Details

sample88.0ms

Algorithm

intervals

Results

55.0ms	173×	body	1280	valid
7.0ms	244×	body	80	valid
7.0ms	39×	body	640	valid
6.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid

simplify135.0ms

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: 28.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.9b	(+ (- (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)
8.0ms	(+ (- (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)))

simplify86.0ms

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

prune66.0ms

Filtered

29 candidates to 41 candidates (-41.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize12.0ms

Local error

Found 3 expressions with local error:

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))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-exp-log`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 64

Calls

3 calls:

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))

series14.0ms

Counts

3 → 9

Calls

3 calls:

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))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	283	367
1	1255	340
2	5001	327

prune119.0ms

Filtered

45 candidates to 73 candidates (-62.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	72	5	77

Merged error: 0.1b

Counts

77 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
29.7b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.7b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite27.0ms

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:

7.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
6.0ms	(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)))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/12 (pow x 4))
4.0ms	(* 1/12 (pow x 4))
8.0ms	(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)))))

simplify200.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (30.0ms)

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

prune270.0ms

Filtered

64 candidates to 94 candidates (-46.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Merged error: 0.1b

Counts

99 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))
0.0b	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
0.1b	(pow (exp x) 3)
6.0b	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `add-log-exp`
7×	`pow1`
5×	`associate-r`
4×	`pow-pow` `flip3-+` `associate-*r/` `flip-+`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `times-frac` `cube-prod` `associate-l` `sum-log` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `associate-+r+` `frac-2neg` `distribute-lft-in` `unpow3` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

19.0ms	(* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))
21.0ms	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
3.0ms	(pow (exp x) 3)
9.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))
38.0ms	(/ (+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3)))))) (* (exp x) (+ (* 2.0 (+ 2.0 (exp x))) (exp (+ x x)))))
4.0ms	(pow (exp x) 3)
14.0ms	(+ (* 2.0 2.0) (+ (exp (+ x x)) (* (exp x) (+ 2.0 (- (pow (exp x) 3) (pow 2.0 3))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	578	1345
1	3604	1165
2	5001	1162

prune181.0ms

Filtered

70 candidates to 100 candidates (-42.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	99	6	105

Merged error: 0.1b

Counts

105 → 6

regimes45.0ms

Accuracy

0% (0.6b 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

1.8s	5706×	body	1280	valid
214.0ms	7807×	body	80	valid
213.0ms	1225×	body	640	valid
66.0ms	605×	body	320	valid
21.0ms	302×	body	160	valid

Details

sample88.0ms

simplify135.0ms

prune2.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify86.0ms

prune66.0ms

localize12.0ms

rewrite18.0ms

series14.0ms

simplify41.0ms

prune119.0ms

localize13.0ms

rewrite27.0ms

series22.0ms

simplify200.0ms

prune270.0ms

localize19.0ms

rewrite55.0ms

series64.0ms

simplify121.0ms

prune181.0ms

regimes45.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling