Details

analyze7.0ms (0.2%)

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)

sample26.0ms (0.9%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify216.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5791	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

Merged error: 0.3b

Counts

2 → 2

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))
0.8b	(/.f64 -1 (*.f64 i i))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_1762`
15×	`times-frac_binary64_1768`
13×	`add-sqr-sqrt_binary64_1783` `add-cube-cbrt_binary64_1794`
9×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
6×	`associate-/l*_binary64_1709`
5×	`associate-/r*_binary64_1708`
4×	`distribute-lft-out_binary64_1715`
3×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
2×	`associate-/r/_binary64_1710` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `div-inv_binary64_1759` `add-log-exp_binary64_1798` `pow1_binary64_1820`
1×	`prod-exp_binary64_1808` `flip3-+_binary64_1765` `flip-+_binary64_1736` `cbrt-unprod_binary64_1792`

Counts

2 → 54

Calls

2 calls:

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

series69.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

34.0ms	(/.f64 -1 (*.f64 i i))
34.0ms	(/.f64 1/4 (+.f64 4 (/.f64 -1 (*.f64 i i))))

simplify69.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5300	918

prune58.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	59	3	62

Merged error: 0.0b

Counts

62 → 3

Compiler

Compiled 914 to 679 computations (25.7% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 -1 i) 4)))
0.2b	(pow.f64 (/.f64 -1 i) 4)
0.8b	(/.f64 -1 (*.f64 i i))
24.0b	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 -1 i) 4))) (-.f64 4 (/.f64 -1 (.f64 i i))))

rewrite71.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`add-sqr-sqrt_binary64_1783`
69×	`times-frac_binary64_1768`
56×	`*-un-lft-identity_binary64_1762`
40×	`add-cube-cbrt_binary64_1794`
30×	`difference-of-squares_binary64_1731` `associate-l_binary64_1705`
27×	`unpow-prod-down_binary64_1838`
19×	`add-exp-log_binary64_1797`
16×	`add-cbrt-cube_binary64_1795`
9×	`associate-/r*_binary64_1708`
8×	`sqr-pow_binary64_1734` `distribute-lft-out--_binary64_1716`
7×	`pow1_binary64_1820`
6×	`associate-/l_binary64_1709` `associate-r*_binary64_1704`
5×	`div-exp_binary64_1810`
4×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `add-log-exp_binary64_1798` `flip--_binary64_1737`
3×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `pow-unpow_binary64_1836`
2×	`frac-2neg_binary64_1773` `frac-times_binary64_1772` `clear-num_binary64_1761` `unswap-sqr_binary64_1730` `pow-exp_binary64_1827` `associate-*r/_binary64_1706` `sub-neg_binary64_1755`
1×	`pow-prod-down_binary64_1830` `associate-l/_binary64_1707` `distribute-rgt-in_binary64_1714` `pow-pow_binary64_1831` `-commutative_binary64_1695` `distribute-lft-in_binary64_1713` `pow-to-exp_binary64_1828`

Counts

4 → 156

Calls

4 calls:

26.0ms	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 -1 i) 4))) (-.f64 4 (/.f64 -1 (.f64 i i))))
14.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 -1 i) 4)))
8.0ms	(pow.f64 (/.f64 -1 i) 4)
5.0ms	(/.f64 -1 (*.f64 i i))

series214.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 -1 i) 4)))
55.0ms	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 -1 i) 4))) (-.f64 4 (/.f64 -1 (.f64 i i))))
42.0ms	(pow.f64 (/.f64 -1 i) 4)
33.0ms	(/.f64 -1 (*.f64 i i))

simplify79.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4913	3329
1	4913	3329

prune255.0ms (9.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	168	3	171

Merged error: 0.0b

Counts

171 → 3

Compiler

Compiled 4131 to 3260 computations (21.1% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1783` `add-exp-log_binary64_1797`
11×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795`
9×	`pow1_binary64_1820`
8×	`-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794` `associate-l*_binary64_1705`
6×	`prod-exp_binary64_1808` `associate-r_binary64_1704`
4×	`unswap-sqr_binary64_1730` `cbrt-unprod_binary64_1792` `unpow-prod-down_binary64_1838`
3×	`pow-prod-down_binary64_1830`
2×	`diff-log_binary64_1851` `sqr-pow_binary64_1734` `sub-neg_binary64_1755` `*-commutative_binary64_1695` `sum-log_binary64_1850`
1×	`associate-+r-_binary64_1698` `flip3--_binary64_1766` `flip3-+_binary64_1765` `flip-+_binary64_1736` `+-commutative_binary64_1694` `pow-exp_binary64_1827` `flip--_binary64_1737` `pow-to-exp_binary64_1828` `associate-+r+_binary64_1696`

Counts

4 → 69

Calls

4 calls:

12.0ms	(+.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))
6.0ms	(.f64 (.f64 i i) -1/4)
6.0ms	(*.f64 (pow.f64 i 6) -4)

series297.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
68.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 (*.f64 i i) -1/4) (pow.f64 i 4)))
65.0ms	(*.f64 (pow.f64 i 6) -4)
34.0ms	(.f64 (.f64 i i) -1/4)

simplify73.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4872	1163
1	4872	1163

prune85.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	81	3	84

Merged error: 0b

Counts

84 → 3

Compiler

Compiled 1610 to 1124 computations (30.2% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1783`
10×	`add-log-exp_binary64_1798`
8×	`add-exp-log_binary64_1797`
7×	`associate-l_binary64_1705`
6×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
5×	`add-cbrt-cube_binary64_1795`
4×	`unpow-prod-down_binary64_1838`
3×	`prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `pow1_binary64_1820` `associate-r_binary64_1704`
2×	`diff-log_binary64_1851` `sqr-pow_binary64_1734` `sub-neg_binary64_1755` `sum-log_binary64_1850`
1×	`associate-+r-_binary64_1698` `flip3--_binary64_1766` `flip3-+_binary64_1765` `flip-+_binary64_1736` `+-commutative_binary64_1694` `pow-exp_binary64_1827` `cbrt-unprod_binary64_1792` `flip--_binary64_1737` `*-commutative_binary64_1695` `pow-to-exp_binary64_1828` `associate-+r+_binary64_1696`

Counts

3 → 50

Calls

3 calls:

11.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 i (*.f64 i -1/4)) (pow.f64 i 4)))
7.0ms	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
6.0ms	(*.f64 (pow.f64 i 6) -4)

series291.0ms (10.4%)

Counts

3 → 9

Calls

3 calls:

147.0ms	(-.f64 (.f64 i (.f64 i -1/4)) (pow.f64 i 4))
72.0ms	(*.f64 (pow.f64 i 6) -4)
72.0ms	(+.f64 (.f64 (pow.f64 i 6) -4) (-.f64 (.f64 i (*.f64 i -1/4)) (pow.f64 i 4)))

simplify63.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5043	981

prune66.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	59	3	62

Merged error: 0b

Counts

62 → 3

Compiler

Compiled 1208 to 909 computations (24.8% saved)

regimes10.0ms (0.4%)

Compiler: Compiled 43 to 37 computations (14% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms (0%)

sample707.0ms (25.4%)

Algorithm

1×

intervals

Results

398.0ms	8000×	body	128	valid
98.0ms	8000×	pre	128	true

Compiler

Compiled 79 to 64 computations (19% saved)

Details

analyze7.0ms (0.2%)

sample26.0ms (0.9%)

simplify216.0ms (7.8%)

prune5.0ms (0.2%)

localize5.0ms (0.2%)

rewrite21.0ms (0.7%)

series69.0ms (2.5%)

simplify69.0ms (2.5%)

prune58.0ms (2.1%)

localize10.0ms (0.4%)

rewrite71.0ms (2.6%)

series214.0ms (7.7%)

simplify79.0ms (2.8%)

prune255.0ms (9.2%)

localize11.0ms (0.4%)

rewrite38.0ms (1.4%)

series297.0ms (10.7%)

simplify73.0ms (2.6%)

prune85.0ms (3%)

localize11.0ms (0.4%)

rewrite28.0ms (1%)

series291.0ms (10.4%)

simplify63.0ms (2.3%)

prune66.0ms (2.4%)

regimes10.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample707.0ms (25.4%)

Profiling