Details

sample36.0ms

Algorithm

intervals

Results

16.0ms	84×	body	1280	valid
4.0ms	41×	body	640	valid
3.0ms	158×	body	80	valid
2.0ms	30×	body	320	valid
1.0ms	17×	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	1614	3
7	5002	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.9b	(- (exp (* a x)) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`exp-prod`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity`
6×	`add-log-exp`
5×	`add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`pow1` `add-exp-log` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `exp-to-pow` `diff-log` `*-commutative` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 35

Calls

2 calls:

4.0ms	(exp (* a x))
6.0ms	(- (exp (* a x)) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
40.0ms	(- (exp (* a x)) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	150	164
1	437	156
2	1627	154
3	5001	154

prune77.0ms

Filtered

41 candidates to 29 candidates (70.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	35	6	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	6	42

Merged error: 9.2b

Counts

42 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.7b	(* (* 1/2 (pow a 2)) x)
13.3b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
16.1b	(* (pow a 3) (pow x 3))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
41×	`associate-l`
33×	`*-un-lft-identity`
28×	`add-exp-log`
27×	`associate-r`
23×	`unswap-sqr`
17×	`add-cube-cbrt` `unpow-prod-down` `prod-exp`
15×	`pow1`
13×	`add-cbrt-cube`
12×	`pow-prod-down`
11×	`sqr-pow`
8×	`pow-unpow`
7×	`pow-to-exp` `pow-exp` `distribute-lft-out`
6×	`add-log-exp`
5×	`+-commutative` `*-commutative` `cbrt-unprod`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
3×	`unpow3` `unpow2`
2×	`pow-pow` `flip3-+` `associate-*r/` `flip-+`
1×	`distribute-rgt-out` `sum-log`

Counts

4 → 142

Calls

4 calls:

16.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
11.0ms	(* (* 1/2 (pow a 2)) x)
55.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
10.0ms	(* (pow a 3) (pow x 3))

series256.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
21.0ms	(* (* 1/2 (pow a 2)) x)
100.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
69.0ms	(* (pow a 3) (pow x 3))

simplify115.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	574	911
1	3184	843
2	5002	829

prune322.0ms

Filtered

154 candidates to 96 candidates (62.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	154	6	160

Merged error: 2.7b

Counts

160 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* x a) (* 1 3))
0.8b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.7b	(* (* 1/2 (pow a 2)) x)
13.3b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* x a) (* 1 3))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
39×	`associate-l`
32×	`*-un-lft-identity`
23×	`associate-r`
19×	`add-exp-log`
17×	`add-cube-cbrt` `unpow-prod-down` `unswap-sqr`
14×	`pow1`
13×	`pow-unpow`
11×	`add-cbrt-cube`
9×	`prod-exp`
7×	`distribute-lft-out`
6×	`add-log-exp`
5×	`+-commutative` `pow-prod-down` `*-commutative`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `cbrt-unprod` `sqr-pow`
3×	`pow-exp` `unpow2`
2×	`pow-to-exp` `pow-pow` `flip3-+` `associate-*r/` `flip-+`
1×	`sum-log`

Counts

4 → 128

Calls

4 calls:

7.0ms	(pow (* x a) (* 1 3))
16.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
10.0ms	(* (* 1/2 (pow a 2)) x)
41.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* x a) (* 1 3))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (* x a) (* 1 3))
65.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
22.0ms	(* (* 1/2 (pow a 2)) x)
105.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* x a) (* 1 3))))

simplify82.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	560	845
1	2627	727
2	5002	720

prune290.0ms

Filtered

140 candidates to 95 candidates (67.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	142	4	146

Merged error: 0.0b

Counts

146 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* x a) 2)
0.2b	(pow (* x a) (* 1 3))
4.6b	(+ (* 1/2 (pow (* x a) 2)) (* a x))
13.3b	(+ (+ (* 1/2 (pow (* x a) 2)) (* a x)) (* 1/6 (pow (* x a) (* 1 3))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
26×	`associate-l`
24×	`unpow-prod-down`
22×	`distribute-lft-out`
21×	`add-sqr-sqrt`
16×	`pow-unpow`
14×	`add-cube-cbrt`
11×	`add-log-exp`
10×	`pow1` `add-exp-log`
9×	`associate-r`
4×	`pow-pow` `pow-exp` `sum-log` `add-cbrt-cube` `unswap-sqr`
3×	`+-commutative` `*-commutative`
2×	`pow-to-exp` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `flip-+` `sqr-pow`
1×	`unpow2`

Counts

4 → 106

Calls

4 calls:

7.0ms	(pow (* x a) 2)
6.0ms	(pow (* x a) (* 1 3))
26.0ms	(+ (* 1/2 (pow (* x a) 2)) (* a x))
44.0ms	(+ (+ (* 1/2 (pow (* x a) 2)) (* a x)) (* 1/6 (pow (* x a) (* 1 3))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (* x a) 2)
43.0ms	(pow (* x a) (* 1 3))
59.0ms	(+ (* 1/2 (pow (* x a) 2)) (* a x))
100.0ms	(+ (+ (* 1/2 (pow (* x a) 2)) (* a x)) (* 1/6 (pow (* x a) (* 1 3))))

simplify83.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	471	679
1	2233	612
2	5002	605

prune196.0ms

Filtered

118 candidates to 68 candidates (57.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

regimes100.0ms

Accuracy

96.5% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 21.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	14
1	42	14
2	42	14

end0.0ms

sample955.0ms

Algorithm

intervals

Results

440.0ms	2752×	body	1280	valid
144.0ms	1354×	body	640	valid
107.0ms	5480×	body	80	valid
55.0ms	751×	body	320	valid
17.0ms	366×	body	160	valid