Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample35.0ms

Algorithm

intervals

Results

15.0ms	97×	body	1280	valid
7.0ms	131×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify137.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune5.0ms

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: 15.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_1858` `add-sqr-sqrt_binary64_1843` `add-log-exp_binary64_1823`
2×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `add-cube-cbrt_binary64_1829` `pow1_binary64_1804`
1×	`diff-log_binary64_1774` `diff-atan_binary64_1731` `sub-neg_binary64_1862` `flip--_binary64_1884` `distribute-lft-out--_binary64_1903` `difference-of-squares_binary64_1887` `flip3--_binary64_1857`

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series19.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(atan.f64 (+.f64 N 1))
15.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify91.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4991	376
1	4991	376

prune97.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Merged error: 0.2b

Counts

28 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_1858` `add-sqr-sqrt_binary64_1843`
4×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `add-cube-cbrt_binary64_1829` `pow1_binary64_1804` `associate-r_binary64_1917`
3×	`associate-l_binary64_1918`
2×	`associate-*r/_binary64_1919` `add-log-exp_binary64_1823`
1×	`cbrt-unprod_binary64_1827` `prod-exp_binary64_1809` `distribute-lft-out_binary64_1902` `*-commutative_binary64_1926` `distribute-rgt-in_binary64_1901` `unswap-sqr_binary64_1886` `distribute-lft-in_binary64_1900` `pow-prod-down_binary64_1785` `flip3-+_binary64_1856` `flip-+_binary64_1883`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series37.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(*.f64 N (+.f64 N 1))
7.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify90.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5174	383

prune160.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	32	6	38

Merged error: 0.1b

Counts

38 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)
0.6b	(cbrt.f64 N)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1825`
23×	`add-sqr-sqrt_binary64_1843`
15×	`add-cube-cbrt_binary64_1829` `*-un-lft-identity_binary64_1858`
11×	`pow1_binary64_1804`
9×	`pow1/3_binary64_1796`
6×	`add-exp-log_binary64_1822` `associate-l_binary64_1918` `associate-r_binary64_1917` `swap-sqr_binary64_1885`
4×	`add-cbrt-cube_binary64_1830` `unswap-sqr_binary64_1886` `add-log-exp_binary64_1823`
2×	`pow-sqr_binary64_1891` `pow-prod-up_binary64_1784` `pow-prod-down_binary64_1785`
1×	`pow2_binary64_1795` `cbrt-unprod_binary64_1827` `prod-exp_binary64_1809` `*-commutative_binary64_1926` `pow-plus_binary64_1799`

Counts

4 → 73

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)

series351.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(*.f64 (cbrt.f64 N) (cbrt.f64 N))
81.0ms	(cbrt.f64 N)
85.0ms	(cbrt.f64 N)
84.0ms	(cbrt.f64 N)

simplify72.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5309	608

prune300.0ms

Filtered

65 candidates to 85 candidates (-30.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	85	6	91

Merged error: 0.1b

Counts

91 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
14.7b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.7b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1843`
24×	`sqrt-prod_binary64_1837`
21×	`pow1_binary64_1804`
14×	`add-cube-cbrt_binary64_1829` `*-un-lft-identity_binary64_1858`
10×	`sqrt-pow1_binary64_1839` `pow1/2_binary64_1794`
8×	`swap-sqr_binary64_1885`
6×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `associate-l_binary64_1918` `associate-r_binary64_1917`
5×	`pow-prod-up_binary64_1784`
4×	`unswap-sqr_binary64_1886` `add-log-exp_binary64_1823`
3×	`pow-sqr_binary64_1891` `pow-prod-down_binary64_1785`
2×	`rem-sqrt-square_binary64_1846`
1×	`pow2_binary64_1795` `cbrt-unprod_binary64_1827` `prod-exp_binary64_1809` `*-commutative_binary64_1926` `sqrt-unprod_binary64_1841` `pow-plus_binary64_1799` `rem-square-sqrt_binary64_1845`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
6.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
10.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
27.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
27.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify77.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4955	1485
1	4955	1485

prune247.0ms

Filtered

47 candidates to 94 candidates (-100.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	92	8	100

Merged error: 0.1b

Counts

100 → 8

regimes92.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms

sample816.0ms

Algorithm

intervals

Results

427.0ms	2825×	body	1280	valid
139.0ms	4078×	body	80	valid
73.0ms	584×	body	640	valid
33.0ms	350×	body	320	valid
12.0ms	163×	body	160	valid

Details

analyze1.0ms

sample35.0ms

simplify137.0ms

prune5.0ms

localize8.0ms

rewrite6.0ms

series19.0ms

simplify91.0ms

prune97.0ms

localize8.0ms

rewrite7.0ms

series37.0ms

simplify90.0ms

prune160.0ms

localize14.0ms

rewrite11.0ms

series351.0ms

simplify72.0ms

prune300.0ms

localize12.0ms

rewrite11.0ms

series71.0ms

simplify77.0ms

prune247.0ms

regimes92.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample816.0ms

Profiling