Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample78.0ms

Algorithm

intervals

Results

60.0ms	186×	body	1280	valid
9.0ms	49×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	2×	body	80	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5718	8

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 30.2b

Counts

2 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
2.5b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `associate-+l+` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 33

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series12.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5310	423

prune50.0ms

Filtered

27 candidates to 39 candidates (-44.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	39	2	41

Merged error: 0.0b

Counts

41 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+`

Counts

4 → 74

Calls

4 calls:

5.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
8.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series25.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
6.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5022	849

prune121.0ms

Filtered

56 candidates to 86 candidates (-53.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0.0b

Counts

88 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (log (pow (exp 1/12) (pow x 4))))
0.0b	(+ (* x x) (+ (* 1/360 (pow x 6)) (log (pow (exp 1/12) (pow x 4)))))
0.0b	(* 1/360 (pow x 6))
1.2b	(log (pow (exp 1/12) (pow x 4)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`log-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `unpow-prod-down`
9×	`add-log-exp`
8×	`associate-+r+`
7×	`associate-r`
6×	`add-cbrt-cube`
4×	`pow1` `sum-log` `sqr-pow`
3×	`rem-log-exp` `associate-l` `prod-exp` `unswap-sqr`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `flip-+`
1×	`log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (* 1/360 (pow x 6)) (log (pow (exp 1/12) (pow x 4))))
8.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (log (pow (exp 1/12) (pow x 4)))))
5.0ms	(* 1/360 (pow x 6))
3.0ms	(log (pow (exp 1/12) (pow x 4)))

series87.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* 1/360 (pow x 6)) (log (pow (exp 1/12) (pow x 4))))
12.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (log (pow (exp 1/12) (pow x 4)))))
4.0ms	(* 1/360 (pow x 6))
43.0ms	(log (pow (exp 1/12) (pow x 4)))

simplify53.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5062	909

prune149.0ms

Filtered

61 candidates to 86 candidates (-41.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0.0b

Counts

89 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (* 2.0 (+ (exp x) 2.0)))
0.0b	(pow (exp x) 3)
0.0b	(pow (exp x) 3)
2.5b	(+ (* 2.0 2.0) (* (exp x) (+ (- (pow (exp x) 3) (pow 2.0 3)) (+ (exp x) 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-cbrt-cube`
8×	`pow-pow`
7×	`add-exp-log`
6×	`unpow-prod-down` `pow-unpow` `exp-prod` `cube-prod` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-*r/`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `pow-to-exp` `associate-+r+` `flip3-+` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `associate-r` `sum-log` `*-commutative`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (exp x) (* 2.0 (+ (exp x) 2.0)))
3.0ms	(pow (exp x) 3)
3.0ms	(pow (exp x) 3)
14.0ms	(+ (* 2.0 2.0) (* (exp x) (+ (- (pow (exp x) 3) (pow 2.0 3)) (+ (exp x) 2.0))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (exp x) (* 2.0 (+ (exp x) 2.0)))
4.0ms	(pow (exp x) 3)
4.0ms	(pow (exp x) 3)
15.0ms	(+ (* 2.0 2.0) (* (exp x) (+ (- (pow (exp x) 3) (pow 2.0 3)) (+ (exp x) 2.0))))

simplify41.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5175	924

prune154.0ms

Filtered

64 candidates to 101 candidates (-57.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	101	3	104

Merged error: 0.0b

Counts

104 → 3

regimes29.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.9s	5729×	body	1280	valid
221.0ms	1204×	body	640	valid
67.0ms	583×	body	320	valid
24.0ms	322×	body	160	valid
6.0ms	162×	body	80	valid

Details

analyze4.0ms

sample78.0ms

simplify40.0ms

prune8.0ms

localize6.0ms

rewrite12.0ms

series12.0ms

simplify52.0ms

prune50.0ms

localize10.0ms

rewrite25.0ms

series25.0ms

simplify51.0ms

prune121.0ms

localize14.0ms

rewrite24.0ms

series87.0ms

simplify53.0ms

prune149.0ms

localize16.0ms

rewrite31.0ms

series29.0ms

simplify41.0ms

prune154.0ms

regimes29.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling