Details

analyze355.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample36.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	193×	body	128	valid
6.0ms	24×	body	2048	valid
4.0ms	13×	body	4096	valid
4.0ms	256×	pre	128	true
2.0ms	12×	body	1024	valid
2.0ms	11×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify113.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune3.0ms (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

40.8b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441`
8×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `pow1_binary64_480`
6×	`add-cube-cbrt_binary64_454`
5×	`sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `flip3--_binary64_423` `associate-*r/_binary64_361` `flip-+_binary64_393` `flip--_binary64_394`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series186.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
29.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
20.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4930	1140
1	4930	1140

prune92.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Error

10.2b

Counts

69 → 8

Compiler

Compiled 1489 to 665 computations (55.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.2b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437`
1×	`*-un-lft-identity_binary64_419` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1/2_binary64_499` `add-sqr-sqrt_binary64_441` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `sqrt-prod_binary64_435`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series61.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

61.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4956	255
1	4956	255

prune22.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	15	9	24

Error

10.2b

Counts

24 → 9

Compiler

Compiled 373 to 258 computations (30.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_441`
17×	`sqrt-prod_binary64_435`
11×	`*-un-lft-identity_binary64_419`
8×	`associate-r_binary64_359`
7×	`add-cube-cbrt_binary64_454` `pow1_binary64_480`
6×	`associate-l_binary64_360`
4×	`sqrt-div_binary64_436` `unswap-sqr_binary64_387` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow-prod-down_binary64_490` `pow1/2_binary64_499` `sqrt-pow1_binary64_437`
2×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458` `flip3--_binary64_423` `associate-*r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sqrt-unprod_binary64_439` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `rem-sqrt-square_binary64_432`

Counts

2 → 51

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series96.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

65.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
31.0ms	(sqrt.f64 (-.f64 im re))

simplify77.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4954	838
1	4954	838

prune57.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	57	9	66

Error

10.2b

Counts

66 → 9

Compiler

Compiled 1009 to 610 computations (39.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.3b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.6b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_441`
28×	`log-prod_binary64_505` `sqrt-prod_binary64_435`
23×	`*-un-lft-identity_binary64_419`
20×	`exp-sum_binary64_465`
15×	`add-cube-cbrt_binary64_454`
11×	`associate-r_binary64_359` `pow1_binary64_480`
8×	`sqrt-div_binary64_436`
6×	`unswap-sqr_binary64_387` `exp-prod_binary64_471` `log-pow_binary64_508` `associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `log-div_binary64_506`
4×	`difference-of-squares_binary64_388` `exp-diff_binary64_467` `add-log-exp_binary64_458` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
3×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
2×	`associate-*r/_binary64_361`
1×	`pow-prod-down_binary64_490` `rem-log-exp_binary64_460` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `rem-exp-log_binary64_459` `rem-sqrt-square_binary64_432`

Counts

4 → 98

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
5.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series375.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
135.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
39.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
31.0ms	(sqrt.f64 (-.f64 im re))

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6248	1612

prune98.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	110	9	119

Error

10.2b

Counts

119 → 9

Compiler

Compiled 1828 to 1016 computations (44.4% saved)

regimes664.0ms (15.8%)

Accuracy

Total 9.1b remaining (47.9%)

Threshold costs 0b (0%)

Compiler

Compiled 4826 to 3337 computations (30.9% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	116
1	49	116

end0.0ms (0%)

sample1.6s (38%)

Algorithm

1×

intervals

Results

306.0ms	6074×	body	128	valid
164.0ms	644×	body	2048	valid
156.0ms	504×	body	4096	valid
115.0ms	8000×	pre	128	true
84.0ms	425×	body	1024	valid
33.0ms	234×	body	512	valid
11.0ms	119×	body	256	valid

Compiler

Compiled 644 to 429 computations (33.4% saved)

Details

analyze355.0ms (8.4%)

sample36.0ms (0.9%)

simplify113.0ms (2.7%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite33.0ms (0.8%)

series186.0ms (4.4%)

simplify93.0ms (2.2%)

prune92.0ms (2.2%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series61.0ms (1.4%)

simplify65.0ms (1.5%)

prune22.0ms (0.5%)

localize7.0ms (0.2%)

rewrite17.0ms (0.4%)

series96.0ms (2.3%)

simplify77.0ms (1.8%)

prune57.0ms (1.4%)

localize10.0ms (0.2%)

rewrite36.0ms (0.9%)

series375.0ms (8.9%)

simplify84.0ms (2%)

prune98.0ms (2.3%)

regimes664.0ms (15.8%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (38%)

Profiling