Details

analyze5.4s

Algorithm

sampling

Space saved by range analysis: 50.097597%

Space saved by search: 51.928123%

Guaranteed chance to sample good point: 4.428816%

sample199.0ms

Algorithm

intervals

Results

87.0ms	89×	body	2560	valid
57.0ms	104×	body	1280	valid
16.0ms	36×	body	640	valid
8.0ms	22×	body	1280	overflowed
6.0ms	302×	pre	80	true
3.0ms	4×	body	2560	overflowed
3.0ms	13×	body	320	valid
2.0ms	8×	body	640	overflowed
1.0ms	5×	body	320	overflowed
1.0ms	10×	body	80	valid
1.0ms	5×	body	160	overflowed
1.0ms	4×	body	160	valid
0.0ms	2×	body	80	overflowed

simplify95.0ms

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: 61.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.1b	(- (exp (* b eps)) 1.0)
2.3b	(- (exp (* a eps)) 1.0)
3.2b	(- (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 (* b eps)) 1.0)
3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series43.0ms

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)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune132.0ms

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: 49.7b

Counts

89 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (exp (* (+ a b) eps)) 1.0)
3.7b	(/ (* 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)))))
14.5b	(* (pow eps 2) (pow b 2))
15.7b	(* (pow eps 3) (pow b 3))

rewrite46.0ms

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:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(/ (* 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)))))
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series653.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (exp (* (+ a b) eps)) 1.0)
624.0ms	(/ (* 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)))))
6.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	848	1789
1	5001	1488

prune334.0ms

Filtered

96 candidates to 167 candidates (-74.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	168	3	171

Merged error: 0.0b

Counts

171 → 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))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify63.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (24.0ms)

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

prune33.0ms

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

localize6.0ms

Local error

Found 1 expressions with local error:

13.4b

(/ (+ 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

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	28	4	32

Merged error: 0b

Counts

32 → 4

regimes155.0ms

Accuracy

0% (2.6b remaining)

Error of 3.1b against oracle of 0.5b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

analyze5.4s

Algorithm

sampling

Space saved by range analysis: 50.097597%

Space saved by search: 51.928123%

Guaranteed chance to sample good point: 4.428816%

sample6.2s

Algorithm

intervals

Results

2.8s	2619×	body	2560	valid
1.9s	3419×	body	1280	valid
345.0ms	1058×	body	640	valid
285.0ms	675×	body	1280	overflowed
197.0ms	9606×	pre	80	true
112.0ms	168×	body	2560	overflowed
104.0ms	376×	body	640	overflowed
81.0ms	369×	body	320	valid
38.0ms	196×	body	320	overflowed
31.0ms	423×	body	80	valid
18.0ms	112×	body	160	valid
11.0ms	85×	body	160	overflowed
7.0ms	106×	body	80	overflowed

Details

analyze5.4s

sample199.0ms

simplify95.0ms

prune4.0ms

localize16.0ms

rewrite23.0ms

series43.0ms

simplify42.0ms

prune132.0ms

localize29.0ms

rewrite46.0ms

series653.0ms

simplify42.0ms

prune334.0ms

localize4.0ms

rewrite12.0ms

series2.0ms

simplify63.0ms

prune33.0ms

localize6.0ms

rewrite7.0ms

series6.0ms

simplify45.0ms

prune24.0ms

regimes155.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze5.4s

sample6.2s

Profiling