Details

analyze2.0ms

Algorithm

Search

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

sample132.0ms

Algorithm

intervals

Results

66.0ms	109×	body	1280	valid
20.0ms	18×	body	2560	valid
20.0ms	53×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	40×	body	80	valid
2.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

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: 34.4b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
3.9b	(sin (+ 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` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 23

Calls

2 calls:

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

simplify34.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4933	268
1	4933	268

prune45.0ms

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: 0.2b

Counts

30 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
4.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite20.0ms

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` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

5.0ms	(+ x (+ x eps))
8.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

series20.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ x eps))
10.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4826	542
1	4826	542

prune97.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 0.2b

Counts

53 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.4b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
4.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
11.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
5.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5173	934

prune144.0ms

Filtered

53 candidates to 73 candidates (-37.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 0.2b

Counts

80 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(log (* (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))) (sqrt (exp (cos (/ (+ x (+ x eps)) 2))))))
0.6b	(* (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))) (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
4.0b	(cos (/ (+ x (+ x eps)) 2))
4.0b	(cos (/ (+ x (+ x eps)) 2))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

52×	`sqrt-pow1`
36×	`add-sqr-sqrt` `exp-prod`
35×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`log-pow`
18×	`sqrt-prod`
16×	`pow1/2` `pow-prod-up`
12×	`pow-prod-down` `pow-sqr`
9×	`add-exp-log`
8×	`swap-sqr`
6×	`associate-r` `associate-l` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
2×	`pow2` `pow-plus` `rem-log-exp` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 105

Calls

4 calls:

19.0ms	(log (* (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))) (sqrt (exp (cos (/ (+ x (+ x eps)) 2))))))
23.0ms	(* (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))) (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (* (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))) (sqrt (exp (cos (/ (+ x (+ x eps)) 2))))))
9.0ms	(* (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))) (sqrt (exp (cos (/ (+ x (+ x eps)) 2)))))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify60.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4911	1157
1	4911	1157

prune193.0ms

Filtered

74 candidates to 117 candidates (-58.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	117	8	125

Merged error: 0.2b

Counts

125 → 8

regimes157.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 15.0b

bsearch114.0ms

Steps

Iters	Range		Point
10	1.132180702977125e-31	5.970639726337698e-21	5.911721216050598e-21
10	-0.2907404391033222	-1.9224311918263173e-14	-1.052604693631611e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	38
1	35	38

end0.0ms

analyze1.0ms

Algorithm

Search

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

sample3.0s

Algorithm

intervals

Results

1.5s	3260×	body	1280	valid
644.0ms	672×	body	2560	valid
507.0ms	1843×	body	640	valid
136.0ms	765×	body	320	valid
62.0ms	1108×	body	80	valid
42.0ms	352×	body	160	valid

Details

analyze2.0ms

sample132.0ms

simplify4.0ms

prune6.0ms

localize10.0ms

rewrite10.0ms

series14.0ms

simplify34.0ms

prune45.0ms

localize12.0ms

rewrite20.0ms

series20.0ms

simplify51.0ms

prune97.0ms

localize16.0ms

rewrite35.0ms

series31.0ms

simplify46.0ms

prune144.0ms

localize20.0ms

rewrite60.0ms

series26.0ms

simplify60.0ms

prune193.0ms

regimes157.0ms

bsearch114.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.0s

Profiling