Details

analyze4.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 49.585176%

Guaranteed chance to sample good point: 99.987899%

sample77.0ms

Algorithm

intervals

Results

60.0ms	191×	body	1280	valid
7.0ms	37×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	2×	body	80	valid

simplify139.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	65	5
5	96	5
6	140	5
7	285	5
8	1642	5
9	5001	5

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: 32.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.6b	(+ (- (exp x) 2.0) (exp (neg x)))

rewrite16.0ms

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` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
12.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify87.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	209	282
1	694	269
2	3196	260
3	5001	260

prune59.0ms

Filtered

29 candidates to 41 candidates (-41.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0b

Counts

42 → 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	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
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+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series27.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
6.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify49.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	438
2	5001	422

prune140.0ms

Filtered

55 candidates to 87 candidates (-58.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	2	89

Merged error: 0b

Counts

89 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (- (+ (exp (neg x)) (exp x)) 2.0) 3)
0.0b	(cbrt (pow (- (+ (exp (neg x)) (exp x)) 2.0) 3))
2.4b	(- (+ (exp (neg x)) (exp x)) 2.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`distribute-lft-out` `difference-of-squares`
4×	`pow1` `add-exp-log` `cube-div` `add-cbrt-cube`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `pow-exp` `associate--l+` `sum-log` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

3 → 77

Calls

3 calls:

9.0ms	(pow (- (+ (exp (neg x)) (exp x)) 2.0) 3)
9.0ms	(cbrt (pow (- (+ (exp (neg x)) (exp x)) 2.0) 3))
8.0ms	(- (+ (exp (neg x)) (exp x)) 2.0)

series29.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(pow (- (+ (exp (neg x)) (exp x)) 2.0) 3)
9.0ms	(cbrt (pow (- (+ (exp (neg x)) (exp x)) 2.0) 3))
7.0ms	(- (+ (exp (neg x)) (exp x)) 2.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	267	772
1	1055	740
2	5001	724

prune72.0ms

Filtered

43 candidates to 86 candidates (-100.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	86	2	88

Merged error: 0b

Counts

88 → 2

regimes25.0ms

Accuracy

0% (0.5b 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	17	7
1	17	7

end0.0ms

analyze6.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 49.585176%

Guaranteed chance to sample good point: 99.987899%

sample2.2s

Algorithm

intervals

Results

1.8s	5678×	body	1280	valid
210.0ms	1189×	body	640	valid
68.0ms	634×	body	320	valid
23.0ms	320×	body	160	valid
7.0ms	179×	body	80	valid

Details

analyze4.0ms

sample77.0ms

simplify139.0ms

prune3.0ms

localize6.0ms

rewrite16.0ms

series9.0ms

simplify87.0ms

prune59.0ms

localize10.0ms

rewrite23.0ms

series27.0ms

simplify49.0ms

prune140.0ms

localize8.0ms

rewrite28.0ms

series29.0ms

simplify37.0ms

prune72.0ms

regimes25.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze6.0ms

sample2.2s

Profiling