Details

sample243.0ms

Algorithm

intervals

Results

88.0ms	84×	body	2560	valid
65.0ms	70×	body	10240	exit
59.0ms	125×	body	1280	valid
6.0ms	326×	pre	80	true
5.0ms	18×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

prune3.0ms

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: 61.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* a eps)) 1.0)
4.6b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`flip3--` `flip--`
5×	`sub-neg`
4×	`frac-times`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`*-commutative`

Counts

4 → 25

Calls

4 calls:

8.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0ms	(- (exp (* a eps)) 1.0)
6.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series172.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
37.0ms	(- (exp (* a eps)) 1.0)
30.0ms	(- (exp (* b eps)) 1.0)
58.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	239	337
1	918	330
2	4182	325
3	5001	325

prune143.0ms

Filtered

37 candidates to 25 candidates (67.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	4	38

Merged error: 49.3b

Counts

38 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)
13.4b	(* (pow a 2) (pow eps 2))
15.0b	(* (pow a 3) (pow eps 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
6×	`unpow2`
5×	`unswap-sqr`
4×	`pow-to-exp` `associate-r` `associate-l`
2×	`sub-neg` `flip3--` `unpow3` `pow-prod-down` `prod-exp` `*-commutative` `flip--`

Counts

4 → 27

Calls

4 calls:

3.0ms	(- (exp (* b eps)) 1.0)
7.0ms	(- (exp (* (+ a b) eps)) 1.0)
5.0ms	(* (pow a 2) (pow eps 2))
5.0ms	(* (pow a 3) (pow eps 3))

series174.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (exp (* b eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
35.0ms	(* (pow a 2) (pow eps 2))
60.0ms	(* (pow a 3) (pow eps 3))

simplify94.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	198	153
1	664	149
2	2975	145
3	5001	145

prune189.0ms

Filtered

39 candidates to 25 candidates (64.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	37	6	43

Merged error: 49.1b

Counts

43 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.8b	(- (exp (* (+ a b) eps)) 1.0)
14.1b	(* (pow eps 2) (pow b 2))
15.6b	(* (pow eps 3) (pow b 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
8×	`associate-/r/` `*-commutative`
6×	`unpow2`
5×	`flip3--` `flip--` `unswap-sqr`
4×	`frac-times` `pow-to-exp` `times-frac` `associate-r/` `associate-r` `associate-l*`
3×	`flip3-+` `flip-+`
2×	`unpow3` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r` `associate-/l/` `associate-/l*`
1×	`sub-neg` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 44

Calls

4 calls:

27.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
5.0ms	(* (pow eps 2) (pow b 2))
5.0ms	(* (pow eps 3) (pow b 3))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))
61.0ms	(* (pow eps 3) (pow b 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	469	754
1	2255	746
2	5001	746

prune309.0ms

Filtered

56 candidates to 43 candidates (76.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	58	4	62

Merged error: 0.0b

Counts

62 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`frac-add`
6×	`frac-2neg` `clear-num`
2×	`div-inv`
1×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`

Counts

1 → 13

Calls

1 calls:

4.0ms

(+ (/ 1 b) (/ 1 a))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(+ (/ 1 b) (/ 1 a))

simplify75.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	136	72
1	359	61
2	1457	60
3	3453	59
4	5001	59

prune13.0ms

Filtered

16 candidates to 6 candidates (37.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	15	5	20

Merged error: 0b

Counts

20 → 5

regimes81.0ms

Accuracy

0% (3.1b remaining)

Error of 3.5b against oracle of 0.4b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.6s	2572×	body	2560	valid
1.7s	3484×	body	1280	valid
1.7s	1979×	body	10240	exit
288.0ms	1019×	body	640	valid
173.0ms	9981×	pre	80	true
63.0ms	332×	body	320	valid
26.0ms	466×	body	80	valid
16.0ms	129×	body	160	valid