Details

sample191.0ms

Algorithm

intervals

Results

68.0ms	74×	body	2560	valid
61.0ms	120×	body	1280	valid
10.0ms	33×	body	640	valid
7.0ms	18×	body	1280	overflowed
6.0ms	316×	pre	80	true
6.0ms	8×	body	320	overflowed
3.0ms	10×	body	640	overflowed
2.0ms	4×	body	2560	overflowed
2.0ms	8×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	16×	body	80	overflowed
1.0ms	5×	body	160	valid
1.0ms	4×	body	160	overflowed

simplify896.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	240	24
4	663	24
5	3008	24
done	5000	24

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: 60.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.8b	(- (exp (* a eps)) 1.0)
2.5b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite26.0ms

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:

11.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series45.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
8.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(- (exp (* b eps)) 1.0)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify401.0ms

Counts

88 → 88

Iterations

Useful iterations: done (399.0ms)

Iter	Nodes	Cost
0	143	1364
1	350	1327
2	1374	1197
done	5000	1190

prune134.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 47.0b

Counts

89 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* (+ a b) eps)) 1.0)
2.7b	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))
4.2b	(* (* 1/6 (pow eps 3)) b)
11.6b	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`pow1`
12×	`*-un-lft-identity`
11×	`prod-exp`
9×	`associate-r`
8×	`add-cube-cbrt`
7×	`associate-l` `cbrt-unprod`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`frac-times` `flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+`
3×	`*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp`

Counts

4 → 86

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
18.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))
7.0ms	(* (* 1/6 (pow eps 3)) b)
15.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (exp (* (+ a b) eps)) 1.0)
63.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))
5.0ms	(* (* 1/6 (pow eps 3)) b)
23.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

simplify979.0ms

Counts

98 → 98

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	217	2550
1	684	2437
2	3553	2116
done	5000	2109

prune270.0ms

Filtered

68 candidates to 98 candidates (-44.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Merged error: 46.8b

Counts

101 → 7

localize38.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))
20.1b	(cbrt (* b (+ (* b (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) eps)))
20.1b	(cbrt (* b (+ (* b (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) eps)))
20.1b	(cbrt (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `cbrt-div` `-un-lft-identity` `associate-r/`
5×	`cbrt-prod`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

12.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))
14.0ms	(cbrt (* b (+ (* b (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) eps)))
12.0ms	(cbrt (* b (+ (* b (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) eps)))
11.0ms	(cbrt (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))
67.0ms	(cbrt (* b (+ (* b (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) eps)))
70.0ms	(cbrt (* b (+ (* b (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) eps)))
63.0ms	(cbrt (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))

simplify608.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	162	2445
1	467	2326
2	1924	2051
done	5001	2051

prune450.0ms

Filtered

61 candidates to 70 candidates (-14.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	70	7	77

Merged error: 46.8b

Counts

77 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* (+ a b) eps)) 1.0)
2.7b	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))
4.2b	(* (* 1/6 (pow eps 3)) b)
11.6b	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`pow1`
12×	`*-un-lft-identity`
11×	`prod-exp`
9×	`associate-r`
8×	`add-cube-cbrt`
7×	`associate-l` `cbrt-unprod`
6×	`add-log-exp`
5×	`pow-prod-down`
4×	`frac-times` `flip3--` `flip3-+` `associate-*r/` `flip--` `flip-+`
3×	`*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp`

Counts

4 → 86

Calls

4 calls:

5.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))
7.0ms	(* (* 1/6 (pow eps 3)) b)
12.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (exp (* (+ a b) eps)) 1.0)
64.0ms	(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2)))) (* b eps)))
5.0ms	(* (* 1/6 (pow eps 3)) b)
23.0ms	(* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (pow eps 2))))

simplify986.0ms

Counts

98 → 98

Iterations

Useful iterations: done (982.0ms)

Iter	Nodes	Cost
0	217	2550
1	684	2437
2	3553	2116
done	5000	2109

prune257.0ms

Filtered

68 candidates to 98 candidates (-44.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Merged error: 46.8b

Counts

105 → 8

regimes511.0ms

Accuracy

52.4% (4.0b remaining)

Error of 52.4b against oracle of 48.4b and baseline of 56.8b

bsearch142.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	14848.343200454	0.11914520210130385
5	-1.5116149063123207e+67	-5.390869519443976e+66	-8.689142308994358e+66

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	171
1	84	171
done	84	171

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.3s	2563×	body	2560	valid
1.8s	3421×	body	1280	valid
353.0ms	1070×	body	640	valid
303.0ms	729×	body	1280	overflowed
203.0ms	10079×	pre	80	true
107.0ms	368×	body	640	overflowed
95.0ms	159×	body	2560	overflowed
77.0ms	332×	body	320	valid
39.0ms	549×	body	80	overflowed
38.0ms	185×	body	320	overflowed
35.0ms	480×	body	80	valid
20.0ms	137×	body	160	valid
12.0ms	86×	body	160	overflowed

Details

sample191.0ms

simplify896.0ms

prune4.0ms

localize25.0ms

rewrite26.0ms

series45.0ms

simplify401.0ms

prune134.0ms

localize27.0ms

rewrite47.0ms

series106.0ms

simplify979.0ms

prune270.0ms

localize38.0ms

rewrite50.0ms

series223.0ms

simplify608.0ms

prune450.0ms

localize29.0ms

rewrite48.0ms

series107.0ms

simplify986.0ms

prune257.0ms

regimes511.0ms

bsearch142.0ms

simplify6.0ms

end0.0ms

sample5.9s

Profiling