Details

sample82.0ms

Algorithm

intervals

Results

56.0ms	190×	body	1280	valid
7.0ms	275×	body	80	valid
6.0ms	34×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify474.0ms

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	67	5
5	100	5
6	144	5
7	296	5
8	1321	5
9	5001	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite13.0ms

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 (- x)))

series68.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (19.0ms)

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

prune83.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

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))

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:

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))

series262.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
53.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
46.0ms	(* 1/360 (pow x 6))
37.0ms	(* 1/12 (pow x 4))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	329	464
1	1456	439
2	5001	423

prune190.0ms

Filtered

87 candidates to 55 candidates (63.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(- (exp x) 2.0)
0.0b	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
3.9b	(+ (* (exp x) (- (exp x) 2.0)) 1)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube`
15×	`add-exp-log`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`flip3-+` `flip-+`
8×	`associate-/l/` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `associate-*l/`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `frac-times` `associate-+l+` `div-exp` `associate-l`
3×	`sub-neg` `associate-r`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `associate-/r/`
1×	`+-commutative` `flip3--` `frac-2neg` `times-frac` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `flip--` `div-inv` `distribute-lft-out` `associate-/l*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

8.0ms	(* (+ (exp x) 2.0) (exp x))
4.0ms	(- (exp x) 2.0)
21.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
9.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

series199.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ (exp x) 2.0) (exp x))
13.0ms	(- (exp x) 2.0)
98.0ms	(/ (* (+ (exp x) 2.0) (+ (* (exp x) (- (exp x) 2.0)) 1)) (* (+ (exp x) 2.0) (exp x)))
60.0ms	(+ (* (exp x) (- (exp x) 2.0)) 1)

simplify87.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	502	938
1	3024	692
2	5001	681

prune190.0ms

Filtered

93 candidates to 66 candidates (71.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
0.0b	(pow (exp x) 2)
3.9b	(+ (pow (* (exp x) (- (exp x) 2.0)) 3) 1)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
12×	`pow1`
11×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`flip3--` `swap-sqr` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-r` `associate-l` `difference-of-squares`
4×	`frac-times` `pow-pow`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-to-exp` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `distribute-lft-out` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

4.0ms	(- (exp x) 2.0)
11.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
4.0ms	(pow (exp x) 2)
7.0ms	(+ (pow (* (exp x) (- (exp x) 2.0)) 3) 1)

series293.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (exp x) 2.0)
33.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
13.0ms	(pow (exp x) 2)
234.0ms	(+ (pow (* (exp x) (- (exp x) 2.0)) 3) 1)

simplify65.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	402	623
1	1944	553
2	5003	543

prune275.0ms

Filtered

104 candidates to 64 candidates (61.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes42.0ms

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

sample2.4s

Algorithm

intervals

Results

1.8s	5735×	body	1280	valid
198.0ms	1207×	body	640	valid
193.0ms	8045×	body	80	valid
60.0ms	587×	body	320	valid
19.0ms	303×	body	160	valid