Details

analyze514.0ms (11.5%)

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)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify164.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Merged error: 28.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
27.6b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
9×	`times-frac_binary64_1117`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
3×	`flip-+_binary64_1085` `associate-/r_binary64_1055` `associate-/l_binary64_1056` `flip3-+_binary64_1114`
2×	`associate-/l/_binary64_1058` `pow1_binary64_1172` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sum-log_binary64_1202` `clear-num_binary64_1110`

Counts

2 → 42

Calls

2 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)))
5.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series239.0ms (5.4%)

Counts

2 → 6

Calls

2 calls:

174.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
65.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5449	1541

prune365.0ms (8.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	38	10	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	10	49

Merged error: 27.3b

Counts

49 → 10

Compiler

Compiled 7364 to 4630 computations (37.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
18.2b	(/.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))))
29.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1111`
28×	`sqrt-prod_binary64_1127`
25×	`add-sqr-sqrt_binary64_1133`
24×	`times-frac_binary64_1117`
23×	`add-cube-cbrt_binary64_1146`
10×	`unpow-prod-down_binary64_1190` `distribute-lft-out_binary64_1062`
8×	`associate-/r*_binary64_1055`
6×	`add-cbrt-cube_binary64_1147` `sqrt-div_binary64_1128` `add-log-exp_binary64_1150` `pow1_binary64_1172` `add-exp-log_binary64_1149`
5×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
3×	`associate-/l*_binary64_1056`
2×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `associate-/l/_binary64_1058` `sqrt-pow1_binary64_1129` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sum-log_binary64_1202` `clear-num_binary64_1110`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/.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)))
5.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series397.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.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))))
78.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
50.0ms	(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)))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune248.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	107	9	116

Merged error: 23.6b

Counts

116 → 9

Compiler

Compiled 5392 to 2875 computations (46.7% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
18.2b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
29.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.6b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1111`
28×	`sqrt-prod_binary64_1127`
25×	`add-sqr-sqrt_binary64_1133`
24×	`times-frac_binary64_1117`
23×	`add-cube-cbrt_binary64_1146`
10×	`unpow-prod-down_binary64_1190` `distribute-lft-out_binary64_1062`
8×	`associate-/l*_binary64_1056`
6×	`add-cbrt-cube_binary64_1147` `sqrt-div_binary64_1128` `add-log-exp_binary64_1150` `pow1_binary64_1172` `add-exp-log_binary64_1149`
5×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
3×	`associate-/r*_binary64_1055`
2×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `associate-/l/_binary64_1058` `sqrt-pow1_binary64_1129` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `+-commutative_binary64_1041` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sum-log_binary64_1202` `clear-num_binary64_1110`

Counts

4 → 94

Calls

4 calls:

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

series300.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (+.f64 (.f64 y.re x.re) (.f64 y.im x.im)))
64.0ms	(+.f64 (.f64 y.re x.re) (.f64 y.im x.im))
46.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
40.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify82.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5077	3253

prune169.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Merged error: 23.6b

Counts

115 → 9

Compiler

Compiled 3975 to 1858 computations (53.3% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b

(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

0.4b

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))

27.4b

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

rewrite60.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_1117`
135×	`*-un-lft-identity_binary64_1111`
71×	`add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
32×	`unpow-prod-down_binary64_1190` `distribute-lft-out_binary64_1062`
24×	`associate-/r*_binary64_1055`
16×	`add-exp-log_binary64_1149`
11×	`associate-/r/_binary64_1057`
10×	`add-cbrt-cube_binary64_1147`
8×	`associate-/l*_binary64_1056` `div-exp_binary64_1162`
7×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
6×	`div-inv_binary64_1108`
5×	`add-log-exp_binary64_1150`
4×	`cbrt-undiv_binary64_1145` `pow1_binary64_1172`
2×	`frac-2neg_binary64_1122` `associate-/l/_binary64_1058` `1-exp_binary64_1155` `rec-exp_binary64_1161` `clear-num_binary64_1110`
1×	`pow-flip_binary64_1185` `+-commutative_binary64_1041` `sum-log_binary64_1202` `inv-pow_binary64_1196`

Counts

3 → 158

Calls

3 calls:

19.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))

15.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

4.0ms

(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

series431.0ms (9.7%)

Counts

3 → 9

Calls

3 calls:

253.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))

104.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

73.0ms

(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5444	7063

prune201.0ms (4.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	167	9	176

Merged error: 23.6b

Counts

176 → 9

Compiler

Compiled 4758 to 2202 computations (53.7% saved)

regimes78.0ms (1.7%)

Compiler: Compiled 556 to 508 computations (8.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	48
1	26	48

end0.0ms (0%)

sample772.0ms (17.3%)

Algorithm

1×

intervals

Results

329.0ms	8000×	body	128	valid
18.0ms	463×	body	128	invalid

Compiler

Compiled 178 to 154 computations (13.5% saved)

Details

analyze514.0ms (11.5%)

sample21.0ms (0.5%)

simplify164.0ms (3.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite19.0ms (0.4%)

series239.0ms (5.4%)

simplify66.0ms (1.5%)

prune365.0ms (8.2%)

localize18.0ms (0.4%)

rewrite45.0ms (1%)

series397.0ms (8.9%)

simplify64.0ms (1.4%)

prune248.0ms (5.5%)

localize21.0ms (0.5%)

rewrite47.0ms (1%)

series300.0ms (6.7%)

simplify82.0ms (1.8%)

prune169.0ms (3.8%)

localize12.0ms (0.3%)

rewrite60.0ms (1.3%)

series431.0ms (9.7%)

simplify119.0ms (2.7%)

prune201.0ms (4.5%)

regimes78.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample772.0ms (17.3%)

Profiling