Details

analyze1.0s (17.6%)

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)

sample43.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
9.0ms	107×	body	128	invalid
3.0ms	76×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify325.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4740	19
1	4740	19

prune6.0ms (0.1%)

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: 2.7b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
2.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-exp-log_binary64_1837`
7×	`add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835`
4×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `div-exp_binary64_1850` `*-un-lft-identity_binary64_1799`
3×	`sum-log_binary64_1890` `prod-exp_binary64_1848` `associate-/r*_binary64_1743` `times-frac_binary64_1805`
2×	`pow1_binary64_1860` `associate-/r/_binary64_1745` `cbrt-undiv_binary64_1833` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`clear-num_binary64_1798` `+-commutative_binary64_1729` `associate-/l*_binary64_1744` `pow-to-exp_binary64_1868` `frac-2neg_binary64_1810` `cbrt-unprod_binary64_1832` `pow-exp_binary64_1867` `div-inv_binary64_1796` `associate-+l+_binary64_1732`

Counts

2 → 38

Calls

2 calls:

10.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
6.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))

series273.0ms (4.8%)

Counts

2 → 6

Calls

2 calls:

252.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
21.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4957	913
1	4957	913

prune95.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 2.6b

Counts

46 → 5

Compiler

Compiled 1790 to 1190 computations (33.5% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (*.f64 k (+.f64 k 10)))
0.0b	(*.f64 k (+.f64 k 10))
2.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_1837`
10×	`add-cbrt-cube_binary64_1835`
9×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
7×	`add-cube-cbrt_binary64_1834`
5×	`pow1_binary64_1860` `add-log-exp_binary64_1838`
4×	`div-exp_binary64_1850` `prod-exp_binary64_1848` `associate-r_binary64_1739`
3×	`associate-/r_binary64_1743` `associate-l*_binary64_1740` `times-frac_binary64_1805` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `associate-*r/_binary64_1741` `associate-/r/_binary64_1745` `associate-+r+_binary64_1731` `cbrt-undiv_binary64_1833` `cbrt-unprod_binary64_1832`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `associate-/l_binary64_1744` `unswap-sqr_binary64_1767` `pow-to-exp_binary64_1868` `frac-2neg_binary64_1810` `pow-exp_binary64_1867` `-commutative_binary64_1730` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `distribute-lft-out_binary64_1750`

Counts

3 → 61

Calls

3 calls:

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

series322.0ms (5.7%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
55.0ms	(*.f64 k (+.f64 k 10))
19.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4944	1132
1	4944	1132

prune61.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Merged error: 2.6b

Counts

75 → 5

Compiler

Compiled 1364 to 762 computations (44.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 k (+.f64 k 10)))
0.0b	(*.f64 k (+.f64 k 10))
0.0b	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
2.6b	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64_1821`
45×	`times-frac_binary64_1805`
39×	`*-un-lft-identity_binary64_1799`
37×	`add-cube-cbrt_binary64_1834`
31×	`associate-r_binary64_1739`
22×	`unpow-prod-down_binary64_1878`
21×	`add-exp-log_binary64_1837`
13×	`add-cbrt-cube_binary64_1835`
8×	`pow1_binary64_1860` `sqr-pow_binary64_1771`
7×	`associate-/l*_binary64_1744`
6×	`div-exp_binary64_1850` `add-log-exp_binary64_1838` `associate-l_binary64_1740`
5×	`prod-exp_binary64_1848` `unswap-sqr_binary64_1767`
4×	`associate-/r/_binary64_1745` `flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`associate-/r_binary64_1743` `associate-r/_binary64_1741` `cbrt-unprod_binary64_1832`
2×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `pow-to-exp_binary64_1868` `associate-+r+_binary64_1731` `cbrt-undiv_binary64_1833` `pow-exp_binary64_1867` `*-commutative_binary64_1730` `div-inv_binary64_1796` `pow-prod-down_binary64_1870`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `distribute-lft-out_binary64_1750`

Counts

4 → 133

Calls

4 calls:

16.0ms	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
7.0ms	(*.f64 k (+.f64 k 10))
7.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
4.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

series423.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

238.0ms	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
110.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
58.0ms	(*.f64 k (+.f64 k 10))
17.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4968	3169
1	4968	3169

prune149.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	145	5	150

Merged error: 2.6b

Counts

150 → 5

Compiler

Compiled 3283 to 1923 computations (41.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.1b	(.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))))))
15.5b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
15.5b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite84.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`add-sqr-sqrt_binary64_1821`
110×	`times-frac_binary64_1805`
64×	`sqrt-prod_binary64_1815`
61×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
48×	`associate-r_binary64_1739`
30×	`add-exp-log_binary64_1837`
24×	`unpow-prod-down_binary64_1878` `associate-l_binary64_1740`
21×	`unswap-sqr_binary64_1767`
18×	`add-cbrt-cube_binary64_1835`
12×	`sqr-pow_binary64_1771`
11×	`div-exp_binary64_1850`
10×	`sqrt-div_binary64_1816`
8×	`pow1_binary64_1860` `prod-exp_binary64_1848`
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×	`associate-/l*_binary64_1744` `div-inv_binary64_1796`
2×	`pow-to-exp_binary64_1868` `pow1/2_binary64_1879` `pow-exp_binary64_1867` `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 → 188

Calls

4 calls:

40.0ms	(.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))))))
6.0ms	(/.f64 a (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))))

series440.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(.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))))))
146.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
27.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
26.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify131.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4932	6556
1	4932	6556

prune354.0ms (6.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	200	5	205

Merged error: 2.6b

Counts

205 → 5

Compiler

Compiled 6898 to 4561 computations (33.9% saved)

regimes96.0ms (1.7%)

Compiler: Compiled 988 to 790 computations (20% 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%)

sample1.5s (26.5%)

Algorithm

1×

intervals

Results

532.0ms	8000×	body	128	valid
287.0ms	3396×	body	128	invalid
92.0ms	2073×	body	128	nan

Compiler

Compiled 267 to 214 computations (19.9% saved)

Details

analyze1.0s (17.6%)

sample43.0ms (0.8%)

simplify325.0ms (5.7%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite20.0ms (0.3%)

series273.0ms (4.8%)

simplify68.0ms (1.2%)

prune95.0ms (1.7%)

localize12.0ms (0.2%)

rewrite23.0ms (0.4%)

series322.0ms (5.7%)

simplify85.0ms (1.5%)

prune61.0ms (1.1%)

localize10.0ms (0.2%)

rewrite48.0ms (0.8%)

series423.0ms (7.4%)

simplify87.0ms (1.5%)

prune149.0ms (2.6%)

localize13.0ms (0.2%)

rewrite84.0ms (1.5%)

series440.0ms (7.7%)

simplify131.0ms (2.3%)

prune354.0ms (6.2%)

regimes96.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (26.5%)

Profiling