Details

sample82.0ms

Algorithm

intervals

Results

58.0ms	187×	body	1280	valid
6.0ms	241×	body	80	valid
5.0ms	32×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	16×	body	160	valid

simplify140.0ms

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

prune2.0ms

Filtered

1 candidates to 0 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: 30.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (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` `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)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
58.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify88.0ms

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

prune86.0ms

Filtered

41 candidates to 29 candidates (70.7%)

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: 0.0b

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))

series267.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
55.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
49.0ms	(* 1/360 (pow x 6))
36.0ms	(* 1/12 (pow x 4))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (44.0ms)

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

prune162.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(* (exp x) (- (exp x) 2.0))
0.0b	(* (+ (exp x) 2.0) (exp x))
4.3b	(+ 1 (* (exp x) (- (exp x) 2.0)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`pow1` `add-cube-cbrt` `associate-r` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`add-exp-log`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
2×	`flip3--` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `diff-log` `sum-log` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

4.0ms	(- (exp x) 2.0)
8.0ms	(* (exp x) (- (exp x) 2.0))
8.0ms	(* (+ (exp x) 2.0) (exp x))
4.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

series133.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (exp x) 2.0)
38.0ms	(* (exp x) (- (exp x) 2.0))
22.0ms	(* (+ (exp x) 2.0) (exp x))
59.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	315	493
1	1420	451
2	5002	451

prune147.0ms

Filtered

88 candidates to 61 candidates (69.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	88	3	91

Merged error: 0b

Counts

91 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
46.8b	(/ (+ (pow x 4) (neg (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
32×	`times-frac`
27×	`add-cube-cbrt`
21×	`add-exp-log` `associate-r`
20×	`difference-of-squares`
17×	`unpow-prod-down`
12×	`add-cbrt-cube`
11×	`sqr-pow`
9×	`associate-l` `prod-exp` `distribute-lft-out` `unswap-sqr`
8×	`associate-/r*`
5×	`distribute-lft-out--` `unpow2`
4×	`pow1` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `div-sub` `pow-exp` `*-commutative` `cbrt-unprod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `associate-+r-` `flip3--` `frac-2neg` `flip3-+` `div-exp` `unsub-neg` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 138

Calls

4 calls:

9.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
15.0ms	(/ (+ (pow x 4) (neg (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 1/12 (pow x 4))
37.0ms	(* 1/12 (pow x 4))
41.0ms	(* 1/12 (pow x 4))
150.0ms	(/ (+ (pow x 4) (neg (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	359	2510
1	1638	2337
2	5001	2205

prune331.0ms

Filtered

150 candidates to 89 candidates (59.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	150	3	153

Merged error: 0b

Counts

153 → 3

regimes15.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.7s	5691×	body	1280	valid
217.0ms	1241×	body	640	valid
203.0ms	8010×	body	80	valid
63.0ms	607×	body	320	valid
20.0ms	308×	body	160	valid

Details

sample82.0ms

simplify140.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series70.0ms

simplify88.0ms

prune86.0ms

localize10.0ms

rewrite23.0ms

series267.0ms

simplify54.0ms

prune162.0ms

localize10.0ms

rewrite25.0ms

series133.0ms

simplify47.0ms

prune147.0ms

localize15.0ms

rewrite39.0ms

series271.0ms

simplify72.0ms

prune331.0ms

regimes15.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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