Details

analyze2.0ms

Algorithm

Search

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

sample106.0ms

Algorithm

intervals

Results

52.0ms	137×	body	1280	valid
26.0ms	23×	body	2560	valid
14.0ms	63×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 43.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (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 → 23

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))

simplify24.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4999	270
1	4999	270

prune58.0ms

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: 0.4b

Counts

30 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
3.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

10.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
5.0ms	(+ x (+ x eps))
10.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))

series37.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms	(+ x (+ x eps))
11.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
8.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4907	890
1	4907	890

prune154.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	66	12	78

Merged error: 0.4b

Counts

78 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

3.9b	(sin (/ (+ x (+ x eps)) 2))
4.8b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
4.8b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
4.8b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))

rewrite34.0ms

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`

Counts

4 → 34

Calls

4 calls:

6.0ms	(sin (/ (+ x (+ x eps)) 2))
9.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
9.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
9.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sin (/ (+ x (+ x eps)) 2))
35.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
35.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
38.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))

simplify62.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4891	751
1	4891	751

prune232.0ms

Filtered

42 candidates to 46 candidates (-9.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	46	12	58

Merged error: 0.3b

Counts

58 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

4.0b	(sin (+ x (* eps 1/2)))
4.8b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
4.8b	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
4.9b	(cbrt (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))))

rewrite28.0ms

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`
1×	`cbrt-div` `sin-sum` `sin-mult`

Counts

4 → 36

Calls

4 calls:

4.0ms	(sin (+ x (* eps 1/2)))
9.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
9.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
5.0ms	(cbrt (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sin (+ x (* eps 1/2)))
35.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
39.0ms	(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) -2)))
29.0ms	(cbrt (* (sin (* eps 1/2)) (sin (+ x (* eps 1/2)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5634	709

prune199.0ms

Filtered

42 candidates to 48 candidates (-14.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	48	12	60

Merged error: 0.3b

Counts

60 → 12

regimes225.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 13.7b

bsearch72.0ms

Steps

Iters	Range		Point
9	2.4966180872489278e-06	0.7425030735014803	3.325528646214861e-05
8	-31.653317132880385	-0.004380114327240192	-0.004478205628609146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	38
1	78	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4455×	body	1280	valid
585.0ms	641×	body	2560	valid
437.0ms	1877×	body	640	valid
123.0ms	686×	body	320	valid
32.0ms	279×	body	160	valid
4.0ms	62×	body	80	valid

Details

analyze2.0ms

sample106.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify24.0ms

prune58.0ms

localize13.0ms

rewrite33.0ms

series37.0ms

simplify52.0ms

prune154.0ms

localize18.0ms

rewrite34.0ms

series116.0ms

simplify62.0ms

prune232.0ms

localize31.0ms

rewrite28.0ms

series109.0ms

simplify41.0ms

prune199.0ms

regimes225.0ms

bsearch72.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling