Details

sample19.4s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 51.857636%

Guaranteed chance to sample good point: 4.428816%

Results

92.0ms	85×	body	2560	valid
61.0ms	108×	body	1280	valid
18.0ms	31×	body	1280	overflowed
11.0ms	34×	body	640	valid
7.0ms	326×	pre	80	true
4.0ms	15×	body	640	overflowed
3.0ms	14×	body	320	valid
3.0ms	4×	body	2560	overflowed
2.0ms	8×	body	320	overflowed
1.0ms	12×	body	80	valid
1.0ms	6×	body	160	overflowed
0.0ms	3×	body	160	valid
0.0ms	6×	body	80	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: 60.9b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.4b	(- (exp (* a eps)) 1.0)
3.1b	(- (exp (* b eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

14.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series94.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
18.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	488	957
1	2299	794
2	5001	789

prune126.0ms

Filtered

63 candidates to 85 candidates (-34.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Merged error: 0.0b

Counts

86 → 3

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 (25.0ms)

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

prune36.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

localize4.0ms

Local error

Found 1 expressions with local error:

14.0b

(/ (+ 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

prune37.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	28	5	33

Merged error: 0.0b

Counts

33 → 5

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ b a) a)
5.7b	(* (/ 1 b) (/ (+ b a) a))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`times-frac`
26×	`add-exp-log` `add-cube-cbrt`
16×	`associate-r` `add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp`
7×	`distribute-lft-out`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`pow1` `cbrt-unprod` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `1-exp` `associate-/l/` `add-log-exp`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip-+`

Counts

2 → 92

Calls

2 calls:

5.0ms	(/ (+ b a) a)
13.0ms	(* (/ 1 b) (/ (+ b a) a))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ (+ b a) a)
6.0ms	(* (/ 1 b) (/ (+ b a) a))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	396	543
1	2015	473
2	5001	465

prune75.0ms

Filtered

65 candidates to 98 candidates (-50.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	3	3
Picked	0	1	1
Done	1	0	1
Total	98	5	103

Merged error: 0b

Counts

103 → 5

regimes171.0ms

Accuracy

66.8% (3.4b remaining)

Error of 3.6b against oracle of 0.2b and baseline of 10.4b

bsearch214.0ms

Steps

Iters	Range		Point
9	3.784526587251285e-14	9.509407427988174e-07	5.498779058377649e-13
7	-3.941582281373312e-80	-1.436491832596214e-81	-3.2581390056302074e-81

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	8
1	24	8

end0.0ms

sample26.2s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 51.857636%

Guaranteed chance to sample good point: 4.428816%

Results

2.7s	2598×	body	2560	valid
1.9s	3477×	body	1280	valid
347.0ms	1053×	body	640	valid
268.0ms	655×	body	1280	overflowed
196.0ms	9596×	pre	80	true
98.0ms	349×	body	640	overflowed
96.0ms	151×	body	2560	overflowed
70.0ms	315×	body	320	valid
36.0ms	185×	body	320	overflowed
30.0ms	437×	body	80	valid
21.0ms	120×	body	160	valid
12.0ms	90×	body	160	overflowed
11.0ms	162×	body	80	overflowed
5.0ms	4×	body	2560	invalid

Details

sample19.4s

simplify96.0ms

prune4.0ms

localize16.0ms

rewrite27.0ms

series94.0ms

simplify56.0ms

prune126.0ms

localize4.0ms

rewrite12.0ms

series3.0ms

simplify65.0ms

prune36.0ms

localize4.0ms

rewrite7.0ms

series6.0ms

simplify45.0ms

prune37.0ms

localize5.0ms

rewrite21.0ms

series11.0ms

simplify46.0ms

prune75.0ms

regimes171.0ms

bsearch214.0ms

simplify1.0ms

end0.0ms

sample26.2s

Profiling