Details

sample214.0ms

Algorithm

intervals

Results

75.0ms	80×	body	2560	valid
57.0ms	117×	body	1280	valid
48.0ms	53×	body	10240	exit
9.0ms	34×	body	640	valid
5.0ms	309×	pre	80	true
2.0ms	9×	body	320	valid
1.0ms	13×	body	80	valid
0.0ms	3×	body	160	valid

simplify92.0ms

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

prune4.0ms

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: 60.7b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.4b	(- (exp (* b eps)) 1.0)
2.6b	(- (exp (* a eps)) 1.0)
4.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite18.0ms

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:

7.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0ms	(- (exp (* b eps)) 1.0)
3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series167.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
40.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify114.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (25.0ms)

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

prune146.0ms

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: 48.5b

Counts

38 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
4.1b	(- (exp (* (+ a b) eps)) 1.0)
12.5b	(* (pow a 2) (pow eps 2))
13.7b	(* (pow a 3) (pow eps 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
6×	`unpow2`
5×	`unswap-sqr`
4×	`frac-times` `pow-to-exp` `flip3--` `associate-r` `associate-l` `flip--`
3×	`sub-neg` `flip3-+` `*-commutative` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp`

Counts

4 → 36

Calls

4 calls:

17.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
4.0ms	(* (pow a 2) (pow eps 2))
5.0ms	(* (pow a 3) (pow eps 3))

series274.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow a 2) (pow eps 2))
68.0ms	(* (pow a 3) (pow eps 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	338	552
1	1453	549
2	5001	538

prune241.0ms

Filtered

48 candidates to 32 candidates (66.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	47	5	52

Merged error: 48.5b

Counts

52 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.1b	(- (exp (* (+ a b) eps)) 1.0)
14.8b	(* (pow eps 2) (pow b 2))
16.4b	(* (pow eps 3) (pow b 3))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sqr-pow`
6×	`unpow2`
5×	`unswap-sqr`
4×	`+-commutative` `distribute-rgt-in` `frac-times` `pow-to-exp` `associate-+r+` `flip3--` `distribute-lft-in` `associate-r` `associate-l` `flip--`
3×	`flip3-+` `*-commutative` `flip-+`
2×	`unpow3` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp`
1×	`sub-neg`

Counts

4 → 40

Calls

4 calls:

23.0ms	(* (- (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))

series372.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
38.0ms	(* (pow eps 2) (pow b 2))
64.0ms	(* (pow eps 3) (pow b 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	393	604
1	1762	601
2	5001	601

prune256.0ms

Filtered

52 candidates to 35 candidates (67.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	52	5	57

Merged error: 47.8b

Counts

57 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
3.9b	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
4.1b	(- (exp (* (+ a b) eps)) 1.0)
14.8b	(* (pow eps 2) (pow b 2))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

21.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
19.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 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))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
215.0ms	(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow eps 2) (pow b 2))

simplify80.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	580	1167
1	2763	1159
2	5001	1159

prune335.0ms

Filtered

65 candidates to 50 candidates (76.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

regimes86.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2583×	body	2560	valid
1.8s	2000×	body	10240	exit
1.7s	3434×	body	1280	valid
298.0ms	1050×	body	640	valid
169.0ms	10001×	pre	80	true
63.0ms	342×	body	320	valid
24.0ms	458×	body	80	valid
19.0ms	134×	body	160	valid