Details

sample107.0ms

Algorithm

intervals

Results

72.0ms	188×	body	1280	valid
12.0ms	292×	body	80	valid
7.0ms	30×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	8×	body	160	valid

simplify213.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite27.0ms

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)
22.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp x) 2.0)
5.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify91.0ms

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

prune184.0ms

Pruning

1 alts after pruning (1 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))

rewrite24.0ms

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:

12.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
6.0ms	(* 1/12 (pow x 4))

series11.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
3.0ms	(* 1/360 (pow x 6))
3.0ms	(* 1/12 (pow x 4))

simplify42.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (36.0ms)

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

prune377.0ms

Pruning

3 alts after pruning (2 fresh and 1 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))

rewrite42.0ms

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:

28.0ms	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
7.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series11.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4)))
3.0ms	(* 1/360 (pow x 6))
3.0ms	(* 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

prune358.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

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))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `sqrt-prod` `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-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* 1/12 (pow x 4))
31.0ms	(sqrt (+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4))))
30.0ms	(sqrt (+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4))))

series20.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 1/12 (pow x 4))
3.0ms	(* 1/12 (pow x 4))
7.0ms	(sqrt (+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4))))
8.0ms	(sqrt (+ (+ (pow x 2) (* 1/360 (pow x 6))) (* 1/12 (pow x 4))))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	254	648
1	970	616
2	5002	600

prune728.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	5689×	body	1280	valid
331.0ms	8367×	body	80	valid
277.0ms	1229×	body	640	valid
87.0ms	584×	body	320	valid
32.0ms	332×	body	160	valid