Details

analyze1.7s

Algorithm: search

sample211.0ms

Algorithm

intervals

Results

94.0ms	86×	body	2560	valid
65.0ms	111×	body	1280	valid
11.0ms	32×	body	640	valid
6.0ms	304×	pre	80	true
6.0ms	9×	body	640	overflowed
5.0ms	12×	body	1280	overflowed
3.0ms	4×	body	2560	overflowed
2.0ms	10×	body	320	valid
2.0ms	9×	body	320	overflowed
1.0ms	14×	body	80	valid
1.0ms	5×	body	160	overflowed
1.0ms	8×	body	80	overflowed
0.0ms	1×	body	1280	invalid
0.0ms	3×	body	160	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

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: 60.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
3.9b	(- (exp (* b eps)) 1.0)
5.3b	(- (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)
5.0ms	(- (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)

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (8.0ms)

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

prune144.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 51.8b

Counts

89 → 5

localize27.0ms

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 eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
5.3b	(- (exp (* (+ a b) eps)) 1.0)
13.7b	(* (pow eps 2) (pow b 2))
15.0b	(* (pow eps 3) (pow b 3))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

24.0ms	(/ (* 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)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series656.0ms

Counts

4 → 12

Calls

4 calls:

626.0ms	(/ (* 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)))))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	848	1843
1	5001	1499

prune340.0ms

Filtered

96 candidates to 167 candidates (-74.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	167	5	172

Merged error: 0.0b

Counts

172 → 5

localize4.0ms

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:

11.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify63.0ms

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

prune42.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 0.0b

Counts

27 → 6

localize4.0ms

Local error

Found 1 expressions with local error:

17.5b

(/ (+ b a) (* b a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

simplify45.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	145	134
1	519	113
2	2023	113
3	5001	113

prune24.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	27	7	34

Merged error: 0.0b

Counts

34 → 7

regimes182.0ms

Accuracy

0% (3.2b remaining)

Error of 3.5b against oracle of 0.2b 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

analyze1.7s

Algorithm: search

sample6.3s

Algorithm

intervals

Results

2.7s	2588×	body	2560	valid
2.0s	3442×	body	1280	valid
353.0ms	1023×	body	640	valid
285.0ms	659×	body	1280	overflowed
196.0ms	9728×	pre	80	true
115.0ms	400×	body	640	overflowed
99.0ms	150×	body	2560	overflowed
89.0ms	372×	body	320	valid
39.0ms	186×	body	320	overflowed
33.0ms	463×	body	80	valid
18.0ms	112×	body	160	valid
17.0ms	232×	body	80	overflowed
14.0ms	99×	body	160	overflowed
1.0ms	1×	body	2560	invalid
0.0ms	1×	body	1280	invalid

Details

analyze1.7s

sample211.0ms

simplify96.0ms

prune4.0ms

localize15.0ms

rewrite23.0ms

series42.0ms

simplify41.0ms

prune144.0ms

localize27.0ms

rewrite50.0ms

series656.0ms

simplify43.0ms

prune340.0ms

localize4.0ms

rewrite12.0ms

series3.0ms

simplify63.0ms

prune42.0ms

localize4.0ms

rewrite7.0ms

series6.0ms

simplify45.0ms

prune24.0ms

regimes182.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.7s

sample6.3s

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