Details

sample1.6s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 77.099609%

Results

92.0ms	79×	body	2560	valid
65.0ms	113×	body	1280	valid
12.0ms	29×	body	1280	overflowed
10.0ms	29×	body	640	valid
7.0ms	316×	pre	80	true
3.0ms	12×	body	320	valid
3.0ms	9×	body	640	overflowed
2.0ms	3×	body	2560	overflowed
1.0ms	20×	body	80	valid
1.0ms	13×	body	80	overflowed
1.0ms	3×	body	320	overflowed
0.0ms	3×	body	160	valid
0.0ms	3×	body	160	overflowed

simplify93.0ms

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: 59.1b

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))
1.9b	(- (exp (* a eps)) 1.0)
2.6b	(- (exp (* b eps)) 1.0)
3.4b	(- (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 (* a eps)) 1.0)
3.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (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))
9.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
13.0ms	(- (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

prune153.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 47.2b

Counts

89 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
3.4b	(- (exp (* (+ a b) eps)) 1.0)
13.6b	(* (pow eps 2) (pow b 2))
15.2b	(* (pow eps 3) (pow b 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`add-log-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1`
3×	`sum-log`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

11.0ms	(+ (* 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))

series51.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* 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))
12.0ms	(* (pow eps 3) (pow b 3))

simplify94.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	510	927
1	2493	815
2	5002	772

prune251.0ms

Filtered

78 candidates to 149 candidates (-91.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	150	6	156

Merged error: 47.2b

Counts

156 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
2.3b	(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
3.4b	(- (exp (* (+ a b) eps)) 1.0)
13.6b	(* (pow eps 2) (pow b 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

19.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
9.0ms	(+ (* 1/6 (pow (* b eps) 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))

series665.0ms

Counts

4 → 12

Calls

4 calls:

625.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
18.0ms	(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
16.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 2) (pow b 2))

simplify118.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	769	1668
1	4458	1375
2	5002	1375

prune241.0ms

Filtered

75 candidates to 121 candidates (-61.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	124	3	127

Merged error: 0.0b

Counts

127 → 3

localize7.0ms

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

prune21.0ms

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	0	2	2
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Merged error: 0.0b

Counts

25 → 4

regimes147.0ms

Accuracy

0% (3.4b remaining)

Error of 3.4b against oracle of 0.1b 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

sample8.0s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 77.099609%

Results

2.8s	2568×	body	2560	valid
2.0s	3472×	body	1280	valid
345.0ms	1025×	body	640	valid
297.0ms	694×	body	1280	overflowed
222.0ms	9997×	pre	80	true
102.0ms	366×	body	640	overflowed
101.0ms	152×	body	2560	overflowed
80.0ms	353×	body	320	valid
37.0ms	536×	body	80	overflowed
35.0ms	173×	body	320	overflowed
32.0ms	459×	body	80	valid
19.0ms	125×	body	160	valid
10.0ms	74×	body	160	overflowed

Details

sample1.6s

simplify93.0ms

prune4.0ms

localize16.0ms

rewrite22.0ms

series42.0ms

simplify41.0ms

prune153.0ms

localize28.0ms

rewrite36.0ms

series51.0ms

simplify94.0ms

prune251.0ms

localize26.0ms

rewrite42.0ms

series665.0ms

simplify118.0ms

prune241.0ms

localize7.0ms

rewrite12.0ms

series3.0ms

simplify63.0ms

prune21.0ms

regimes147.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.0s

Profiling