 2))
1.0b	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))

rewrite59.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`sqrt-prod_binary64_435`
74×	`add-sqr-sqrt_binary64_441`
71×	`times-frac_binary64_425`
57×	`*-un-lft-identity_binary64_419`
53×	`add-cube-cbrt_binary64_454`
25×	`associate-r_binary64_359`
15×	`add-exp-log_binary64_457` `associate-/r*_binary64_363`
13×	`add-cbrt-cube_binary64_455`
11×	`pow1_binary64_480`
7×	`sqrt-div_binary64_436` `sqrt-pow1_binary64_437`
6×	`unswap-sqr_binary64_387` `pow-flip_binary64_493`
5×	`rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
4×	`flip3-+_binary64_422` `associate-l/_binary64_362` `add-log-exp_binary64_458` `div-inv_binary64_416` `frac-times_binary64_429` `flip-+_binary64_393` `div-exp_binary64_470` `associate-/l_binary64_364`
3×	`pow1/2_binary64_499` `associate-l_binary64_360` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `inv-pow_binary64_504` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-*r/_binary64_361` `frac-2neg_binary64_430`
1×	`pow-prod-down_binary64_490` `1-exp_binary64_463` `rec-exp_binary64_469` `*-commutative_binary64_350`

Counts

4 → 174

Calls

8 calls:

16.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2))))
16.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
5.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
4.0ms	(/.f64 1 (sqrt.f64 2))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series462.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

272.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2))))
190.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 2)))
0.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
0.0ms	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 654 to 666 computations (-1.8% saved)

simplify120.0ms (0%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4928	3636
1	4928	3636

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
0.3b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`times-frac_binary64_425` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `add-log-exp_binary64_458` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `pow1_binary64_480` `associate-/l*_binary64_364`

Counts

1 → 27

Calls

2 calls:

5.0ms	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
0.0ms	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

series48.0ms (0%)

Counts

1 → 3

Calls

1 calls:

48.0ms

(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

Compiler

Compiled 36 to 48 computations (-33.3% saved)

simplify86.0ms (0%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5462	340

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)) (sqrt.f64 (sqrt.f64 2)))
0.2b	(pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)
0.2b	(.f64 (cos.f64 th) (/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)) (sqrt.f64 (sqrt.f64 2))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)
0.3b	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)) (sqrt.f64 (sqrt.f64 2)))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
37.5b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3))

rewrite288.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1332×	`sqrt-prod_binary64_435`
1314×	`times-frac_binary64_425`
748×	`cbrt-prod_binary64_450`
720×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
372×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
74×	`associate-/l*_binary64_364`
26×	`div-inv_binary64_416`
18×	`associate-/r*_binary64_363`
12×	`unpow3_binary64_485` `cube-mult_binary64_449` `sqr-pow_binary64_391`
11×	`add-exp-log_binary64_457`
10×	`add-cbrt-cube_binary64_455`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458`
3×	`cube-div_binary64_448` `pow-unpow_binary64_496` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
2×	`clear-num_binary64_418` `cbrt-div_binary64_451` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `frac-2neg_binary64_430`
1×	`flip3-+_binary64_422` `pow1/3_binary64_501` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `flip-+_binary64_393` `pow-pow_binary64_491`

Counts

4 → 945

Calls

8 calls:

38.0ms	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)) (sqrt.f64 (sqrt.f64 2)))
20.0ms	(pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.1s (0.3%)

Counts

4 → 60

Calls

4 calls:

391.0ms	(pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)
262.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
262.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3))
185.0ms	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) 3)) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 2184 to 2160 computations (1.1% saved)

simplify409.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1005 → 1005

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5093	38711

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))
0.1b	(sqrt.f64 (cos.f64 th))
0.1b	(sqrt.f64 (cos.f64 th))
0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (*.f64 a2 a2))))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.5b	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
0.5b	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite64.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

208×	`sqrt-prod_binary64_435`
146×	`times-frac_binary64_425`
119×	`add-sqr-sqrt_binary64_441`
114×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
24×	`associate-/r*_binary64_363`
22×	`associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
15×	`associate-/l*_binary64_364`
9×	`pow1_binary64_480`
6×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416`
3×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `unswap-sqr_binary64_387` `frac-2neg_binary64_430`
2×	`sqrt-undiv_binary64_440`
1×	`associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350`

Counts

4 → 248

Calls

8 calls:

10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
7.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (*.f64 a2 a2))))

series365.0ms (0.1%)

Counts

4 → 27

Calls

4 calls:

164.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
72.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
68.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
62.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1338 to 1104 computations (17.5% saved)

simplify103.0ms (0%)

Algorithm

1×	egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5038	5764

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2))))
0.2b	(.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cos.f64 th))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
5.9b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
5.9b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))

rewrite315.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1466×	`sqrt-prod_binary64_435`
819×	`times-frac_binary64_425`
455×	`add-sqr-sqrt_binary64_441`
441×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
412×	`associate-r_binary64_359`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
16×	`div-inv_binary64_416`
11×	`pow1_binary64_480`
10×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
9×	`associate-/r*_binary64_363`
8×	`rem-sqrt-square_binary64_432`
6×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458`
3×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `associate-/l_binary64_364`
2×	`sqrt-div_binary64_436` `pow1/2_binary64_499` `sqrt-pow1_binary64_437` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `-commutative_binary64_350` `associate-l_binary64_360` `frac-2neg_binary64_430` `flip-+_binary64_393`

Counts

4 → 581

Calls

8 calls:

137.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
8.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.6s (0.5%)

Counts

4 → 66

Calls

4 calls:

478.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
471.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
439.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 2)))))
261.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 4103 to 3711 computations (9.6% saved)

simplify313.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

647 → 647

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4996	32300
1	4996	32300

prune1.0min (19%)

Pruning

902 alts after pruning (892 fresh and 10 done)

	Pruned	Kept	Total
New	1733	422	2155
Fresh	70	470	540
Picked	0	0	0
Done	0	10	10
Total	1803	902	2705

Error

Counts

2705 → 902

Compiler

Compiled 61492 to 41254 computations (32.9% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
0.2b	(.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 2))) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))) (sqrt.f64 (sqrt.f64 2))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
1.0b	(/.f64 1 (sqrt.f64 2))
1.0b	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
5.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`sqrt-prod_binary64_435`
43×	`add-sqr-sqrt_binary64_441`
40×	`times-frac_binary64_425`
36×	`*-un-lft-identity_binary64_419`
34×	`add-cube-cbrt_binary64_454`
11×	`pow1_binary64_480`
9×	`sqrt-pow1_binary64_437`
8×	`add-exp-log_binary64_457`
7×	`rem-sqrt-square_binary64_432`
6×	`pow-flip_binary64_493` `add-cbrt-cube_binary64_455` `associate-/r*_binary64_363`
5×	`sqrt-div_binary64_436` `pow1/2_binary64_499`
4×	`add-log-exp_binary64_458`
3×	`associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `inv-pow_binary64_504` `div-inv_binary64_416` `flip-+_binary64_393` `div-exp_binary64_470`
1×	`clear-num_binary64_418` `1-exp_binary64_463` `rec-exp_binary64_469` `frac-2neg_binary64_430` `cbrt-undiv_binary64_453`

Counts

4 → 116

Calls

8 calls:

5.0ms	(/.f64 1 (sqrt.f64 2))
5.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series270.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

137.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
133.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	(sqrt.f64 (/.f64 1 (sqrt.f64 2)))
0.0ms	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 1764 to 1476 computations (16.3% saved)

simplify65.0ms (0%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5013	1977

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 a1 (sqrt.f64 2))
0.2b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.2b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.5b	(/.f64 a1 (sqrt.f64 2))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
31×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
22×	`associate-r_binary64_359` `sqrt-prod_binary64_435`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`associate-/r*_binary64_363`
4×	`pow1_binary64_480`
3×	`unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
2×	`add-log-exp_binary64_458` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

2 → 81

Calls

4 calls:

9.0ms	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
4.0ms	(/.f64 a1 (sqrt.f64 2))
0.0ms	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.0ms	(/.f64 a1 (sqrt.f64 2))

series83.0ms (0%)

Counts

2 → 6

Calls

2 calls:

43.0ms	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
39.0ms	(/.f64 a1 (sqrt.f64 2))

Compiler

Compiled 72 to 90 computations (-25% saved)

simplify116.0ms (0%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4748	1020
1	4748	1020

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (cos.f64 th) (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.5b	(.f64 (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))))
6.4b	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
6.4b	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
6.4b	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))

rewrite88.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

190×	`cbrt-prod_binary64_450`
163×	`add-sqr-sqrt_binary64_441`
154×	`times-frac_binary64_425`
103×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
77×	`sqrt-prod_binary64_435`
31×	`swap-sqr_binary64_386`
25×	`associate-r_binary64_359` `associate-l_binary64_360`
16×	`unswap-sqr_binary64_387`
11×	`pow1_binary64_480`
9×	`pow1/3_binary64_501`
7×	`cbrt-div_binary64_451` `div-inv_binary64_416`
6×	`add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
2×	`pow-prod-down_binary64_490` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
1×	`associate-l/_binary64_362` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `pow-plus_binary64_482` `*-commutative_binary64_350` `pow2_binary64_500`

Counts

4 → 211

Calls

8 calls:

32.0ms	(.f64 (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))))
6.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
6.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
6.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.4s (0.4%)

Counts

4 → 54

Calls

4 calls:

363.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
360.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))
342.0ms	(.f64 (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))) (cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))))
327.0ms	(cbrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 5088 to 4188 computations (17.7% saved)

simplify153.0ms (0%)

Algorithm

1×	egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4941	10647
1	4941	10647

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.2b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
21.9b	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
21.9b	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
21.9b	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
18×	`times-frac_binary64_425`
12×	`sqrt-prod_binary64_435`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/r*_binary64_363`
4×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`associate-l/_binary64_362` `pow1/3_binary64_501` `cbrt-div_binary64_451` `cbrt-prod_binary64_450` `associate-/l_binary64_364`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 69

Calls

8 calls:

7.0ms	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
7.0ms	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
7.0ms	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))

series1.2s (0.4%)

Counts

4 → 29

Calls

4 calls:

395.0ms	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
385.0ms	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
374.0ms	(cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
56.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 2504 to 1878 computations (25% saved)

simplify132.0ms (0%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4934	1644
1	4934	1644

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (cos.f64 th))
0.1b	(sqrt.f64 (cos.f64 th))
0.1b	(sqrt.f64 (cos.f64 th))
0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))))
0.5b	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
0.5b	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
0.5b	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite78.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

291×	`sqrt-prod_binary64_435`
180×	`times-frac_binary64_425`
142×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
33×	`associate-/r*_binary64_363`
21×	`associate-/l*_binary64_364`
12×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`clear-num_binary64_418` `add-log-exp_binary64_458` `div-inv_binary64_416` `frac-2neg_binary64_430` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`sqrt-undiv_binary64_440`

Counts

4 → 285

Calls

8 calls:

7.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))) (sqrt.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 a2))))

series267.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

73.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
67.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
67.0ms	(/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))
59.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1478 to 1190 computations (19.5% saved)

simplify136.0ms (0%)

Algorithm

1×	egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5071	6768

prune1.3min (23.4%)

Pruning

1211 alts after pruning (1196 fresh and 15 done)

	Pruned	Kept	Total
New	583	328	911
Fresh	19	868	887
Picked	0	0	0
Done	0	15	15
Total	602	1211	1813

Error

Counts

1813 → 1211

Compiler

Compiled 24262 to 12468 computations (48.6% saved)

simplify2.1s (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	6614	127797

regimes52.3s (16.1%)

Compiler: Compiled 613262 to 451553 computations (26.4% saved)

bsearch0.0ms (0%)

regimes4.2s (1.3%)

Compiler: Compiled 44594 to 37363 computations (16.2% saved)

bsearch0.0ms (0%)

regimes1.4s (0.4%)

Compiler: Compiled 11644 to 10593 computations (9% saved)

bsearch0.0ms (0%)

regimes461.0ms (0.1%)

Compiler: Compiled 2941 to 2951 computations (-0.3% saved)

bsearch0.0ms (0%)

regimes1.1s (0.3%)

Compiler: Compiled 2564 to 2624 computations (-2.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

regimes784.0ms (0.2%)

Compiler: Compiled 2309 to 2385 computations (-3.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

regimes762.0ms (0.2%)

Compiler: Compiled 2246 to 2322 computations (-3.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

regimes424.0ms (0.1%)

Compiler: Compiled 1803 to 1869 computations (-3.7% saved)

bsearch1.0ms (0%)

Steps

Iters	Range		Point
0	0.9980821832494426	0.9996877175922909	0.9988849504208668

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes186.0ms (0.1%)

Compiler: Compiled 1193 to 1239 computations (-3.9% saved)

bsearch0.0ms (0%)

regimes233.0ms (0.1%)

Compiler: Compiled 543 to 674 computations (-24.1% saved)

bsearch82.0ms (0%)

Steps

Iters	Range		Point
6	1.823783433691056e-147	2.5520338995615692e-146	1.7098555952575793e-146
10	-1.688516976144709e-158	-4.2343382723043966e-172	-1.6684151299955752e-158

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes132.0ms (0%)

Compiler: Compiled 123 to 199 computations (-61.8% saved)

bsearch72.0ms (0%)

Steps

Iters	Range		Point
6	1.823783433691056e-147	2.5520338995615692e-146	2.0146837817686424e-146
10	-1.688516976144709e-158	-4.2343382723043966e-172	-1.6684151299955752e-158

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes46.0ms (0%)

Compiler: Compiled 72 to 130 computations (-80.6% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Compiler: Compiled 33 to 75 computations (-127.3% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Accuracy

Total 0.4b remaining (100%)

Threshold costs 0.4b (100%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch22.0ms (0%)

Compiler: Compiled 433 to 284 computations (34.4% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	647
1	101	647

end0.0ms (0%)

sample1.3min (23.6%)

Algorithm

1×

intervals

Results

582.0ms	1828×	body	1024	valid
497.0ms	1592×	body	1024	invalid
366.0ms	4839×	body	128	valid
192.0ms	848×	body	512	valid
174.0ms	766×	body	512	invalid
76.0ms	479×	body	256	valid
59.0ms	394×	body	256	invalid
53.0ms	627×	body	128	invalid
3.0ms	6×	body	2048	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 76967 to 56587 computations (26.5% saved)

Pareto

0.5312379456900446