Details

sample48.0ms

Algorithm

intervals

Results

17.0ms	77×	body	1280	valid
8.0ms	182×	body	80	valid
8.0ms	49×	body	640	valid
3.0ms	31×	body	320	valid
1.0ms	13×	body	160	valid

simplify61.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.0b	(- (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)

series12.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(exp (* a x))
8.0ms	(- (exp (* a x)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

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

prune161.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.9b	(* (* 1/2 (pow a 2)) x)
13.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
17.7b	(* (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)))
10.0ms	(* (* 1/2 (pow a 2)) x)
6.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
11.0ms	(* (pow a 3) (pow x 3))

series50.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.0ms	(* (* 1/2 (pow a 2)) x)
21.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
11.0ms	(* (pow a 3) (pow x 3))

simplify99.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (14.0ms)

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

prune808.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
1.0b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.9b	(* (* 1/2 (pow a 2)) x)
13.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite25.0ms

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(pow (* a x) 3)
14.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
21.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify76.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	376	525
1	2297	478
2	5003	478

prune558.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
0.2b	(pow (* a x) 2)
4.4b	(+ (* a x) (* 1/2 (pow (* a x) 2)))
13.1b	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite21.0ms

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) 3)
2.0ms	(pow (* a x) 2)
3.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
12.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(pow (* a x) 3)
5.0ms	(pow (* a x) 2)
14.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
21.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify64.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	285	425
1	1622	392
2	5002	392

prune414.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes476.0ms

Accuracy

98.6% (0.3b remaining)

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

bsearch13.0ms

Steps

Iters	Range		Point
8	-0.0010372006076222768	-6.185764844485224e-08	-0.00014477752003782106

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	34	24

end0.0ms

sample1.4s

Algorithm

intervals

Results

634.0ms	2663×	body	1280	valid
217.0ms	1326×	body	640	valid
199.0ms	5661×	body	80	valid
91.0ms	790×	body	320	valid
32.0ms	387×	body	160	valid