Details

analyze1.0s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify138.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (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

27.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
26.7b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
9×	`times-frac_binary64_425`
7×	`add-log-exp_binary64_458`
5×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`flip3-+_binary64_422` `flip-+_binary64_393`
3×	`associate-/r_binary64_363` `pow1_binary64_480` `associate-/l_binary64_364`
2×	`sum-log_binary64_510` `associate-/r/_binary64_365` `+-commutative_binary64_349` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

3 → 53

Calls

3 calls:

9.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series206.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

142.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
43.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
21.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify127.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5573	1768

prune109.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	7	63

Error

26.4b

Counts

63 → 7

Compiler

Compiled 1588 to 642 computations (59.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.2b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_419`
28×	`sqrt-prod_binary64_435`
25×	`add-sqr-sqrt_binary64_441`
24×	`times-frac_binary64_425`
23×	`add-cube-cbrt_binary64_454`
10×	`unpow-prod-down_binary64_498` `distribute-lft-out_binary64_370`
8×	`associate-/r*_binary64_363`
6×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
3×	`associate-/l*_binary64_364`
2×	`pow1/2_binary64_499` `associate-/r/_binary64_365` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `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

4 → 94

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series295.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
39.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
38.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
36.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune177.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	101	12	113

Error

24.4b

Counts

113 → 12

Compiler

Compiled 3736 to 1584 computations (57.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite82.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_419`
30×	`sqrt-prod_binary64_435`
25×	`add-sqr-sqrt_binary64_441`
24×	`times-frac_binary64_425`
23×	`add-cube-cbrt_binary64_454`
12×	`unpow-prod-down_binary64_498` `distribute-lft-out_binary64_370`
8×	`associate-/r*_binary64_363`
6×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
3×	`associate-/l*_binary64_364`
2×	`pow1/2_binary64_499` `associate-/r/_binary64_365` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `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

4 → 96

Calls

4 calls:

27.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
16.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
14.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series300.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
38.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
28.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5305	3217

prune241.0ms (3.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	108	12	120

Error

24.4b

Counts

120 → 12

Compiler

Compiled 3981 to 2365 computations (40.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

15.8b	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
15.8b	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
30.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.2b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_419`
10×	`add-sqr-sqrt_binary64_441` `sqrt-prod_binary64_435`
8×	`add-cube-cbrt_binary64_454`
6×	`cbrt-prod_binary64_450` `pow1_binary64_480`
4×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `cbrt-div_binary64_451` `distribute-lft-out_binary64_370` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
2×	`pow1/3_binary64_501` `pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 60

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
6.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series413.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
177.0ms	(cbrt.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
30.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4978	1446
1	4978	1446

prune169.0ms (2.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	9	9
Picked	1	0	1
Done	0	2	2
Total	72	12	84

Error

24.4b

Counts

84 → 12

Compiler

Compiled 3566 to 1348 computations (62.2% saved)

regimes627.0ms (9.4%)

Accuracy

Total 2.9b remaining (11.1%)

Threshold costs 0b (0%)

Compiler

Compiled 5024 to 3607 computations (28.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	48
1	26	48

end0.0ms (0%)

sample2.3s (34.1%)

Algorithm

1×

intervals

Results

555.0ms	8000×	body	128	valid
29.0ms	434×	body	128	invalid

Compiler

Compiled 1029 to 738 computations (28.3% saved)

Details

analyze1.0s (15.5%)

sample39.0ms (0.6%)

simplify138.0ms (2.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite24.0ms (0.4%)

series206.0ms (3.1%)

simplify127.0ms (1.9%)

prune109.0ms (1.6%)

localize16.0ms (0.2%)

rewrite42.0ms (0.6%)

series295.0ms (4.4%)

simplify70.0ms (1.1%)

prune177.0ms (2.7%)

localize23.0ms (0.3%)

rewrite82.0ms (1.2%)

series300.0ms (4.5%)

simplify96.0ms (1.4%)

prune241.0ms (3.6%)

localize16.0ms (0.2%)

rewrite49.0ms (0.7%)

series413.0ms (6.2%)

simplify86.0ms (1.3%)

prune169.0ms (2.5%)

regimes627.0ms (9.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (34.1%)

Profiling