Details

analyze514.0ms (11.3%)

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)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify162.0ms (3.5%)

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)

localize14.0ms (0.3%)

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-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
9×	`times-frac_binary64_773`
7×	`add-log-exp_binary64_806`
5×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
4×	`flip-+_binary64_741` `flip3-+_binary64_770`
3×	`associate-/r_binary64_711` `pow1_binary64_828` `associate-/l_binary64_712`
2×	`associate-/l/_binary64_714` `associate-/r/_binary64_713` `+-commutative_binary64_697` `sum-log_binary64_858`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `div-exp_binary64_818` `clear-num_binary64_766` `div-inv_binary64_764`

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

series285.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

175.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
72.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
38.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5573	1768

prune339.0ms (7.4%)

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 7062 to 4278 computations (39.4% 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 (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_767`
28×	`sqrt-prod_binary64_783`
25×	`add-sqr-sqrt_binary64_789`
24×	`times-frac_binary64_773`
23×	`add-cube-cbrt_binary64_802`
10×	`distribute-lft-out_binary64_718` `unpow-prod-down_binary64_846`
8×	`associate-/r*_binary64_711`
6×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803` `sqrt-div_binary64_784`
5×	`flip-+_binary64_741` `flip3-+_binary64_770`
3×	`associate-/l*_binary64_712`
2×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `associate-/r/_binary64_713` `pow1/2_binary64_847` `sqrt-pow1_binary64_785`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `+-commutative_binary64_697` `sum-log_binary64_858` `div-exp_binary64_818` `clear-num_binary64_766` `div-inv_binary64_764`

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))))
9.0ms	(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))

series404.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(/.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))))
72.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
48.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
42.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune231.0ms (5.1%)

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 5259 to 2683 computations (49% saved)

localize15.0ms (0.3%)

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 (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_767`
30×	`sqrt-prod_binary64_783`
25×	`add-sqr-sqrt_binary64_789`
24×	`times-frac_binary64_773`
23×	`add-cube-cbrt_binary64_802`
12×	`distribute-lft-out_binary64_718` `unpow-prod-down_binary64_846`
8×	`associate-/r*_binary64_711`
6×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803` `sqrt-div_binary64_784`
5×	`flip-+_binary64_741` `flip3-+_binary64_770`
3×	`associate-/l*_binary64_712`
2×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `associate-/r/_binary64_713` `pow1/2_binary64_847` `sqrt-pow1_binary64_785`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `+-commutative_binary64_697` `sum-log_binary64_858` `div-exp_binary64_818` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 96

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)))
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))

series402.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(/.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))))
67.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
49.0ms	(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)))

simplify82.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5305	3217

prune199.0ms (4.4%)

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 4148 to 2485 computations (40.1% saved)

localize12.0ms (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))))

rewrite56.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_767`
32×	`times-frac_binary64_773`
31×	`add-sqr-sqrt_binary64_789`
24×	`add-cube-cbrt_binary64_802`
21×	`associate-r_binary64_707`
17×	`add-exp-log_binary64_805`
16×	`distribute-lft-out_binary64_718` `unpow-prod-down_binary64_846`
11×	`add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806`
7×	`pow1_binary64_828`
6×	`flip-+_binary64_741` `flip3-+_binary64_770`
5×	`associate-/r*_binary64_711`
4×	`associate-/r/_binary64_713` `prod-exp_binary64_816` `div-exp_binary64_818`
3×	`associate-l_binary64_708` `unswap-sqr_binary64_735` `associate-/l*_binary64_712`
2×	`frac-times_binary64_777` `cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `1-exp_binary64_811` `+-commutative_binary64_697` `sum-log_binary64_858` `associate-*l/_binary64_710` `rec-exp_binary64_817` `div-inv_binary64_764`
1×	`frac-2neg_binary64_778` `pow-flip_binary64_841` `-commutative_binary64_698` `associate-r/_binary64_709` `pow-prod-down_binary64_838` `clear-num_binary64_766` `un-div-inv_binary64_765` `inv-pow_binary64_852`

Counts

4 → 113

Calls

4 calls:

21.0ms	(.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)))
8.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series333.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(.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))))
72.0ms	(+.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)))
35.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

simplify110.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4945	2873
1	4945	2873

prune161.0ms (3.5%)

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 3334 to 1897 computations (43.1% saved)

regimes124.0ms (2.7%)

Compiler: Compiled 1049 to 847 computations (19.3% saved)

bsearch1.0ms (0%)

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%)

sample811.0ms (17.8%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
19.0ms	472×	body	128	invalid

Compiler

Compiled 263 to 192 computations (27% saved)

Details

analyze514.0ms (11.3%)

sample23.0ms (0.5%)

simplify162.0ms (3.5%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

rewrite23.0ms (0.5%)

series285.0ms (6.3%)

simplify71.0ms (1.6%)

prune339.0ms (7.4%)

localize18.0ms (0.4%)

rewrite46.0ms (1%)

series404.0ms (8.9%)

simplify63.0ms (1.4%)

prune231.0ms (5.1%)

localize15.0ms (0.3%)

rewrite50.0ms (1.1%)

series402.0ms (8.8%)

simplify82.0ms (1.8%)

prune199.0ms (4.4%)

localize12.0ms (0.3%)

rewrite56.0ms (1.2%)

series333.0ms (7.3%)

simplify110.0ms (2.4%)

prune161.0ms (3.5%)

regimes124.0ms (2.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample811.0ms (17.8%)

Profiling