Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample102.0ms

Algorithm

intervals

Results

49.0ms	112×	body	1280	valid
16.0ms	59×	body	640	valid
13.0ms	14×	body	2560	valid
7.0ms	23×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	8×	body	160	valid

simplify140.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune6.0ms

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: 35.8b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0b	(sin.f64 (+.f64 x eps))

rewrite12.0ms

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` `sin-sum_binary64_1707` `add-cube-cbrt_binary64_1829` `pow1_binary64_1804`
1×	`diff-log_binary64_1774` `associate--l+_binary64_1914` `diff-sin_binary64_1724` `sub-neg_binary64_1862` `flip--_binary64_1884` `distribute-lft-out--_binary64_1903` `difference-of-squares_binary64_1887` `flip3--_binary64_1857`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series54.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
16.0ms	(sin.f64 (+.f64 x eps))

simplify44.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4944	426
1	4944	426

prune135.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.5b

Counts

30 → 3

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1858`
8×	`add-log-exp_binary64_1823`
7×	`add-sqr-sqrt_binary64_1843`
5×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `add-cube-cbrt_binary64_1829` `pow1_binary64_1804`
3×	`sum-log_binary64_1773` `associate-l_binary64_1918` `distribute-lft-out_binary64_1902` `associate-r_binary64_1917`
1×	`+-commutative_binary64_1925` `cbrt-unprod_binary64_1827` `sin-cos-mult_binary64_1730` `prod-exp_binary64_1809` `*-commutative_binary64_1926` `unswap-sqr_binary64_1886` `pow-prod-down_binary64_1785` `flip3-+_binary64_1856` `associate-+r+_binary64_1909` `flip-+_binary64_1883`

Counts

3 → 41

Calls

3 calls:

6.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series280.0ms

Counts

3 → 9

Calls

3 calls:

211.0ms	(+.f64 x (+.f64 x eps))
50.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
20.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify99.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4966	830
1	4966	830

prune264.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.4b

Counts

53 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.6b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1843`
12×	`add-cube-cbrt_binary64_1829` `*-un-lft-identity_binary64_1858`
9×	`log-prod_binary64_1776` `exp-prod_binary64_1812`
8×	`pow1_binary64_1804` `log-pow_binary64_1779`
7×	`associate-r_binary64_1917`
6×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822`
5×	`add-log-exp_binary64_1823`
3×	`associate-l_binary64_1918` `distribute-rgt-in_binary64_1901` `distribute-lft-in_binary64_1900`
1×	`cbrt-unprod_binary64_1827` `prod-exp_binary64_1809` `*-commutative_binary64_1926` `rem-log-exp_binary64_1821` `rem-exp-log_binary64_1820` `unswap-sqr_binary64_1886` `pow-prod-down_binary64_1785`

Counts

4 → 61

Calls

4 calls:

13.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
9.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series119.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
44.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
17.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify83.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5142	1478

prune368.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	72	9	81

Merged error: 0.4b

Counts

81 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64_1829` `*-un-lft-identity_binary64_1858` `add-sqr-sqrt_binary64_1843`
4×	`add-cbrt-cube_binary64_1830` `add-exp-log_binary64_1822` `pow1_binary64_1804` `add-log-exp_binary64_1823`
3×	`cbrt-prod_binary64_1825`
1×	`pow1/3_binary64_1796`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
14.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series139.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify96.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5620	696

prune251.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	44	9	53

Merged error: 0.4b

Counts

53 → 9

regimes277.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.1b

bsearch86.0ms

Steps

Iters	Range	Point
8	6420957976956075/19342813113834066795298816	3965348807300087/18889465931478580854784	1.181394862584651e-08
8	-341604615952879/1180591620717411303424	-4328019243294623/19342813113834066795298816	-8.40520369698623e-09

Iters

Range

Point

6420957976956075/19342813113834066795298816

3965348807300087/18889465931478580854784

1.181394862584651e-08

-341604615952879/1180591620717411303424

-4328019243294623/19342813113834066795298816

-8.40520369698623e-09

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	81
1	49	81

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3394×	body	1280	valid
585.0ms	623×	body	2560	valid
457.0ms	1733×	body	640	valid
162.0ms	802×	body	320	valid
68.0ms	1093×	body	80	valid
49.0ms	355×	body	160	valid

Details

analyze2.0ms

sample102.0ms

simplify140.0ms

prune6.0ms

localize11.0ms

rewrite12.0ms

series54.0ms

simplify44.0ms

prune135.0ms

localize19.0ms

rewrite21.0ms

series280.0ms

simplify99.0ms

prune264.0ms

localize22.0ms

rewrite44.0ms

series119.0ms

simplify83.0ms

prune368.0ms

localize29.0ms

rewrite31.0ms

series139.0ms

simplify96.0ms

prune251.0ms

regimes277.0ms

bsearch86.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling