Details

analyze69.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample39.0ms (1%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true
0.0ms	2×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify282.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.3b

Counts

2 → 1

Compiler

Compiled 24 to 17 computations (29.2% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
13.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
7×	`add-sqr-sqrt_binary64_1805`
6×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
5×	`add-log-exp_binary64_1822`
4×	`associate-/l*_binary64_1728` `times-frac_binary64_1789` `pow1_binary64_1844`
3×	`difference-of-squares_binary64_1752` `sqrt-prod_binary64_1799`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `flip--_binary64_1758`
1×	`div-sub_binary64_1788` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `associate-/r*_binary64_1727` `diff-log_binary64_1875` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

3 → 52

Calls

3 calls:

15.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
8.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series184.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
62.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
44.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify127.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5039	1000

prune103.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 0b

Counts

62 → 2

Compiler

Compiled 1075 to 365 computations (66% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
0.0b	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
0.1b	(*.f64 b (/.f64 b a))

rewrite63.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`times-frac_binary64_1789`
71×	`add-sqr-sqrt_binary64_1805`
65×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
22×	`add-exp-log_binary64_1821`
18×	`associate-/r*_binary64_1727`
16×	`add-cbrt-cube_binary64_1819`
13×	`associate-r_binary64_1723`
11×	`associate-/r/_binary64_1729`
9×	`div-exp_binary64_1834`
8×	`pow1_binary64_1844`
7×	`div-inv_binary64_1780`
6×	`associate-/l*_binary64_1728`
5×	`flip3--_binary64_1787` `cbrt-undiv_binary64_1817` `flip--_binary64_1758`
4×	`add-log-exp_binary64_1822`
3×	`associate-l_binary64_1724` `sqrt-prod_binary64_1799`
2×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `unswap-sqr_binary64_1751` `rec-exp_binary64_1833`
1×	`associate-r/_binary64_1725` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `pow1/2_binary64_1863` `-commutative_binary64_1714` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 158

Calls

4 calls:

13.0ms	(*.f64 b (/.f64 b a))
13.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
9.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))

series187.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
56.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
53.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
21.0ms	(*.f64 b (/.f64 b a))

simplify169.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4979	3563
1	4979	3563

prune257.0ms (6.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Merged error: 0b

Counts

172 → 2

Compiler

Compiled 3550 to 1211 computations (65.9% saved)

localize18.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
0.1b	(*.f64 b (/.f64 b a))
0.2b	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))

rewrite53.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1805`
21×	`*-un-lft-identity_binary64_1783` `times-frac_binary64_1789`
20×	`add-cube-cbrt_binary64_1818`
17×	`add-exp-log_binary64_1821`
16×	`associate-l_binary64_1724` `associate-r_binary64_1723`
13×	`add-cbrt-cube_binary64_1819`
8×	`pow1_binary64_1844`
6×	`prod-exp_binary64_1832`
5×	`unswap-sqr_binary64_1751`
4×	`cbrt-unprod_binary64_1816`
3×	`associate-*r/_binary64_1725` `sqrt-prod_binary64_1799` `div-exp_binary64_1834` `add-log-exp_binary64_1822`
2×	`flip3--_binary64_1787` `distribute-lft-in_binary64_1732` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `frac-times_binary64_1793` `pow-prod-down_binary64_1854` `flip--_binary64_1758` `sub-neg_binary64_1776`
1×	`1-exp_binary64_1827` `pow1/2_binary64_1863` `associate-*l/_binary64_1726` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `rec-exp_binary64_1833`

Counts

3 → 88

Calls

3 calls:

19.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
17.0ms	(*.f64 b (/.f64 b a))
2.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))

series148.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
58.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
23.0ms	(*.f64 b (/.f64 b a))

simplify147.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4938	1412
1	4938	1412

prune145.0ms (3.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	97	2	99

Merged error: 0b

Counts

99 → 2

Compiler

Compiled 1703 to 596 computations (65% saved)

regimes254.0ms (6.6%)

Compiler: Compiled 1223 to 761 computations (37.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms (0%)

sample1.5s (39.4%)

Algorithm

1×

intervals

Results

560.0ms	8000×	body	128	valid
307.0ms	8000×	pre	128	true
4.0ms	113×	pre	128	false

Compiler

Compiled 171 to 108 computations (36.8% saved)

Details

analyze69.0ms (1.8%)

sample39.0ms (1%)

simplify282.0ms (7.4%)

prune7.0ms (0.2%)

localize16.0ms (0.4%)

rewrite32.0ms (0.8%)

series184.0ms (4.8%)

simplify127.0ms (3.3%)

prune103.0ms (2.7%)

localize18.0ms (0.5%)

rewrite63.0ms (1.6%)

series187.0ms (4.9%)

simplify169.0ms (4.4%)

prune257.0ms (6.7%)

localize18.0ms (0.5%)

rewrite53.0ms (1.4%)

series148.0ms (3.9%)

simplify147.0ms (3.8%)

prune145.0ms (3.8%)

regimes254.0ms (6.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (39.4%)

Profiling