Details

analyze6.0ms (0.3%)

Algorithm

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)

sample22.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify136.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5047	13

prune11.0ms (0.5%)

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

0.3b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.4b	(/.f64 1 (*.f64 i i))

rewrite20.0ms (0.9%)

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))

series30.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

17.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
13.0ms	(/.f64 1 (*.f64 i i))

simplify79.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5049	1212

prune87.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Error

Counts

89 → 3

Compiler

Compiled 1228 to 940 computations (23.5% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

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)))

rewrite72.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 161

Calls

3 calls:

37.0ms	(*.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)))

series41.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

22.0ms	(*.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)))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

simplify93.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5200	3334

prune226.0ms (10.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	170	3	173

Error

Counts

173 → 3

Compiler

Compiled 3781 to 3284 computations (13.1% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.0b	(.f64 (.f64 i i) -1/4)
0.0b	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))

rewrite33.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cancel-sign-sub-inv_binary64_1749`
10×	`add-log-exp_binary64_1822`
9×	`add-sqr-sqrt_binary64_1805`
8×	`associate-+r+_binary64_1715` `add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
6×	`unpow-prod-down_binary64_1862`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
2×	`sqr-pow_binary64_1755` `diff-log_binary64_1875` `sum-log_binary64_1874` `sub-neg_binary64_1776`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `flip-+_binary64_1757` `associate-l_binary64_1724` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751` `flip--_binary64_1758` `associate-+r-_binary64_1717`

Counts

3 → 58

Calls

3 calls:

13.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))
8.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
7.0ms	(.f64 (.f64 i i) -1/4)

series111.0ms (5%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
31.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))
17.0ms	(.f64 (.f64 i i) -1/4)

simplify121.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4862	1048
1	4862	1048

prune68.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	67	3	70

Error

Counts

70 → 3

Compiler

Compiled 1324 to 928 computations (29.9% saved)

regimes66.0ms (3%)

Accuracy

Total 0.1b remaining (99.6%)

Threshold costs 0.1b (99.6%)

Compiler

Compiled 660 to 558 computations (15.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	26
1	24	26

end0.0ms (0%)

sample975.0ms (43.9%)

Algorithm

1×

intervals

Results

409.0ms	8000×	body	128	valid
96.0ms	8000×	pre	128	true

Compiler

Compiled 350 to 298 computations (14.9% saved)

Details

analyze6.0ms (0.3%)

sample22.0ms (1%)

simplify136.0ms (6.1%)

prune11.0ms (0.5%)

localize6.0ms (0.3%)

rewrite20.0ms (0.9%)

series30.0ms (1.4%)

simplify79.0ms (3.6%)

prune87.0ms (3.9%)

localize8.0ms (0.4%)

rewrite72.0ms (3.3%)

series41.0ms (1.8%)

simplify93.0ms (4.2%)

prune226.0ms (10.1%)

localize9.0ms (0.4%)

rewrite33.0ms (1.5%)

series111.0ms (5%)

simplify121.0ms (5.4%)

prune68.0ms (3%)

regimes66.0ms (3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample975.0ms (43.9%)

Profiling