Details

analyze872.0ms (10.8%)

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)

sample35.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify260.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	5232	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: 28.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
28.0b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite25.0ms (0.3%)

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`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `pow1_binary64_1844`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`div-sub_binary64_1788` `+-commutative_binary64_1713` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

3 → 55

Calls

3 calls:

10.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series238.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

142.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
54.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
41.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify168.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4981	1822
1	4981	1822

prune144.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	10	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	10	65

Merged error: 27.7b

Counts

65 → 10

Compiler

Compiled 1701 to 733 computations (56.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
16.6b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
33.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
33.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite148.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

372×	`times-frac_binary64_1789`
294×	`*-un-lft-identity_binary64_1783`
226×	`sqrt-prod_binary64_1799`
192×	`add-sqr-sqrt_binary64_1805`
190×	`add-cube-cbrt_binary64_1818`
52×	`distribute-lft-out_binary64_1734` `unpow-prod-down_binary64_1862`
33×	`associate-/l*_binary64_1728`
22×	`sqrt-div_binary64_1800`
18×	`associate-/r/_binary64_1729`
14×	`associate-/r*_binary64_1727`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `flip-+_binary64_1757` `flip3-+_binary64_1786`
9×	`div-inv_binary64_1780`
6×	`pow1_binary64_1844`
4×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `add-log-exp_binary64_1822`
3×	`div-sub_binary64_1788` `associate-/l/_binary64_1730`
2×	`pow1/2_binary64_1863` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796`
1×	`flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 318

Calls

4 calls:

44.0ms	(/.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
14.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re 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)))

series360.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
142.0ms	(/.f64 (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
34.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify348.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

330 → 330

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4978	19342
1	4978	19342

prune856.0ms (10.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	325	5	330
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	329	11	340

Merged error: 25.3b

Counts

340 → 11

Compiler

Compiled 13075 to 6601 computations (49.5% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im))))
16.7b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
33.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
33.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite115.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64_1783`
40×	`add-sqr-sqrt_binary64_1805`
34×	`times-frac_binary64_1789`
31×	`sqrt-prod_binary64_1799`
30×	`associate-r_binary64_1723`
28×	`add-exp-log_binary64_1821`
26×	`add-cube-cbrt_binary64_1818`
18×	`add-cbrt-cube_binary64_1819`
9×	`div-exp_binary64_1834`
8×	`distribute-lft-out_binary64_1734` `prod-exp_binary64_1832` `unpow-prod-down_binary64_1862` `sqrt-div_binary64_1800` `pow1_binary64_1844`
6×	`associate-/l/_binary64_1730` `associate-/r*_binary64_1727`
5×	`cbrt-undiv_binary64_1817` `unswap-sqr_binary64_1751`
4×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `cbrt-unprod_binary64_1816` `flip-+_binary64_1757` `associate-*l/_binary64_1726` `frac-times_binary64_1793` `flip3-+_binary64_1786` `flip--_binary64_1758` `add-log-exp_binary64_1822`
3×	`associate-l_binary64_1724`
2×	`associate-*r/_binary64_1725` `un-div-inv_binary64_1781` `1-exp_binary64_1827` `div-inv_binary64_1780` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`
1×	`associate-/l_binary64_1728` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `pow-prod-down_binary64_1854`

Counts

4 → 130

Calls

4 calls:

47.0ms	(/.f64 (.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im))))
24.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (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	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series390.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
136.0ms	(/.f64 (.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (*.f64 y.im y.im))))
37.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5036	4117

prune225.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	142	11	153

Merged error: 25.3b

Counts

153 → 11

Compiler

Compiled 4651 to 2261 computations (51.4% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re))))
16.7b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
33.1b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
33.1b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite91.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64_1789`
182×	`*-un-lft-identity_binary64_1783`
116×	`add-sqr-sqrt_binary64_1805`
114×	`add-cube-cbrt_binary64_1818`
88×	`sqrt-prod_binary64_1799`
34×	`distribute-lft-out_binary64_1734` `unpow-prod-down_binary64_1862`
33×	`associate-/r*_binary64_1727`
17×	`add-exp-log_binary64_1821`
11×	`add-cbrt-cube_binary64_1819` `associate-/r/_binary64_1729` `associate-/l*_binary64_1728`
8×	`div-exp_binary64_1834`
7×	`pow1_binary64_1844`
6×	`div-inv_binary64_1780` `sqrt-div_binary64_1800`
5×	`flip3--_binary64_1787` `flip--_binary64_1758`
4×	`cbrt-undiv_binary64_1817` `add-log-exp_binary64_1822`
3×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
2×	`associate-/l/_binary64_1730` `1-exp_binary64_1827` `pow1/2_binary64_1863` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`
1×	`inv-pow_binary64_1868` `pow-flip_binary64_1857`

Counts

4 → 227

Calls

4 calls:

29.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re))))
14.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
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)))

series290.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re))))
104.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
32.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
31.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify184.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5195	10472

prune450.0ms (5.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	239	11	250

Merged error: 25.3b

Counts

250 → 11

Compiler

Compiled 9349 to 3856 computations (58.8% saved)

regimes482.0ms (6%)

Compiler: Compiled 4639 to 3412 computations (26.4% saved)

bsearch7.0ms (0.1%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	105
1	64	105

end0.0ms (0%)

sample2.2s (27.1%)

Algorithm

1×

intervals

Results

427.0ms	8000×	body	128	valid
22.0ms	426×	body	128	invalid

Compiler

Compiled 981 to 705 computations (28.1% saved)

Details

analyze872.0ms (10.8%)

sample35.0ms (0.4%)

simplify260.0ms (3.2%)

prune2.0ms (0%)

localize17.0ms (0.2%)

rewrite25.0ms (0.3%)

series238.0ms (2.9%)

simplify168.0ms (2.1%)

prune144.0ms (1.8%)

localize17.0ms (0.2%)

rewrite148.0ms (1.8%)

series360.0ms (4.5%)

simplify348.0ms (4.3%)

prune856.0ms (10.6%)

localize22.0ms (0.3%)

rewrite115.0ms (1.4%)

series390.0ms (4.8%)

simplify99.0ms (1.2%)

prune225.0ms (2.8%)

localize28.0ms (0.3%)

rewrite91.0ms (1.1%)

series290.0ms (3.6%)

simplify184.0ms (2.3%)

prune450.0ms (5.6%)

regimes482.0ms (6%)

bsearch7.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.2s (27.1%)

Profiling