Details

analyze4.0ms

Algorithm: search

sample75.0ms

Algorithm

intervals

Results

59.0ms	184×	body	1280	valid
6.0ms	36×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	8×	body	80	valid

simplify136.0ms

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

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: 27.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.4b	(+ (- (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)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify85.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (18.0ms)

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

prune65.0ms

Filtered

29 candidates to 41 candidates (-41.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0.0b

Counts

42 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(+ (* 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:

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

series26.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
12.0ms	(+ (* 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

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

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

prune138.0ms

Filtered

55 candidates to 87 candidates (-58.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(* (exp x) (- (exp x) 2.0))
3.1b	(+ 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)
7.0ms	(* (+ (exp x) 2.0) (exp x))
8.0ms	(* (exp x) (- (exp x) 2.0))
4.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(- (exp x) 2.0)
4.0ms	(* (+ (exp x) 2.0) (exp x))
4.0ms	(* (exp x) (- (exp x) 2.0))
7.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune100.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0.0b

Counts

91 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp x))
0.0b	(cbrt (exp x))
0.0b	(* (exp x) (- (exp x) 2.0))
3.1b	(+ 1 (* (exp x) (- (exp x) 2.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`pow1` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`add-exp-log` `associate-r`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in`
3×	`associate-l`
2×	`pow1/3` `associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cbrt (exp x))
15.0ms	(cbrt (exp x))
4.0ms	(* (exp x) (- (exp x) 2.0))
8.0ms	(+ 1 (* (exp x) (- (exp x) 2.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	245	396
1	1037	365
2	5001	361

prune82.0ms

Filtered

55 candidates to 75 candidates (-36.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

regimes66.0ms

Accuracy

43.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	25
1	41	25

end0.0ms

analyze4.0ms

Algorithm: search

sample2.2s

Algorithm

intervals

Results

1.8s	5639×	body	1280	valid
217.0ms	1218×	body	640	valid
70.0ms	639×	body	320	valid
22.0ms	318×	body	160	valid
7.0ms	186×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample75.0ms

simplify136.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify85.0ms

prune65.0ms

localize10.0ms

rewrite23.0ms

series26.0ms

simplify51.0ms

prune138.0ms

localize10.0ms

rewrite25.0ms

series17.0ms

simplify47.0ms

prune100.0ms

localize16.0ms

rewrite17.0ms

series42.0ms

simplify37.0ms

prune82.0ms

regimes66.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze4.0ms

sample2.2s

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