Details

analyze1.8s

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

sample203.0ms

Algorithm

intervals

Results

87.0ms	81×	body	2560	valid
60.0ms	111×	body	1280	valid
11.0ms	34×	body	640	valid
9.0ms	23×	body	1280	overflowed
6.0ms	320×	pre	80	true
4.0ms	7×	body	2560	overflowed
4.0ms	15×	body	640	overflowed
3.0ms	14×	body	320	valid
1.0ms	6×	body	320	overflowed
1.0ms	12×	body	80	valid
1.0ms	12×	body	80	overflowed
1.0ms	4×	body	160	valid
0.0ms	1×	body	160	overflowed

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5021	24

prune13.0ms

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: 60.6b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b	(- (exp (* a eps)) 1.0)
3.3b	(- (exp (* b eps)) 1.0)
4.6b	(- (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×	`associate-r/` `associate-l/`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 71

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))
7.0ms	(- (exp (* a eps)) 1.0)
9.0ms	(- (exp (* b eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4967	1144
1	4967	1144

prune140.0ms

Filtered

70 candidates to 83 candidates (-18.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	80	5	85

Merged error: 49.8b

Counts

85 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* a eps)) 1.0)
4.1b	(* b (* 1/6 (pow eps 3)))
4.6b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1` `add-sqr-sqrt`
10×	`*-un-lft-identity` `prod-exp`
8×	`add-log-exp`
6×	`add-cube-cbrt` `cbrt-unprod`
4×	`associate-r` `associate-l` `pow-prod-down`
2×	`sub-neg` `flip3--` `diff-log` `associate-r/` `-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `flip3-+` `pow-exp` `flip-+` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

3.0ms	(- (exp (* a eps)) 1.0)
6.0ms	(* b (* 1/6 (pow eps 3)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(* b (* 1/6 (pow eps 3)))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4969	956
1	4969	956

prune145.0ms

Filtered

55 candidates to 80 candidates (-45.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 49.1b

Counts

85 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (exp (* a eps)) 1.0)
4.6b	(- (exp (* (+ a b) eps)) 1.0)
5.4b	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
6.8b	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/`
8×	`add-log-exp`
6×	`add-cube-cbrt` `associate-l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-r` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
13.0ms	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
11.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
16.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

simplify26.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5037	1402

prune130.0ms

Filtered

61 candidates to 99 candidates (-62.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Merged error: 49.1b

Counts

106 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (pow (exp a) eps) 1.0) (+ (* b eps) (* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))))))
4.6b	(- (exp (* (+ a b) eps)) 1.0)
5.4b	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
6.8b	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
27×	`pow1`
20×	`prod-exp` `cbrt-unprod`
16×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
14×	`associate-*r/`
8×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/`
6×	`add-cube-cbrt` `associate-l` `add-log-exp`
5×	`flip3--` `flip3-+` `flip--` `flip-+`
4×	`cbrt-undiv` `frac-times` `div-exp`
2×	`associate-r` `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 → 105

Calls

4 calls:

14.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (pow (exp a) eps) 1.0) (+ (* b eps) (* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
13.0ms	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
11.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

series681.0ms

Counts

4 → 12

Calls

4 calls:

635.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (pow (exp a) eps) 1.0) (+ (* b eps) (* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))))))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
15.0ms	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
18.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4975	2668
1	4975	2668

prune149.0ms

Filtered

73 candidates to 117 candidates (-60.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	115	9	124

Merged error: 28.0b

Counts

124 → 9

regimes231.0ms

Accuracy

20.5% (6.8b remaining)

Error of 31.7b against oracle of 24.9b and baseline of 33.5b

bsearch368.0ms

Steps

Iters	Range		Point
5	-3.2024604074188695e+105	-8.740980225602877e+104	-8.908678098616857e+104

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	46
1	46	46

end0.0ms

analyze1.6s

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

sample6.1s

Algorithm

intervals

Results

2.7s	2560×	body	2560	valid
1.9s	3420×	body	1280	valid
350.0ms	1060×	body	640	valid
270.0ms	660×	body	1280	overflowed
193.0ms	9701×	pre	80	true
98.0ms	156×	body	2560	overflowed
96.0ms	354×	body	640	overflowed
82.0ms	373×	body	320	valid
35.0ms	178×	body	320	overflowed
31.0ms	444×	body	80	valid
21.0ms	143×	body	160	valid
16.0ms	117×	body	160	overflowed
16.0ms	236×	body	80	overflowed

Details

analyze1.8s

sample203.0ms

simplify26.0ms

prune13.0ms

localize16.0ms

rewrite22.0ms

series42.0ms

simplify45.0ms

prune140.0ms

localize26.0ms

rewrite25.0ms

series55.0ms

simplify46.0ms

prune145.0ms

localize23.0ms

rewrite34.0ms

series53.0ms

simplify26.0ms

prune130.0ms

localize23.0ms

rewrite47.0ms

series681.0ms

simplify43.0ms

prune149.0ms

regimes231.0ms

bsearch368.0ms

simplify1.0ms

end0.0ms

analyze1.6s

sample6.1s

Profiling