Details

sample37.0ms

Algorithm

intervals

Results

17.0ms	86×	body	1280	valid
5.0ms	47×	body	640	valid
4.0ms	169×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	15×	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

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: 29.7b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.9b	(- (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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify42.0ms

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

prune50.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	3	31

Merged error: 8.6b

Counts

31 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
3.9b	(- (exp (* a x)) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

2.0ms	(exp (* a x))
5.0ms	(pow (- (exp (* a x)) 1.0) 3)
5.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
7.0ms	(- (exp (* a x)) 1.0)

series131.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
52.0ms	(pow (- (exp (* a x)) 1.0) 3)
34.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
34.0ms	(- (exp (* a x)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	269	550
1	1076	527
2	5001	516

prune126.0ms

Filtered

92 candidates to 49 candidates (53.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	92	3	95

Merged error: 8.6b

Counts

95 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

2.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.0b	(* (* 1/2 (pow a 2)) x)
12.0b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
17.7b	(* (pow a 3) (pow x 3))

rewrite35.0ms

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

series236.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 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 3) (pow x 3))))
62.0ms	(* (pow a 3) (pow x 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (15.0ms)

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

prune252.0ms

Filtered

125 candidates to 75 candidates (60.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	125	3	128

Merged error: 2.7b

Counts

128 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (pow a 2))
2.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
7.0b	(* (* 1/2 (pow a 2)) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

5.0ms	(* 1/2 (pow a 2))
5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.0ms	(* (* 1/2 (pow a 2)) x)

series108.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 1/2 (pow a 2))
60.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
23.0ms	(* (* 1/2 (pow a 2)) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	296	366
1	1630	322
2	5001	319

prune97.0ms

Filtered

77 candidates to 47 candidates (61.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Merged error: 0.1b

Counts

80 → 3

regimes113.0ms

Accuracy

96.3% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 21.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7

end0.0ms

sample1.0s

Algorithm

intervals

Results

470.0ms	2689×	body	1280	valid
151.0ms	1317×	body	640	valid
132.0ms	5512×	body	80	valid
56.0ms	732×	body	320	valid
24.0ms	414×	body	160	valid