Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

sample225.0ms

Algorithm

intervals

Results

86.0ms	81×	body	2560	valid
59.0ms	109×	body	1280	valid
45.0ms	47×	body	5120	exit
9.0ms	28×	body	640	valid
6.0ms	303×	pre	80	true
3.0ms	12×	body	320	valid
1.0ms	22×	body	80	valid
1.0ms	4×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune14.0ms

Filtered

1 candidates to 1 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: 58.1b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (pow (exp a) eps) 1.0)
0.5b	(pow (exp a) eps)
1.2b	(pow (exp b) eps)
1.5b	(pow (exp (+ a b)) eps)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt` `pow-pow`
11×	`unpow-prod-down`
10×	`exp-prod`
9×	`pow-unpow`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `exp-sum` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 77

Calls

4 calls:

5.0ms	(- (pow (exp a) eps) 1.0)
3.0ms	(pow (exp a) eps)
3.0ms	(pow (exp b) eps)
7.0ms	(pow (exp (+ a b)) eps)

series41.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (pow (exp a) eps) 1.0)
9.0ms	(pow (exp a) eps)
9.0ms	(pow (exp b) eps)
13.0ms	(pow (exp (+ a b)) eps)

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	645
1	4981	645

prune113.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Merged error: 51.0b

Counts

91 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (exp b) eps)
1.5b	(pow (exp (+ a b)) eps)
2.9b	(* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))
4.5b	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `associate-r`
23×	`add-exp-log` `add-cbrt-cube`
20×	`*-un-lft-identity`
17×	`associate-*r/`
14×	`add-cube-cbrt`
13×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`unpow-prod-down` `pow-pow`
8×	`frac-times` `associate-/r/`
7×	`exp-prod` `times-frac`
6×	`pow-unpow` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
4×	`associate-l` `pow-prod-down` `associate-*l/` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `div-exp`
2×	`pow-to-exp` `sub-neg` `pow-exp` `*-commutative` `distribute-lft-out--`
1×	`distribute-rgt-in` `distribute-lft-in` `exp-sum` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

3.0ms	(pow (exp b) eps)
5.0ms	(pow (exp (+ a b)) eps)
14.0ms	(* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))
24.0ms	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (exp b) eps)
12.0ms	(pow (exp (+ a b)) eps)
30.0ms	(* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))
454.0ms	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4976	2738
1	4976	2738

prune297.0ms

Filtered

92 candidates to 127 candidates (-38.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	125	6	131

Merged error: 45.3b

Counts

131 → 6

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (pow (exp (+ a b)) eps) 1.0)
1.2b	(pow (exp b) eps)
1.5b	(pow (exp (+ a b)) eps)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt` `pow-pow`
8×	`unpow-prod-down`
7×	`exp-prod`
6×	`pow-unpow`
5×	`pow1` `add-log-exp`
3×	`add-exp-log` `add-cbrt-cube` `difference-of-squares` `sqr-pow`
2×	`pow-to-exp` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `exp-sum` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 57

Calls

3 calls:

8.0ms	(- (pow (exp (+ a b)) eps) 1.0)
3.0ms	(pow (exp b) eps)
6.0ms	(pow (exp (+ a b)) eps)

series42.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(- (pow (exp (+ a b)) eps) 1.0)
9.0ms	(pow (exp b) eps)
13.0ms	(pow (exp (+ a b)) eps)

simplify65.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4913	553
1	4913	553

prune124.0ms

Filtered

41 candidates to 66 candidates (-61.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	65	7	72

Merged error: 45.3b

Counts

72 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))
4.6b	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))))
4.6b	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* eps (* (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))) (- (pow (exp b) eps) 1.0)))))
4.6b	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* eps (* (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))) (- (pow (exp b) eps) 1.0)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
36×	`associate-*r/`
31×	`add-sqr-sqrt`
24×	`associate-/r/`
21×	`times-frac`
19×	`*-un-lft-identity`
16×	`frac-times`
12×	`flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
11×	`add-cube-cbrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r`
4×	`unpow-prod-down` `distribute-lft-out--` `add-log-exp` `sqr-pow`
3×	`cbrt-div` `pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv`
2×	`sub-neg`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 116

Calls

4 calls:

14.0ms	(* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))
19.0ms	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))))
21.0ms	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* eps (* (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))) (- (pow (exp b) eps) 1.0)))))
20.0ms	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* eps (* (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))) (- (pow (exp b) eps) 1.0)))))

series48.1s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))
15.4s	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* (* eps (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))) (- (pow (exp b) eps) 1.0))))
16.4s	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* eps (* (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))) (- (pow (exp b) eps) 1.0)))))
16.3s	(cbrt (/ (- (pow (exp (+ a b)) eps) 1.0) (* eps (* (+ a (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))) (- (pow (exp b) eps) 1.0)))))

simplify96.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5481	17459

prune2.1s

Filtered

118 candidates to 128 candidates (-8.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	128	7	135

Merged error: 45.3b

Counts

135 → 7

regimes318.0ms

Accuracy

68.1% (1.2b remaining)

Error of 47.5b against oracle of 46.3b and baseline of 50.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	110
1	73	110

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2589×	body	2560	valid
1.8s	3461×	body	1280	valid
1.5s	1601×	body	5120	exit
320.0ms	1023×	body	640	valid
192.0ms	9603×	pre	80	true
71.0ms	333×	body	320	valid
30.0ms	468×	body	80	valid
17.0ms	126×	body	160	valid
1.0ms	2×	body	2560	invalid

Details

analyze1.7s

sample225.0ms

simplify40.0ms

prune14.0ms

localize17.0ms

rewrite21.0ms

series41.0ms

simplify53.0ms

prune113.0ms

localize22.0ms

rewrite50.0ms

series506.0ms

simplify57.0ms

prune297.0ms

localize19.0ms

rewrite18.0ms

series42.0ms

simplify65.0ms

prune124.0ms

localize30.0ms

rewrite79.0ms

series48.1s

simplify96.0ms

prune2.1s

regimes318.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.8s

Profiling