Details

sample6.2s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 6.103516%

Results

85.0ms	78×	body	2560	valid
67.0ms	118×	body	1280	valid
12.0ms	36×	body	640	valid
9.0ms	21×	body	1280	overflowed
7.0ms	315×	pre	80	true
4.0ms	14×	body	640	overflowed
2.0ms	4×	body	2560	overflowed
2.0ms	7×	body	320	valid
1.0ms	6×	body	320	overflowed
1.0ms	16×	body	80	valid
1.0ms	13×	body	80	overflowed
0.0ms	1×	body	160	valid
0.0ms	1×	body	160	overflowed

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: 59.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
4.2b	(- (exp (* a eps)) 1.0)
6.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite22.0ms

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* b eps)) 1.0)
7.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (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

prune137.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 50.5b

Counts

89 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
6.1b	(- (exp (* (+ a b) eps)) 1.0)
14.9b	(* (pow a 2) (pow eps 2))
16.1b	(* (pow a 3) (pow eps 3))

rewrite49.0ms

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:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 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)
9.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series287.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 3) (pow eps 3))

simplify139.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	815	1849
1	4766	1505
2	5001	1505

prune328.0ms

Filtered

91 candidates to 167 candidates (-83.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	167	4	171

Merged error: 0.0b

Counts

171 → 4

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:

2.0ms

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

simplify65.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (26.0ms)

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

prune34.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

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: 0.0b

Counts

26 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

13.8b

(/ (+ 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

prune25.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	27	5	32

Merged error: 0.0b

Counts

32 → 5

regimes152.0ms

Accuracy

0% (3.2b remaining)

Error of 3.4b against oracle of 0.2b 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

sample12.5s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 6.103516%

Results

2.7s	2578×	body	2560	valid
1.9s	3455×	body	1280	valid
349.0ms	1060×	body	640	valid
276.0ms	663×	body	1280	overflowed
215.0ms	9983×	pre	80	true
112.0ms	390×	body	640	overflowed
98.0ms	151×	body	2560	overflowed
75.0ms	338×	body	320	valid
36.0ms	183×	body	320	overflowed
34.0ms	492×	body	80	overflowed
31.0ms	456×	body	80	valid
16.0ms	113×	body	160	valid
13.0ms	99×	body	160	overflowed
7.0ms	5×	body	2560	invalid

Details

sample6.2s

simplify96.0ms

prune4.0ms

localize18.0ms

rewrite22.0ms

series40.0ms

simplify41.0ms

prune137.0ms

localize27.0ms

rewrite49.0ms

series287.0ms

simplify139.0ms

prune328.0ms

localize4.0ms

rewrite12.0ms

series3.0ms

simplify65.0ms

prune34.0ms

localize4.0ms

rewrite7.0ms

series6.0ms

simplify45.0ms

prune25.0ms

regimes152.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample12.5s

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