Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	87×	body	1280	valid
5.0ms	46×	body	640	valid
3.0ms	168×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	9×	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: 30.7b

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
33.0ms	(- (exp (* a x)) 1.0)

simplify43.0ms

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

prune72.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.2b	(* (* 1/2 (pow a 2)) x)
11.8b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
16.4b	(* (pow a 3) (pow x 3))

rewrite40.0ms

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)
6.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
12.0ms	(* (pow a 3) (pow x 3))

series233.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
23.0ms	(* (* 1/2 (pow a 2)) x)
94.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
60.0ms	(* (pow a 3) (pow x 3))

simplify98.0ms

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

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* a x) 3)
1.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.2b	(* (* 1/2 (pow a 2)) x)
11.8b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite26.0ms

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)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (* a x) 3)
60.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
21.0ms	(* (* 1/2 (pow a 2)) x)
96.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify78.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (12.0ms)

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

prune207.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 2)
0.3b	(pow (* a x) 3)
5.4b	(+ (* a x) (* 1/2 (pow (* a x) 2)))
11.8b	(+ (+ (* 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) 2)
2.0ms	(pow (* a x) 3)
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)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (* a x) 2)
46.0ms	(pow (* a x) 3)
59.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
102.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify62.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (10.0ms)

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

prune152.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes220.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	32
1	34	32

end0.0ms

sample924.0ms

Algorithm

intervals

Results

431.0ms	2729×	body	1280	valid
134.0ms	1294×	body	640	valid
107.0ms	5499×	body	80	valid
50.0ms	757×	body	320	valid
17.0ms	395×	body	160	valid