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

sample210.0ms

Algorithm

intervals

Results

93.0ms	83×	body	2560	valid
61.0ms	101×	body	1280	valid
13.0ms	38×	body	640	valid
8.0ms	19×	body	1280	overflowed
6.0ms	307×	pre	80	true
5.0ms	17×	body	640	overflowed
4.0ms	6×	body	2560	overflowed
3.0ms	14×	body	320	valid
1.0ms	6×	body	320	overflowed
1.0ms	17×	body	80	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	160	overflowed
0.0ms	1×	body	80	overflowed

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	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: 59.4b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.3b	(- (exp (* a eps)) 1.0)
4.2b	(- (exp (* b eps)) 1.0)
6.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite24.0ms

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

series39.0ms

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

simplify35.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4887	1142
1	4887	1142

prune134.0ms

Filtered

70 candidates to 83 candidates (-18.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Merged error: 49.6b

Counts

85 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (exp (* a eps)) 1.0)
4.2b	(* b (* 1/6 (pow eps 3)))
6.3b	(- (exp (* (+ a b) eps)) 1.0)
13.3b	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

rewrite26.0ms

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:

4.0ms	(- (exp (* a eps)) 1.0)
6.0ms	(* b (* 1/6 (pow eps 3)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
11.0ms	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(* b (* 1/6 (pow eps 3)))
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (* b b) (+ (* b (* 1/6 (pow eps 3))) (* eps (* eps 1/2))))

simplify36.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5002	956

prune141.0ms

Filtered

55 candidates to 80 candidates (-45.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

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

Merged error: 49.2b

Counts

85 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (exp (* a eps)) 1.0)
3.7b	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
6.3b	(- (exp (* (+ a b) eps)) 1.0)
6.9b	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

rewrite36.0ms

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:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

simplify27.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5256	1418

prune127.0ms

Filtered

62 candidates to 99 candidates (-59.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	99	7	106

Merged error: 49.2b

Counts

106 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (* 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)))))))
4.2b	(* (- (pow (exp a) eps) 1.0) (+ (* b eps) (* b (* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2))))))
6.3b	(- (exp (* (+ a b) eps)) 1.0)
6.9b	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
15×	`pow1`
11×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
10×	`associate-r/` `associate-l*`
8×	`frac-times` `flip3--` `associate-/r/` `flip--`
7×	`add-cube-cbrt` `flip3-+` `pow-prod-down` `flip-+`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `difference-of-squares`
2×	`*-commutative` `associate-/l/` `distribute-lft-out--`
1×	`sub-neg` `unpow-prod-down` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

16.0ms	(/ (* 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)))))))
12.0ms	(* (- (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)
11.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

series706.0ms

Counts

4 → 12

Calls

4 calls:

613.0ms	(/ (* 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)))))))
63.0ms	(* (- (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)
17.0ms	(* b (* (* eps eps) (+ (* (* b 1/6) eps) 1/2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5103	3337

prune198.0ms

Filtered

86 candidates to 116 candidates (-34.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	5	116
Fresh	1	3	4
Picked	1	0	1
Done	1	1	2
Total	114	9	123

Merged error: 26.4b

Counts

123 → 9

regimes319.0ms

Accuracy

37.4% (5.6b remaining)

Error of 29.7b against oracle of 24.1b and baseline of 33.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	82
1	48	82

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.7s	2539×	body	2560	valid
1.9s	3424×	body	1280	valid
350.0ms	1074×	body	640	valid
283.0ms	673×	body	1280	overflowed
199.0ms	9736×	pre	80	true
112.0ms	166×	body	2560	overflowed
103.0ms	377×	body	640	overflowed
81.0ms	352×	body	320	valid
39.0ms	187×	body	320	overflowed
34.0ms	473×	body	80	valid
20.0ms	138×	body	160	valid
15.0ms	226×	body	80	overflowed
14.0ms	106×	body	160	overflowed
2.0ms	1×	body	2560	invalid

Details

analyze1.7s

sample210.0ms

simplify39.0ms

prune13.0ms

localize16.0ms

rewrite24.0ms

series39.0ms

simplify35.0ms

prune134.0ms

localize24.0ms

rewrite26.0ms

series52.0ms

simplify36.0ms

prune141.0ms

localize23.0ms

rewrite36.0ms

series51.0ms

simplify27.0ms

prune127.0ms

localize23.0ms

rewrite48.0ms

series706.0ms

simplify49.0ms

prune198.0ms

regimes319.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.1s

Profiling