Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

sample33.0ms

Algorithm

intervals

Results

12.0ms	64×	body	1280	valid
9.0ms	56×	body	640	valid
3.0ms	32×	body	320	valid
2.0ms	92×	body	80	valid
1.0ms	12×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	228	6
1	228	6

prune2.0ms

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: 39.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.2b	(- (exp x) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(/ (- (exp x) 1.0) x)
3.0ms	(- (exp x) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4909	534
1	4909	534

prune68.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	2	58

Merged error: 0.0b

Counts

58 → 2

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (* x 1/6))
0.0b	(* x (+ 1/2 (* x 1/6)))
0.3b	(* x 1/6)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
2×	`flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log`

Counts

3 → 51

Calls

3 calls:

3.0ms	(+ 1/2 (* x 1/6))
5.0ms	(* x (+ 1/2 (* x 1/6)))
3.0ms	(* x 1/6)

series13.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+ 1/2 (* x 1/6))
7.0ms	(* x (+ 1/2 (* x 1/6)))
2.0ms	(* x 1/6)

simplify55.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4818	397
1	4818	397

prune62.0ms

Filtered

41 candidates to 60 candidates (-46.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	60	2	62

Merged error: 0.0b

Counts

62 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0)))
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0))))
4.2b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

158×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
38×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
4×	`pow-pow`
3×	`pow-unpow` `exp-prod` `associate-/r*`
2×	`associate-+r+` `flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 192

Calls

4 calls:

3.0ms	(pow (exp x) 3)
5.0ms	(+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0)))
20.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0))))
12.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow (exp x) 3)
6.0ms	(+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0)))
22.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0))))
6.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5219	5008

prune340.0ms

Filtered

110 candidates to 204 candidates (-85.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	204	2	206

Merged error: 0.0b

Counts

206 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0)))
0.0b	(pow (- (pow (exp x) 3) (pow 1.0 3)) 3)
0.1b	(cbrt (pow (- (pow (exp x) 3) (pow 1.0 3)) 3))
4.2b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt`
110×	`unpow-prod-down` `cube-prod`
80×	`difference-of-squares`
60×	`*-un-lft-identity`
56×	`cbrt-prod`
42×	`sqr-pow`
25×	`distribute-lft-out--`
10×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1` `difference-cubes` `add-exp-log` `add-cbrt-cube`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `associate-+r+` `unpow3`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `pow1/3` `diff-log` `pow-exp` `sum-log` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 182

Calls

4 calls:

5.0ms	(+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0)))
17.0ms	(pow (- (pow (exp x) 3) (pow 1.0 3)) 3)
16.0ms	(cbrt (pow (- (pow (exp x) 3) (pow 1.0 3)) 3))
12.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0)))
12.0ms	(pow (- (pow (exp x) 3) (pow 1.0 3)) 3)
6.0ms	(cbrt (pow (- (pow (exp x) 3) (pow 1.0 3)) 3))
6.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	6279	3046

prune266.0ms

Filtered

86 candidates to 194 candidates (-125.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	193	3	196

Merged error: 0b

Counts

196 → 3

regimes35.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch14.0ms

Steps

Iters	Range		Point
9	-0.0015572991419870413	-3.809160991875718e-13	-0.00016894931581893413

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	41
1	45	41

end0.0ms

sample927.0ms

Algorithm

intervals

Results

448.0ms	2281×	body	1280	valid
209.0ms	1596×	body	640	valid
69.0ms	2850×	body	80	valid
68.0ms	817×	body	320	valid
25.0ms	456×	body	160	valid

Details

analyze4.0ms

sample33.0ms

simplify11.0ms

prune2.0ms

localize4.0ms

rewrite11.0ms

series8.0ms

simplify43.0ms

prune68.0ms

localize5.0ms

rewrite12.0ms

series13.0ms

simplify55.0ms

prune62.0ms

localize13.0ms

rewrite52.0ms

series37.0ms

simplify60.0ms

prune340.0ms

localize15.0ms

rewrite59.0ms

series29.0ms

simplify45.0ms

prune266.0ms

regimes35.0ms

bsearch14.0ms

simplify1.0ms

end0.0ms

sample927.0ms

Profiling