Details

analyze801.0ms (6.5%)

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)

sample91.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms	68×	body	1024	valid
17.0ms	51×	body	1024	invalid
11.0ms	140×	body	128	valid
7.0ms	29×	body	512	invalid
7.0ms	28×	body	512	valid
5.0ms	29×	body	128	invalid
3.0ms	20×	body	256	valid
2.0ms	11×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify96.0ms (0.8%)

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

0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize13.0ms (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)))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite147.0ms (1.2%)

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)

series665.0ms (5.4%)

Error

0.2b

Counts

3 → 40

Calls

3 calls:

357.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
192.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
80.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1429 to 1264 computations (11.5% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5013	2823

prune148.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Error

Counts

136 → 8

Compiler

Compiled 2792 to 1120 computations (59.9% 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))
7.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
7.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite247.0ms (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:

21.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
10.0ms	(/.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)

series679.0ms (5.5%)

Error

Counts

4 → 60

Calls

4 calls:

193.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
192.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
118.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
114.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3615 to 2585 computations (28.5% saved)

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5260	5433

prune258.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	229	7	236

Error

Counts

236 → 7

Compiler

Compiled 6794 to 2259 computations (66.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 2))))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) 2)))
7.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
7.3b	(sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 2))

rewrite169.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64_441`
39×	`sqrt-prod_binary64_435`
23×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
17×	`sqrt-div_binary64_436` `associate-r_binary64_359`
15×	`pow1_binary64_480`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`associate-l_binary64_360`
7×	`associate-*r/_binary64_361`
6×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`pow1/2_binary64_499` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `associate-*l/_binary64_362`
3×	`rem-sqrt-square_binary64_432`
2×	`div-inv_binary64_416` `*-commutative_binary64_350`
1×	`sqrt-unprod_binary64_439`

Counts

4 → 110

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) 2)))
14.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 2))))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3866 to 1045 computations (73% saved)

series842.0ms (6.8%)

Error

Counts

4 → 60

Calls

4 calls:

338.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 2))))
176.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 2))
152.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) 2)))
110.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3241 to 2464 computations (24% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4971	4199
1	4971	4199

prune186.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	170	7	177

Error

Counts

177 → 7

Compiler

Compiled 4645 to 1557 computations (66.5% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.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))

rewrite77.0ms (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:

8.0ms	(/.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)

series700.0ms (5.6%)

Error

Counts

3 → 44

Calls

3 calls:

353.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
230.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
83.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1637 to 1411 computations (13.8% saved)

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5001	1788

prune77.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Error

Counts

111 → 7

Compiler

Compiled 1686 to 610 computations (63.8% saved)

regimes1.8s (14.4%)

Accuracy

Total 0.3b remaining (91.7%)

Threshold costs 0.3b (91.7%)

Compiler

Compiled 21375 to 15737 computations (26.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample5.0s (40.5%)

Algorithm

1×

intervals

Results

622.0ms	1806×	body	1024	valid
520.0ms	1515×	body	1024	invalid
397.0ms	4845×	body	128	valid
225.0ms	898×	body	512	valid
183.0ms	767×	body	512	invalid
80.0ms	448×	body	256	valid
60.0ms	371×	body	256	invalid
56.0ms	663×	body	128	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 2691 to 1975 computations (26.6% saved)

Details

analyze801.0ms (6.5%)

sample91.0ms (0.7%)

simplify96.0ms (0.8%)

prune5.0ms (0%)

localize13.0ms (0.1%)

rewrite147.0ms (1.2%)

series665.0ms (5.4%)

simplify85.0ms (0.7%)

prune148.0ms (1.2%)

localize12.0ms (0.1%)

rewrite247.0ms (2%)

series679.0ms (5.5%)

simplify91.0ms (0.7%)

prune258.0ms (2.1%)

localize12.0ms (0.1%)

rewrite169.0ms (1.4%)

series842.0ms (6.8%)

simplify94.0ms (0.8%)

prune186.0ms (1.5%)

localize11.0ms (0.1%)

rewrite77.0ms (0.6%)

series700.0ms (5.6%)

simplify84.0ms (0.7%)

prune77.0ms (0.6%)

regimes1.8s (14.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.0s (40.5%)

Profiling