Details

sample87.0ms

Algorithm

intervals

Results

62.0ms	194×	body	1280	valid
7.0ms	253×	body	80	valid
6.0ms	32×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	7×	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: 27.8b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
2.7b	(+ (- (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)
10.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series66.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
53.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify92.0ms

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

prune77.0ms

Filtered

41 candidates to 29 candidates (70.7%)

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

localize11.0ms

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))

rewrite24.0ms

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:

8.0ms	(+ (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))

series262.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
125.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
46.0ms	(* 1/360 (pow x 6))
38.0ms	(* 1/12 (pow x 4))

simplify49.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	327	476
1	1399	443
2	5001	425

prune152.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
29.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `sqrt-prod` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
4×	`sqrt-div` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

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

series263.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 1/12 (pow x 4))
37.0ms	(* 1/12 (pow x 4))
95.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
96.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify201.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	259	662
1	1019	626
2	4841	616
3	5001	616

prune251.0ms

Filtered

94 candidates to 64 candidates (68.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (sqrt (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
29.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

94×	`sqrt-prod`
52×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`add-cube-cbrt` `pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow-prod-up` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

24.0ms	(* (sqrt (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (sqrt (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
7.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
7.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
7.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sqrt (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (sqrt (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
102.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
96.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
98.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	294	2012
1	1322	1868
2	5001	1827

prune340.0ms

Filtered

148 candidates to 78 candidates (52.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	148	5	153

Merged error: 0.0b

Counts

153 → 5

regimes48.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b 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

sample2.6s

Algorithm

intervals

Results

1.9s	5713×	body	1280	valid
232.0ms	8162×	body	80	valid
221.0ms	1226×	body	640	valid
67.0ms	598×	body	320	valid
21.0ms	298×	body	160	valid

Details

sample87.0ms

simplify140.0ms

prune2.0ms

localize7.0ms

rewrite16.0ms

series66.0ms

simplify92.0ms

prune77.0ms

localize11.0ms

rewrite24.0ms

series262.0ms

simplify49.0ms

prune152.0ms

localize13.0ms

rewrite28.0ms

series263.0ms

simplify201.0ms

prune251.0ms

localize16.0ms

rewrite50.0ms

series398.0ms

simplify67.0ms

prune340.0ms

regimes48.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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