Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	85×	body	1280	valid
5.0ms	47×	body	640	valid
4.0ms	179×	body	80	valid
2.0ms	28×	body	320	valid
0.0ms	10×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	3
7	5001	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.5b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series48.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
36.0ms	(- (exp (* a x)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune67.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.2b	(* (* 1/2 (pow a 2)) x)
12.8b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
19.0b	(* (pow a 3) (pow x 3))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `cube-mult` `associate-+l+` `distribute-lft-in` `flip3-+` `unpow3` `associate-*r/` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 113

Calls

4 calls:

7.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.0ms	(* (* 1/2 (pow a 2)) x)
7.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
12.0ms	(* (pow a 3) (pow x 3))

series251.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
26.0ms	(* (* 1/2 (pow a 2)) x)
100.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
67.0ms	(* (pow a 3) (pow x 3))

simplify101.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	471	797
1	2758	738
2	5001	738

prune309.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.2b	(* (* 1/2 (pow a 2)) x)
12.8b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`prod-exp`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
5×	`cbrt-unprod`
4×	`associate-l`
3×	`pow-unpow` `pow-prod-down` `pow-exp`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `pow-pow` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `rem-cube-cbrt`
1×	`+-commutative` `cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sum-log` `unswap-sqr` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

2.0ms	(pow (* a x) 3)
7.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.0ms	(* (* 1/2 (pow a 2)) x)
6.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (* a x) 3)
62.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
22.0ms	(* (* 1/2 (pow a 2)) x)
99.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify75.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	376	530
1	2297	478
2	5001	478

prune201.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 2)
0.2b	(pow (* a x) 3)
5.2b	(+ (* a x) (* 1/2 (pow (* a x) 2)))
12.8b	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
10×	`pow1` `add-exp-log`
7×	`add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`pow-pow` `pow-exp` `sum-log`
2×	`+-commutative` `pow-to-exp` `unpow-prod-down` `flip3-+` `pow-prod-down` `prod-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`cube-mult` `associate-+l+` `unpow3` `cube-prod` `cbrt-unprod` `unpow2`

Counts

4 → 64

Calls

4 calls:

2.0ms	(pow (* a x) 2)
2.0ms	(pow (* a x) 3)
3.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
16.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (* a x) 2)
48.0ms	(pow (* a x) 3)
64.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
104.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify66.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	285	425
1	1624	392
2	5001	392

prune153.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

end0.0ms

sample952.0ms

Algorithm

intervals

Results

445.0ms	2736×	body	1280	valid
133.0ms	1275×	body	640	valid
107.0ms	5395×	body	80	valid
57.0ms	774×	body	320	valid
18.0ms	389×	body	160	valid