Details

analyze543.0ms (10.9%)

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)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify168.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

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

Merged error: 26.5b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

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))
26.0b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
9×	`times-frac_binary64_1431`
7×	`add-log-exp_binary64_1461`
5×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
4×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
3×	`associate-/r_binary64_1371` `associate-/l_binary64_1372` `pow1_binary64_1483`
2×	`sum-log_binary64_1513` `associate-/r/_binary64_1373` `+-commutative_binary64_1357` `associate-/l/_binary64_1374`
1×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `div-inv_binary64_1422` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`

Counts

3 → 53

Calls

3 calls:

10.0ms	(/.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))

series299.0ms (6%)

Counts

3 → 9

Calls

3 calls:

189.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
71.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
39.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5214	1768

prune91.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 25.7b

Counts

63 → 9

Compiler

Compiled 1621 to 674 computations (58.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
16.8b	(/.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))))
32.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
32.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1425`
28×	`sqrt-prod_binary64_1440`
25×	`add-sqr-sqrt_binary64_1446`
24×	`times-frac_binary64_1431`
23×	`add-cube-cbrt_binary64_1457`
10×	`unpow-prod-down_binary64_1501` `distribute-lft-out_binary64_1378`
8×	`associate-/r*_binary64_1371`
6×	`sqrt-div_binary64_1441` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
5×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
3×	`associate-/l*_binary64_1372`
2×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `associate-/r/_binary64_1373` `associate-/l/_binary64_1374` `rem-sqrt-square_binary64_1438`
1×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `+-commutative_binary64_1357` `cbrt-undiv_binary64_1456`

Counts

4 → 94

Calls

4 calls:

15.0ms	(/.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)))
6.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
5.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series412.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(/.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))))
81.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
43.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5447	3187

prune148.0ms (3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	104	11	115

Merged error: 24.4b

Counts

115 → 11

Compiler

Compiled 3668 to 1530 computations (58.3% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
16.8b	(/.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))))
32.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
32.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1425`
30×	`sqrt-prod_binary64_1440`
25×	`add-sqr-sqrt_binary64_1446`
24×	`times-frac_binary64_1431`
23×	`add-cube-cbrt_binary64_1457`
12×	`unpow-prod-down_binary64_1501` `distribute-lft-out_binary64_1378`
8×	`associate-/r*_binary64_1371`
6×	`sqrt-div_binary64_1441` `add-cbrt-cube_binary64_1458` `pow1_binary64_1483` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
5×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
3×	`associate-/l*_binary64_1372`
2×	`pow1/2_binary64_1502` `sqrt-pow1_binary64_1442` `associate-/r/_binary64_1373` `associate-/l/_binary64_1374` `rem-sqrt-square_binary64_1438`
1×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `+-commutative_binary64_1357` `cbrt-undiv_binary64_1456`

Counts

4 → 96

Calls

4 calls:

15.0ms	(/.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))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series388.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(/.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))))
79.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
45.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
44.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4984	3217
1	4984	3217

prune182.0ms (3.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	108	11	119

Merged error: 24.4b

Counts

119 → 11

Compiler

Compiled 3913 to 2311 computations (40.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.4b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
25.8b	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite59.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_1425`
32×	`times-frac_binary64_1431`
31×	`add-sqr-sqrt_binary64_1446`
24×	`add-cube-cbrt_binary64_1457`
21×	`associate-r_binary64_1367`
17×	`add-exp-log_binary64_1460`
16×	`unpow-prod-down_binary64_1501` `distribute-lft-out_binary64_1378`
11×	`add-cbrt-cube_binary64_1458`
8×	`add-log-exp_binary64_1461`
7×	`pow1_binary64_1483`
6×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
5×	`associate-/r*_binary64_1371`
4×	`prod-exp_binary64_1471` `associate-/r/_binary64_1373` `div-exp_binary64_1473`
3×	`unswap-sqr_binary64_1393` `associate-l_binary64_1368` `associate-/l*_binary64_1372`
2×	`cbrt-unprod_binary64_1455` `div-inv_binary64_1422` `sum-log_binary64_1513` `+-commutative_binary64_1357` `1-exp_binary64_1466` `associate-*l/_binary64_1370` `cbrt-undiv_binary64_1456` `rec-exp_binary64_1472` `frac-times_binary64_1435`
1×	`frac-2neg_binary64_1436` `pow-flip_binary64_1496` `inv-pow_binary64_1507` `un-div-inv_binary64_1423` `clear-num_binary64_1424` `associate-r/_binary64_1369` `-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 113

Calls

4 calls:

23.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
11.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series327.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
68.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
45.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
34.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5125	2873

prune137.0ms (2.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	6	7
Picked	0	1	1
Done	1	2	3
Total	126	10	136

Merged error: 24.4b

Counts

136 → 10

Compiler

Compiled 2867 to 1538 computations (46.4% saved)

regimes363.0ms (7.3%)

Compiler: Compiled 4319 to 3142 computations (27.3% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	105
1	47	105

end0.0ms (0%)

sample1.4s (27.6%)

Algorithm

1×

intervals

Results

370.0ms	8000×	body	128	valid
21.0ms	472×	body	128	invalid

Compiler

Compiled 917 to 651 computations (29% saved)

Details

analyze543.0ms (10.9%)

sample22.0ms (0.4%)

simplify168.0ms (3.4%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite23.0ms (0.5%)

series299.0ms (6%)

simplify54.0ms (1.1%)

prune91.0ms (1.8%)

localize18.0ms (0.4%)

rewrite46.0ms (0.9%)

series412.0ms (8.3%)

simplify82.0ms (1.7%)

prune148.0ms (3%)

localize19.0ms (0.4%)

rewrite50.0ms (1%)

series388.0ms (7.8%)

simplify62.0ms (1.2%)

prune182.0ms (3.6%)

localize13.0ms (0.3%)

rewrite59.0ms (1.2%)

series327.0ms (6.6%)

simplify83.0ms (1.7%)

prune137.0ms (2.7%)

regimes363.0ms (7.3%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27.6%)

Profiling