Details

sample201.0ms

Algorithm

intervals

Results

93.0ms	87×	body	2560	valid
60.0ms	111×	body	1280	valid
10.0ms	31×	body	640	valid
6.0ms	323×	pre	80	true
5.0ms	67×	body	80	overflowed
3.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	10×	body	80	valid

simplify96.0ms

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 (100.0%)

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:

0.3b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.9b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

9.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series42.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune151.0ms

Filtered

88 candidates to 66 candidates (25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 52.5b

Counts

89 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* b eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)
12.2b	(* (pow a 2) (pow eps 2))
14.0b	(* (pow a 3) (pow eps 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`*-un-lft-identity` `prod-exp`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

4.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series37.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* b eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 3) (pow eps 3))

simplify80.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	470	772
1	2119	679
2	5002	636

prune267.0ms

Filtered

150 candidates to 80 candidates (46.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	148	8	156

Merged error: 52.0b

Counts

156 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
3.0b	(- (exp (* b eps)) 1.0)
4.5b	(- (exp (* (+ a b) eps)) 1.0)
12.2b	(* (pow a 2) (pow eps 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
8×	`add-cube-cbrt` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `associate-*l/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 110

Calls

4 calls:

21.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
3.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))

series280.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
7.0ms	(- (exp (* b eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow a 2) (pow eps 2))

simplify100.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	731	1540
1	3896	1264
2	5002	1260

prune253.0ms

Filtered

122 candidates to 77 candidates (36.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	126	4	130

Merged error: 0.1b

Counts

130 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

11.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify64.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2755	90
4	5001	90

prune21.0ms

Filtered

22 candidates to 14 candidates (36.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Merged error: 0.1b

Counts

26 → 4

regimes147.0ms

Accuracy

0% (3.2b remaining)

Error of 3.5b against oracle of 0.3b 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

sample5.8s

Algorithm

intervals

Results

2.7s	2590×	body	2560	valid
1.9s	3411×	body	1280	valid
330.0ms	1025×	body	640	valid
188.0ms	10006×	pre	80	true
132.0ms	2006×	body	80	overflowed
86.0ms	364×	body	320	valid
33.0ms	476×	body	80	valid
19.0ms	134×	body	160	valid

Details

sample201.0ms

simplify96.0ms

prune4.0ms

localize16.0ms

rewrite23.0ms

series42.0ms

simplify42.0ms

prune151.0ms

localize28.0ms

rewrite30.0ms

series37.0ms

simplify80.0ms

prune267.0ms

localize26.0ms

rewrite39.0ms

series280.0ms

simplify100.0ms

prune253.0ms

localize4.0ms

rewrite11.0ms

series2.0ms

simplify64.0ms

prune21.0ms

regimes147.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

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