Details

analyze555.0ms (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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune6.0ms (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

26.4b

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))
0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
25.9b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`times-frac_binary64_1789`
7×	`add-log-exp_binary64_1822`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
4×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `pow1_binary64_1844`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `+-commutative_binary64_1713` `sum-log_binary64_1874`
1×	`div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782`

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))

series153.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
40.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
20.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5573	1768

prune91.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Error

25.6b

Counts

63 → 8

Compiler

Compiled 1594 to 654 computations (59% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.8b	(/.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))))
31.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1783`
28×	`sqrt-prod_binary64_1799`
25×	`add-sqr-sqrt_binary64_1805`
24×	`times-frac_binary64_1789`
23×	`add-cube-cbrt_binary64_1818`
10×	`distribute-lft-out_binary64_1734` `unpow-prod-down_binary64_1862`
8×	`associate-/r*_binary64_1727`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
3×	`associate-/l*_binary64_1728`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782`

Counts

4 → 94

Calls

4 calls:

14.0ms	(/.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))

series212.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.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))))
36.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
27.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune146.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	103	11	114

Error

23.9b

Counts

114 → 11

Compiler

Compiled 3687 to 1551 computations (57.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
14.8b	(/.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))))
31.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite108.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`*-un-lft-identity_binary64_1783`
101×	`add-sqr-sqrt_binary64_1805`
94×	`times-frac_binary64_1789`
71×	`sqrt-prod_binary64_1799`
53×	`add-cube-cbrt_binary64_1818`
30×	`associate-l_binary64_1724` `associate-r_binary64_1723`
28×	`add-exp-log_binary64_1821`
24×	`distribute-lft-out_binary64_1734` `unpow-prod-down_binary64_1862`
18×	`add-cbrt-cube_binary64_1819`
15×	`unswap-sqr_binary64_1751`
10×	`sqrt-div_binary64_1800`
9×	`div-exp_binary64_1834`
8×	`prod-exp_binary64_1832` `associate-/r*_binary64_1727` `pow1_binary64_1844`
6×	`associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786`
5×	`cbrt-undiv_binary64_1817`
4×	`cbrt-unprod_binary64_1816` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `div-inv_binary64_1780`
2×	`associate-/l/_binary64_1730` `1-exp_binary64_1827` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`
1×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `frac-times_binary64_1793` `clear-num_binary64_1782` `pow-prod-down_binary64_1854`

Counts

4 → 184

Calls

4 calls:

45.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
14.0ms	(/.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))))
11.0ms	(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)))

series304.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(/.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))))
125.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify153.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4973	7451
1	4973	7451

prune335.0ms (7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	196	11	207

Error

23.9b

Counts

207 → 11

Compiler

Compiled 6962 to 4028 computations (42.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.2b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.5b	(/.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))))
25.5b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite66.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`*-un-lft-identity_binary64_1783`
138×	`times-frac_binary64_1789`
72×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
34×	`distribute-lft-out_binary64_1734` `unpow-prod-down_binary64_1862`
24×	`associate-/r*_binary64_1727`
17×	`add-exp-log_binary64_1821`
11×	`add-cbrt-cube_binary64_1819` `associate-/r/_binary64_1729`
8×	`associate-/l*_binary64_1728` `flip-+_binary64_1757` `div-exp_binary64_1834` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
6×	`div-inv_binary64_1780`
5×	`pow1_binary64_1844`
4×	`cbrt-undiv_binary64_1817`
2×	`associate-/l/_binary64_1730` `+-commutative_binary64_1713` `1-exp_binary64_1827` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`inv-pow_binary64_1868` `pow-flip_binary64_1857`

Counts

4 → 171

Calls

4 calls:

20.0ms	(/.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)))
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))

series250.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(/.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))))
57.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
39.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
19.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5153	7314

prune226.0ms (4.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	184	10	194

Error

23.9b

Counts

194 → 10

Compiler

Compiled 5102 to 2390 computations (53.2% saved)

regimes337.0ms (7%)

Accuracy

Total 2.2b remaining (8.9%)

Threshold costs 0b (0%)

Compiler

Compiled 4059 to 2912 computations (28.3% saved)

bsearch2.0ms (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%)

sample1.3s (28.1%)

Algorithm

1×

intervals

Results

368.0ms	8000×	body	128	valid
23.0ms	519×	body	128	invalid

Compiler

Compiled 865 to 605 computations (30.1% saved)

Details

analyze555.0ms (11.5%)

sample22.0ms (0.5%)

simplify98.0ms (2%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite21.0ms (0.4%)

series153.0ms (3.2%)

simplify77.0ms (1.6%)

prune91.0ms (1.9%)

localize16.0ms (0.3%)

rewrite40.0ms (0.8%)

series212.0ms (4.4%)

simplify69.0ms (1.4%)

prune146.0ms (3%)

localize14.0ms (0.3%)

rewrite108.0ms (2.2%)

series304.0ms (6.3%)

simplify153.0ms (3.2%)

prune335.0ms (7%)

localize12.0ms (0.2%)

rewrite66.0ms (1.4%)

series250.0ms (5.2%)

simplify129.0ms (2.7%)

prune226.0ms (4.7%)

regimes337.0ms (7%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (28.1%)

Profiling