Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	99×	body	1280	valid
4.0ms	39×	body	640	valid
4.0ms	182×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid

simplify59.0ms

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

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.7b	(- (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:

2.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series50.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify39.0ms

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

prune68.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.0b	(* (* 1/2 (pow a 2)) x)
10.3b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
15.5b	(* (pow a 3) (pow x 3))

rewrite33.0ms

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:

5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
10.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
9.0ms	(* (pow a 3) (pow x 3))

series237.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
20.0ms	(* (* 1/2 (pow a 2)) x)
101.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
60.0ms	(* (pow a 3) (pow x 3))

simplify103.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (14.0ms)

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

prune297.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/2 (pow a 2))
1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.0b	(* (* 1/2 (pow a 2)) x)
10.3b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
18×	`add-sqr-sqrt`
14×	`associate-r`
13×	`add-cbrt-cube`
11×	`prod-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down`
3×	`*-commutative`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-*r/` `pow-prod-down` `pow-exp` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `sum-log`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* 1/2 (pow a 2))
5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
6.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 1/2 (pow a 2))
62.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
21.0ms	(* (* 1/2 (pow a 2)) x)
97.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify83.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	395	565
1	2284	513
2	5001	513

prune221.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a x) (* 1/6 (pow (* a x) 3)))
0.1b	(* 1/6 (pow (* a x) 3))
0.2b	(pow (* a x) 3)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

3.0ms	(+ (* a x) (* 1/6 (pow (* a x) 3)))
5.0ms	(* 1/6 (pow (* a x) 3))
4.0ms	(pow (* a x) 3)

series230.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(+ (* a x) (* 1/6 (pow (* a x) 3)))
73.0ms	(* 1/6 (pow (* a x) 3))
46.0ms	(pow (* a x) 3)

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	200	286
1	1072	261
2	5001	260

prune126.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes190.0ms

Accuracy

97.3% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 21.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

551.0ms	2716×	body	1280	valid
133.0ms	1323×	body	640	valid
107.0ms	5353×	body	80	valid
48.0ms	749×	body	320	valid
18.0ms	416×	body	160	valid