Details

sample116.0ms

Algorithm

intervals

Results

59.0ms	151×	body	1280	valid
29.0ms	25×	body	2560	valid
12.0ms	51×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	4×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	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: 40.7b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify61.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4864	273
1	4864	273

prune58.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	24	6	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	6	31

Merged error: 0.2b

Counts

31 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
3.7b	(sin (/ (+ x (+ x eps)) 2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

5.0ms	(+ x (+ x eps))
10.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
9.0ms	(sin (/ (+ x (+ x eps)) 2))

series22.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ x eps))
12.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify47.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5055	545

prune111.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	47	9	56

Merged error: 0.2b

Counts

56 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

3.7b	(sin (/ (+ x (+ x eps)) 2))
5.9b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.9b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.9b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 37

Calls

4 calls:

6.0ms	(sin (/ (+ x (+ x eps)) 2))
8.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
8.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
8.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sin (/ (+ x (+ x eps)) 2))
28.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
28.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
30.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify32.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5922	721

prune204.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	48	10	58

Merged error: 0.2b

Counts

58 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b	(sin (/ (+ x (+ x eps)) 2))
5.9b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.9b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.9b	(cbrt (* (* (* (cbrt (sin (/ (+ x (+ x eps)) 2))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
2×	`cbrt-div` `sin-mult`

Counts

4 → 36

Calls

4 calls:

7.0ms	(sin (/ (+ x (+ x eps)) 2))
8.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
8.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
26.0ms	(cbrt (* (* (* (cbrt (sin (/ (+ x (+ x eps)) 2))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sin (/ (+ x (+ x eps)) 2))
28.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
31.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
29.0ms	(cbrt (* (* (* (cbrt (sin (/ (+ x (+ x eps)) 2))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (cbrt (sin (/ (+ x (+ x eps)) 2)))) (sin (/ eps 2))))

simplify32.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6030	693

prune212.0ms

Filtered

42 candidates to 48 candidates (-14.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	48	10	58

Merged error: 0.2b

Counts

58 → 10

regimes181.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.9b

bsearch84.0ms

Steps

Iters	Range		Point
11	6.401380870969369e-19	14704714838.838829	4.4008113468725445e-06
9	-60.40944958396893	-0.00021233150198250738	-0.005055611703658554

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	38
1	35	38

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	4391×	body	1280	valid
660.0ms	707×	body	2560	valid
467.0ms	1887×	body	640	valid
121.0ms	695×	body	320	valid
37.0ms	234×	body	160	valid
5.0ms	86×	body	80	valid

Details

sample116.0ms

simplify3.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series14.0ms

simplify61.0ms

prune58.0ms

localize13.0ms

rewrite25.0ms

series22.0ms

simplify47.0ms

prune111.0ms

localize17.0ms

rewrite30.0ms

series93.0ms

simplify32.0ms

prune204.0ms

localize23.0ms

rewrite49.0ms

series94.0ms

simplify32.0ms

prune212.0ms

regimes181.0ms

bsearch84.0ms

simplify1.0ms

end0.0ms

sample3.3s

Profiling