Details

sample183.0ms

Algorithm

intervals

Results

84.0ms	78×	body	2560	valid
58.0ms	107×	body	1280	valid
11.0ms	37×	body	640	valid
6.0ms	301×	pre	80	true
3.0ms	45×	body	80	overflowed
3.0ms	13×	body	320	valid
1.0ms	17×	body	80	valid
1.0ms	4×	body	160	valid

simplify97.0ms

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: 59.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.8b	(- (exp (* a eps)) 1.0)
2.9b	(- (exp (* b eps)) 1.0)
4.6b	(- (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:

10.0ms	(* (- (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)

series166.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
33.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune301.0ms

Filtered

88 candidates to 66 candidates (75.0%)

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: 48.2b

Counts

89 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (exp (* b eps)) 1.0)
4.6b	(- (exp (* (+ a b) eps)) 1.0)
14.6b	(* (pow a 2) (pow eps 2))
15.9b	(* (pow a 3) (pow eps 3))

rewrite29.0ms

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

series182.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow a 2) (pow eps 2))
67.0ms	(* (pow a 3) (pow eps 3))

simplify88.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (73.0ms)

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

prune517.0ms

Filtered

150 candidates to 80 candidates (53.3%)

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: 47.2b

Counts

156 → 8

localize31.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (* 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)))
2.9b	(- (exp (* b eps)) 1.0)
4.6b	(- (exp (* (+ a b) eps)) 1.0)
14.6b	(* (pow a 2) (pow eps 2))

rewrite40.0ms

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:

20.0ms	(/ (* 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)))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))

series887.0ms

Counts

4 → 12

Calls

4 calls:

768.0ms	(/ (* 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)))
32.0ms	(- (exp (* b eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
35.0ms	(* (pow a 2) (pow eps 2))

simplify100.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	731	1576
1	3906	1263
2	5002	1259

prune453.0ms

Filtered

122 candidates to 77 candidates (63.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	127	3	130

Merged error: 0.0b

Counts

130 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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:

12.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify68.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (28.0ms)

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

prune30.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

regimes78.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.7s	2583×	body	2560	valid
1.8s	3372×	body	1280	valid
330.0ms	1081×	body	640	valid
193.0ms	9971×	pre	80	true
122.0ms	1966×	body	80	overflowed
81.0ms	388×	body	320	valid
28.0ms	431×	body	80	valid
20.0ms	150×	body	160	valid

Details

sample183.0ms

simplify97.0ms

prune3.0ms

localize16.0ms

rewrite23.0ms

series166.0ms

simplify43.0ms

prune301.0ms

localize28.0ms

rewrite29.0ms

series182.0ms

simplify88.0ms

prune517.0ms

localize31.0ms

rewrite40.0ms

series887.0ms

simplify100.0ms

prune453.0ms

localize5.0ms

rewrite12.0ms

series11.0ms

simplify68.0ms

prune30.0ms

regimes78.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.5s

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