Details

sample111.0ms

Algorithm

intervals

Results

78.0ms	201×	body	1280	valid
12.0ms	281×	body	80	valid
7.0ms	31×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
2.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite30.0ms

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)
25.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify96.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	211	282
1	715	269
2	3477	260
3	5001	260

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite27.0ms

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:

11.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
8.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series141.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
52.0ms	(* 1/360 (pow x 6))
36.0ms	(* 1/12 (pow x 4))

simplify47.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (36.0ms)

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

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
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-+l+` `flip3-+` `flip-+`

Counts

3 → 63

Calls

3 calls:

27.0ms	(+ (+ (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))

series146.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
53.0ms	(* 1/360 (pow x 6))
40.0ms	(* 1/12 (pow x 4))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	278	363
1	1216	338
2	5001	329

prune159.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))
0.1b	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
17.8b	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt` `unpow-prod-down`
15×	`add-exp-log`
14×	`cbrt-prod` `associate-r`
9×	`add-cbrt-cube`
8×	`cube-prod`
6×	`associate-l` `prod-exp` `unswap-sqr` `sqr-pow`
5×	`pow1`
4×	`cube-div` `distribute-lft-out` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`cube-mult` `cbrt-div` `flip3-+` `unpow3` `*-commutative` `cbrt-unprod` `flip-+`
1×	`pow-pow` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))
20.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
19.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series224.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/360 (pow x 6))
37.0ms	(* 1/12 (pow x 4))
76.0ms	(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
59.0ms	(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	418	926
1	1871	851
2	5002	838

prune250.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes14.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	5644×	body	1280	valid
334.0ms	7939×	body	80	valid
287.0ms	1269×	body	640	valid
93.0ms	615×	body	320	valid
31.0ms	324×	body	160	valid