Details

analyze2.0ms

Algorithm

Search

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

sample103.0ms

Algorithm

intervals

Results

57.0ms	146×	body	1280	valid
22.0ms	24×	body	2560	valid
14.0ms	64×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	5×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune1.0ms

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: 40.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.3b	(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))

series49.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
13.0ms	(cos.f64 (+.f64 x eps))

simplify48.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4945	429
1	4945	429

prune38.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	20	9	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	9	30

Merged error: 0.7b

Counts

30 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.4b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out_binary64` `times-frac_binary64`
9×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(+.f64 x (+.f64 x eps))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series110.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 x (+.f64 x eps))
49.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
21.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
24.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify96.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5073	1327

prune91.0ms

Filtered

63 candidates to 90 candidates (-42.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	86	13	99

Merged error: 0.4b

Counts

99 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
4.0b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
1×	`sin-sum_binary64`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
4.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
82.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
86.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
22.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5008	708

prune94.0ms

Filtered

45 candidates to 53 candidates (-17.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	54	12	66

Merged error: 0.1b

Counts

66 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))
82.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
81.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
85.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

simplify103.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4913	1136
1	4913	1136

prune122.0ms

Filtered

59 candidates to 85 candidates (-44.1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	80	17	97

Merged error: 0.1b

Counts

97 → 17

regimes127.0ms

Accuracy

0% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	57
1	28	57

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	4340×	body	1280	valid
613.0ms	679×	body	2560	valid
451.0ms	1893×	body	640	valid
115.0ms	718×	body	320	valid
32.0ms	282×	body	160	valid
5.0ms	88×	body	80	valid

Details

analyze2.0ms

sample103.0ms

simplify15.0ms

prune1.0ms

localize8.0ms

rewrite12.0ms

series49.0ms

simplify48.0ms

prune38.0ms

localize13.0ms

rewrite38.0ms

series110.0ms

simplify96.0ms

prune91.0ms

localize16.0ms

rewrite12.0ms

series277.0ms

simplify49.0ms

prune94.0ms

localize24.0ms

rewrite16.0ms

series357.0ms

simplify103.0ms

prune122.0ms

regimes127.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.2s

Profiling