Details

analyze137.0ms (5.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5047	13
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample27.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify48.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5047	13

prune5.0ms (0.2%)

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

0.2b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.6b	(/.f64 1 (*.f64 i i))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1805`
35×	`times-frac_binary64_1789`
33×	`*-un-lft-identity_binary64_1783`
17×	`add-cube-cbrt_binary64_1818`
15×	`add-exp-log_binary64_1821`
12×	`difference-of-squares_binary64_1752`
10×	`pow1_binary64_1844`
9×	`add-cbrt-cube_binary64_1819` `associate-/r*_binary64_1727`
8×	`distribute-lft-out--_binary64_1735`
6×	`associate-/l*_binary64_1728` `div-inv_binary64_1780` `pow-flip_binary64_1857`
5×	`div-exp_binary64_1834`
3×	`prod-exp_binary64_1832` `cbrt-undiv_binary64_1817`
2×	`associate-/r/_binary64_1729` `1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833` `add-log-exp_binary64_1822`
1×	`flip3--_binary64_1787` `inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854` `flip--_binary64_1758` `pow2_binary64_1864`

Counts

2 → 81

Calls

2 calls:

8.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

series29.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
12.0ms	(/.f64 1 (*.f64 i i))

simplify84.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5049	1212

prune83.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Error

Counts

89 → 4

Compiler

Compiled 1260 to 964 computations (23.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 2 (/.f64 1 i))
0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

rewrite80.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`add-sqr-sqrt_binary64_1805`
108×	`*-un-lft-identity_binary64_1783`
107×	`times-frac_binary64_1789`
55×	`add-cube-cbrt_binary64_1818`
30×	`associate-r_binary64_1723`
24×	`difference-of-squares_binary64_1752`
21×	`associate-l_binary64_1724`
20×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `div-inv_binary64_1780`
16×	`distribute-lft-out--_binary64_1735`
14×	`distribute-lft-out_binary64_1734`
13×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
8×	`associate-/r/_binary64_1729`
6×	`associate-/l*_binary64_1728` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `add-log-exp_binary64_1822` `pow1_binary64_1844`
4×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `unswap-sqr_binary64_1751`
3×	`flip3--_binary64_1787` `flip--_binary64_1758`
2×	`flip-+_binary64_1757` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`associate-r/_binary64_1725` `associate-l/_binary64_1726` `diff-log_binary64_1875` `*-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854` `sub-neg_binary64_1776`

Counts

4 → 190

Calls

4 calls:

35.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
8.0ms	(-.f64 2 (/.f64 1 i))
8.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series52.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
10.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
9.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
8.0ms	(-.f64 2 (/.f64 1 i))

simplify85.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4910	3644
1	4910	3644

prune291.0ms (10.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	203	3	206

Error

Counts

206 → 3

Compiler

Compiled 4395 to 3817 computations (13.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1805`
21×	`*-un-lft-identity_binary64_1783` `times-frac_binary64_1789`
13×	`add-cube-cbrt_binary64_1818`
12×	`difference-of-squares_binary64_1752`
7×	`associate-/r*_binary64_1727`
4×	`sqr-pow_binary64_1755` `unpow-prod-down_binary64_1862` `distribute-lft-out--_binary64_1735`
3×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728` `add-exp-log_binary64_1821`
2×	`associate-/r/_binary64_1729`
1×	`flip3--_binary64_1787` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758` `add-log-exp_binary64_1822` `pow1_binary64_1844`

Counts

1 → 45

Calls

1 calls:

7.0ms

(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

series19.0ms (0.7%)

Counts

1 → 3

Calls

1 calls:

19.0ms

(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

simplify71.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5729	834

prune50.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	49	2	51

Error

Counts

51 → 2

Compiler

Compiled 726 to 639 computations (12% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 16 (pow.f64 i -4))
0.0b	(+.f64 4 (pow.f64 i -2))
0.3b	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
21.8b	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 4 (pow.f64 i -2)))

rewrite51.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64_1805`
50×	`*-un-lft-identity_binary64_1783`
43×	`times-frac_binary64_1789`
30×	`add-cube-cbrt_binary64_1818`
27×	`associate-l_binary64_1724`
24×	`difference-of-squares_binary64_1752`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `unpow-prod-down_binary64_1862`
9×	`sqr-pow_binary64_1755`
8×	`distribute-lft-out--_binary64_1735` `add-log-exp_binary64_1822`
7×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
6×	`pow1_binary64_1844`
4×	`associate-/r/_binary64_1729` `associate-r_binary64_1723`
3×	`flip3--_binary64_1787` `associate-/l*_binary64_1728` `flip-+_binary64_1757` `flip3-+_binary64_1786` `flip--_binary64_1758`
2×	`associate-*r/_binary64_1725` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
1×	`+-commutative_binary64_1713` `distribute-lft-in_binary64_1732` `associate-l/_binary64_1726` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `sum-log_binary64_1874` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `sub-neg_binary64_1776`

Counts

4 → 132

Calls

4 calls:

21.0ms	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 4 (pow.f64 i -2)))
7.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
6.0ms	(-.f64 16 (pow.f64 i -4))
5.0ms	(+.f64 4 (pow.f64 i -2))

series152.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(-.f64 16 (pow.f64 i -4))
45.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 i -4)))
31.0ms	(+.f64 4 (pow.f64 i -2))
30.0ms	(*.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 4 (pow.f64 i -2)))

simplify69.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4868	2493
1	4868	2493

prune182.0ms (6.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	144	2	146

Error

Counts

146 → 2

Compiler

Compiled 2893 to 2479 computations (14.3% saved)

regimes77.0ms (2.8%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 758 to 666 computations (12.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample1.1s (39.1%)

Algorithm

1×

intervals

Results

406.0ms	8000×	body	128	valid
109.0ms	8000×	pre	128	true

Compiler

Compiled 397 to 350 computations (11.8% saved)

Details

analyze137.0ms (5.1%)

sample27.0ms (1%)

simplify48.0ms (1.8%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite19.0ms (0.7%)

series29.0ms (1.1%)

simplify84.0ms (3.1%)

prune83.0ms (3%)

localize8.0ms (0.3%)

rewrite80.0ms (2.9%)

series52.0ms (1.9%)

simplify85.0ms (3.1%)

prune291.0ms (10.7%)

localize5.0ms (0.2%)

rewrite11.0ms (0.4%)

series19.0ms (0.7%)

simplify71.0ms (2.6%)

prune50.0ms (1.8%)

localize9.0ms (0.3%)

rewrite51.0ms (1.9%)

series152.0ms (5.6%)

simplify69.0ms (2.5%)

prune182.0ms (6.7%)

regimes77.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (39.1%)

Profiling