Details

sample233.0ms

Algorithm

intervals

Results

93.0ms	98×	body	2560	valid
58.0ms	60×	body	10240	exit
45.0ms	97×	body	1280	valid
9.0ms	34×	body	640	valid
5.0ms	317×	pre	80	true
3.0ms	16×	body	320	valid
1.0ms	10×	body	80	valid
0.0ms	2×	body	160	valid

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 61.8b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.1b	(- (exp (* b eps)) 1.0)
3.2b	(- (exp (* a eps)) 1.0)
5.8b	(- (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:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series162.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

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

prune301.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 52.4b

Counts

89 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (* 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)))))
5.8b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow eps 2) (pow b 2))
14.5b	(* (pow eps 3) (pow b 3))

rewrite53.0ms

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)) (* (- (exp (* a eps)) 1.0) (+ (* 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))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* 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)))))
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))
60.0ms	(* (pow eps 3) (pow b 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	848	1843
1	5001	1499

prune587.0ms

Filtered

167 candidates to 96 candidates (57.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Merged error: 0.2b

Counts

173 → 3

localize5.0ms

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))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(+ (/ 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	2775	90
4	5001	90

prune35.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Merged error: 0.2b

Counts

25 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 b) b)
0.1b	(/ (- (/ 1 a)) a)
5.8b	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
32.6b	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

1240×	`times-frac`
1158×	`*-un-lft-identity`
577×	`add-sqr-sqrt`
241×	`add-cube-cbrt`
210×	`distribute-lft-out`
199×	`distribute-rgt-neg-in`
176×	`div-inv`
126×	`difference-of-squares`
98×	`distribute-lft-out--`
56×	`associate-/l*`
52×	`distribute-lft-neg-in`
25×	`associate-/r*`
17×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/l/`
4×	`neg-mul-1` `div-sub`
3×	`neg-sub0` `frac-2neg` `clear-num` `associate-/r/`
2×	`associate-+l-` `flip3-+` `frac-add` `flip-+` `pow-div`
1×	`+-commutative` `rec-exp` `flip3--` `pow-flip` `1-exp` `distribute-frac-neg` `sum-log` `frac-sub` `flip--` `distribute-neg-frac` `inv-pow`

Counts

4 → 533

Calls

4 calls:

6.0ms	(/ (/ 1 b) b)
8.0ms	(/ (- (/ 1 a)) a)
135.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
155.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (/ 1 b) b)
30.0ms	(/ (- (/ 1 a)) a)
24.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
38.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify100.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1343	6820
1	5001	5868

prune468.0ms

Filtered

545 candidates to 181 candidates (33.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	542	3	545
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	543	5	548

Merged error: 0.2b

Counts

548 → 5

regimes75.0ms

Accuracy

0% (2.9b remaining)

Error of 3.1b against oracle of 0.3b 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

sample6.7s

Algorithm

intervals

Results

2.4s	2554×	body	2560	valid
1.7s	2036×	body	10240	exit
1.7s	3505×	body	1280	valid
272.0ms	1017×	body	640	valid
167.0ms	10040×	pre	80	true
71.0ms	387×	body	320	valid
22.0ms	421×	body	80	valid
14.0ms	120×	body	160	valid

Details

sample233.0ms

simplify93.0ms

prune3.0ms

localize15.0ms

rewrite23.0ms

series162.0ms

simplify44.0ms

prune301.0ms

localize28.0ms

rewrite53.0ms

series1.4s

simplify44.0ms

prune587.0ms

localize5.0ms

rewrite12.0ms

series10.0ms

simplify65.0ms

prune35.0ms

localize10.0ms

rewrite360.0ms

series107.0ms

simplify100.0ms

prune468.0ms

regimes75.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.7s

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