Details

sample6.9s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 3.808594%

Results

86.0ms	77×	body	2560	valid
76.0ms	120×	body	1280	valid
12.0ms	35×	body	640	valid
9.0ms	20×	body	1280	overflowed
6.0ms	314×	pre	80	true
4.0ms	14×	body	640	overflowed
2.0ms	7×	body	320	overflowed
1.0ms	2×	body	2560	overflowed
1.0ms	6×	body	320	valid
1.0ms	17×	body	80	valid
1.0ms	14×	body	80	overflowed
0.0ms	1×	body	160	valid
0.0ms	1×	body	160	overflowed

simplify94.0ms

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: 59.7b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b	(- (exp (* b eps)) 1.0)
3.7b	(- (exp (* a eps)) 1.0)
6.3b	(- (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))
3.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (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)

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (8.0ms)

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

prune135.0ms

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: 49.9b

Counts

89 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

4.4b	(/ (* 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)))
6.3b	(- (exp (* (+ a b) eps)) 1.0)
12.6b	(* (pow a 2) (pow eps 2))
14.3b	(* (pow a 3) (pow eps 3))

rewrite48.0ms

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:

21.0ms	(/ (* 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))

series295.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (* 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)))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 3) (pow eps 3))

simplify140.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	815	1795
1	4665	1494
2	5002	1458

prune321.0ms

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))

simplify63.0ms

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

prune35.0ms

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:

12.8b

(/ (+ 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))

simplify44.0ms

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

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

regimes157.0ms

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

sample13.2s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 3.808594%

Results

2.8s	2603×	body	2560	valid
2.0s	3460×	body	1280	valid
359.0ms	1040×	body	640	valid
302.0ms	680×	body	1280	overflowed
205.0ms	9996×	pre	80	true
115.0ms	388×	body	640	overflowed
96.0ms	145×	body	2560	overflowed
77.0ms	327×	body	320	valid
39.0ms	186×	body	320	overflowed
35.0ms	497×	body	80	overflowed
34.0ms	454×	body	80	valid
18.0ms	116×	body	160	valid
14.0ms	96×	body	160	overflowed
4.0ms	4×	body	2560	invalid

Details

sample6.9s

simplify94.0ms

prune4.0ms

localize17.0ms

rewrite23.0ms

series40.0ms

simplify44.0ms

prune135.0ms

localize27.0ms

rewrite48.0ms

series295.0ms

simplify140.0ms

prune321.0ms

localize4.0ms

rewrite12.0ms

series3.0ms

simplify63.0ms

prune35.0ms

localize4.0ms

rewrite7.0ms

series6.0ms

simplify44.0ms

prune24.0ms

regimes157.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample13.2s

Profiling