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

53.0ms	140×	body	1280	valid
22.0ms	24×	body	2560	valid
14.0ms	59×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 41.0b

Counts

2 → 1

localize15.0ms

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.4b	(cos.f64 (+.f64 x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 23

Calls

2 calls:

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

series16.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
6.0ms	(cos.f64 (+.f64 x eps))

simplify30.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4999	270
1	4999	270

prune48.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	6	30

Merged error: 0.3b

Counts

30 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
6.0ms	(+.f64 x (+.f64 x eps))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
7.0ms	(+.f64 x (+.f64 x eps))
14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune104.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	67	11	78

Merged error: 0.3b

Counts

78 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
3.4b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`sin-sum_binary64`
6×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`add-log-exp_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `unswap-sqr_binary64`

Counts

3 → 52

Calls

3 calls:

10.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
9.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
5.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series37.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
13.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
6.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify78.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4816	851
1	4816	851

prune95.0ms

Filtered

44 candidates to 61 candidates (-38.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	54	7	61
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 0.1b

Counts

72 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
0.1b	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
0.2b	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 70

Calls

4 calls:

8.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
5.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
5.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
11.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
11.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
11.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
30.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5030	1237

prune107.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	79	15	94

Merged error: 0.0b

Counts

94 → 15

regimes168.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	27
1	25	27

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4439×	body	1280	valid
597.0ms	646×	body	2560	valid
454.0ms	1872×	body	640	valid
121.0ms	678×	body	320	valid
33.0ms	288×	body	160	valid
5.0ms	77×	body	80	valid

Details

analyze2.0ms

sample102.0ms

simplify7.0ms

prune3.0ms

localize15.0ms

rewrite12.0ms

series16.0ms

simplify30.0ms

prune48.0ms

localize13.0ms

rewrite38.0ms

series45.0ms

simplify61.0ms

prune104.0ms

localize11.0ms

rewrite24.0ms

series37.0ms

simplify78.0ms

prune95.0ms

localize21.0ms

rewrite31.0ms

series77.0ms

simplify61.0ms

prune107.0ms

regimes168.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling