Details

analyze1.2s (16%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample40.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
6.0ms	75×	body	128	invalid
6.0ms	62×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify316.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4740	19
1	4740	19

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 3.1b

Counts

2 → 1

Compiler

Compiled 54 to 45 computations (16.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(+.f64 1 (*.f64 k (+.f64 k 10)))
0.0b	(*.f64 a (pow.f64 k m))
3.1b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_1837`
18×	`add-sqr-sqrt_binary64_1821`
13×	`add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799`
11×	`add-cube-cbrt_binary64_1834` `associate-r_binary64_1739`
7×	`prod-exp_binary64_1848`
6×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `associate-l_binary64_1740`
4×	`div-exp_binary64_1850` `unswap-sqr_binary64_1767` `unpow-prod-down_binary64_1878`
3×	`associate-/r*_binary64_1743` `times-frac_binary64_1805` `cbrt-unprod_binary64_1832` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `pow-to-exp_binary64_1868` `associate-r/_binary64_1741` `associate-/r/_binary64_1745` `associate-+r+_binary64_1731` `cbrt-undiv_binary64_1833` `pow-exp_binary64_1867` `sqr-pow_binary64_1771` `-commutative_binary64_1730`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `associate-/l*_binary64_1744` `frac-2neg_binary64_1810` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `distribute-lft-out_binary64_1750`

Counts

4 → 86

Calls

4 calls:

8.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
7.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(*.f64 a (pow.f64 k m))
4.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

series427.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
105.0ms	(*.f64 a (pow.f64 k m))
59.0ms	(*.f64 k (+.f64 k 10))
20.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4955	1457
1	4955	1457

prune160.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	5	99

Merged error: 3.0b

Counts

99 → 5

Compiler

Compiled 3156 to 1980 computations (37.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.0b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
16.0b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
16.0b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite87.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`add-sqr-sqrt_binary64_1821`
134×	`times-frac_binary64_1805`
76×	`add-cube-cbrt_binary64_1834` `sqrt-prod_binary64_1815` `*-un-lft-identity_binary64_1799`
48×	`associate-r_binary64_1739`
45×	`unpow-prod-down_binary64_1878`
33×	`add-exp-log_binary64_1837`
24×	`associate-l_binary64_1740`
21×	`unswap-sqr_binary64_1767`
19×	`sqr-pow_binary64_1771`
18×	`add-cbrt-cube_binary64_1835`
13×	`div-exp_binary64_1850`
10×	`sqrt-div_binary64_1816`
8×	`pow1_binary64_1860` `prod-exp_binary64_1848`
7×	`associate-/l*_binary64_1744`
6×	`associate-/r*_binary64_1743` `associate-/r/_binary64_1745`
5×	`cbrt-undiv_binary64_1833` `flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`add-log-exp_binary64_1838` `cbrt-unprod_binary64_1832`
3×	`pow-to-exp_binary64_1868` `pow-exp_binary64_1867` `div-inv_binary64_1796`
2×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`
1×	`clear-num_binary64_1798` `frac-2neg_binary64_1810` `associate-r/_binary64_1741` `-commutative_binary64_1730` `pow-prod-down_binary64_1870` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 218

Calls

4 calls:

41.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
8.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series447.0ms (6%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
139.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
29.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
28.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify116.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4981	7880
1	4981	7880

prune441.0ms (5.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	230	5	235

Merged error: 3.0b

Counts

235 → 5

Compiler

Compiled 8013 to 5243 computations (34.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 a)
0.6b	(cbrt.f64 a)
0.6b	(cbrt.f64 a)
3.1b	(/.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (pow.f64 k m) (cbrt.f64 a))) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-exp-log_binary64_1837`
18×	`prod-exp_binary64_1848`
16×	`add-cbrt-cube_binary64_1835`
9×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `div-exp_binary64_1850` `cbrt-prod_binary64_1830` `*-un-lft-identity_binary64_1799`
8×	`cbrt-unprod_binary64_1832`
5×	`cbrt-undiv_binary64_1833`
4×	`pow1_binary64_1860` `add-log-exp_binary64_1838`
3×	`pow1/3_binary64_1881` `associate-/r*_binary64_1743` `times-frac_binary64_1805`
2×	`pow-to-exp_binary64_1868` `associate-/r/_binary64_1745` `pow-exp_binary64_1867`
1×	`clear-num_binary64_1798` `associate-/l*_binary64_1744` `frac-2neg_binary64_1810` `div-inv_binary64_1796` `flip3-+_binary64_1802` `flip-+_binary64_1773`

Counts

4 → 66

Calls

4 calls:

15.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (pow.f64 k m) (cbrt.f64 a))) (+.f64 1 (.f64 k (+.f64 k 10))))
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)

series744.0ms (10%)

Counts

4 → 12

Calls

4 calls:

281.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (pow.f64 k m) (cbrt.f64 a))) (+.f64 1 (.f64 k (+.f64 k 10))))
155.0ms	(cbrt.f64 a)
155.0ms	(cbrt.f64 a)
153.0ms	(cbrt.f64 a)

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5223	1161

prune77.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	78	5	83

Merged error: 3.0b

Counts

83 → 5

Compiler

Compiled 1778 to 854 computations (52% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.1b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
3.1b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
7.3b	(sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10)))))
7.3b	(sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10)))))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64_1837`
18×	`sqrt-prod_binary64_1815`
14×	`add-sqr-sqrt_binary64_1821` `add-cbrt-cube_binary64_1835`
12×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799` `times-frac_binary64_1805`
8×	`div-exp_binary64_1850` `associate-/r/_binary64_1745`
6×	`pow1_binary64_1860` `prod-exp_binary64_1848` `associate-/r*_binary64_1743`
4×	`add-log-exp_binary64_1838` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`sqrt-div_binary64_1816` `clear-num_binary64_1798` `associate-/l*_binary64_1744` `pow-to-exp_binary64_1868` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `cbrt-unprod_binary64_1832` `pow-exp_binary64_1867` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`

Counts

4 → 90

Calls

4 calls:

7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
6.0ms	(sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10)))))
6.0ms	(sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10)))))

series1.5s (20.1%)

Counts

4 → 12

Calls

4 calls:

513.0ms	(sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10)))))
506.0ms	(sqrt.f64 (/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10)))))
237.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
235.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4958	2742
1	4958	2742

prune150.0ms (2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	102	5	107

Merged error: 3.0b

Counts

107 → 5

Compiler

Compiled 3808 to 2136 computations (43.9% saved)

regimes44.0ms (0.6%)

Compiler: Compiled 342 to 273 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	17	19

end0.0ms (0%)

sample1.4s (18.4%)

Algorithm

1×

intervals

Results

541.0ms	8000×	body	128	valid
274.0ms	3252×	body	128	invalid
89.0ms	2010×	body	128	nan

Compiler

Compiled 141 to 112 computations (20.6% saved)

Details

analyze1.2s (16%)

sample40.0ms (0.5%)

simplify316.0ms (4.3%)

prune9.0ms (0.1%)

localize10.0ms (0.1%)

rewrite31.0ms (0.4%)

series427.0ms (5.7%)

simplify57.0ms (0.8%)

prune160.0ms (2.2%)

localize12.0ms (0.2%)

rewrite87.0ms (1.2%)

series447.0ms (6%)

simplify116.0ms (1.6%)

prune441.0ms (5.9%)

localize13.0ms (0.2%)

rewrite25.0ms (0.3%)

series744.0ms (10%)

simplify47.0ms (0.6%)

prune77.0ms (1%)

localize12.0ms (0.2%)

rewrite38.0ms (0.5%)

series1.5s (20.1%)

simplify77.0ms (1%)

prune150.0ms (2%)

regimes44.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (18.4%)

Profiling