Details

sample226.0ms

Algorithm

intervals

Results

71.0ms	77×	body	2560	valid
62.0ms	119×	body	1280	valid
55.0ms	68×	body	10240	exit
10.0ms	34×	body	640	valid
8.0ms	324×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	10×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	239	24
4	653	24
5	2845	24
done	5001	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
4.8b	(- (exp (* b eps)) 1.0)
6.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite40.0ms

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:

25.0ms	(* (- (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)

series175.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
40.0ms	(- (exp (* a eps)) 1.0)
34.0ms	(- (exp (* b eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify542.0ms

Counts

88 → 88

Iterations

Useful iterations: done (540.0ms)

Iter	Nodes	Cost
0	143	1364
1	345	1326
2	1271	1196
done	5000	1190

prune338.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.8b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* a eps)) 1.0)
2.8b	(* (* 1/6 (pow eps 3)) b)
6.0b	(- (exp (* (+ a b) eps)) 1.0)
16.3b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`associate-l`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `associate-r`
4×	`unpow-prod-down` `cbrt-unprod` `unswap-sqr`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-exp` `-commutative` `flip--` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+`

Counts

4 → 78

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
10.0ms	(* (* 1/6 (pow eps 3)) b)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
14.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
216.0ms	(* (* 1/6 (pow eps 3)) b)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
127.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify1.0s

Counts

90 → 90

Iterations

Useful iterations: 2 (417.0ms)

Iter	Nodes	Cost
0	173	1423
1	471	1336
2	1978	1195
done	5000	1195

prune437.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 49.2b

localize26.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (* 1/6 (pow eps 3)) b)
5.9b	(* b (* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))))
6.0b	(- (exp (* (+ a b) eps)) 1.0)
7.8b	(* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

11.0ms	(* (* 1/6 (pow eps 3)) b)
15.0ms	(* b (* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (* 1/6 (pow eps 3)) b)
124.0ms	(* b (* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
123.0ms	(* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify857.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	157	1557
1	421	1477
2	1678	1259
done	5000	1259

prune399.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 49.2b

localize33.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (* 1/6 (pow eps 3)) b)
5.9b	(* b (* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))))
6.0b	(- (exp (* (+ a b) eps)) 1.0)
7.8b	(* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

10.0ms	(* (* 1/6 (pow eps 3)) b)
15.0ms	(* b (* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 1/6 (pow eps 3)) b)
125.0ms	(* b (* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b))))
49.0ms	(- (exp (* (+ a b) eps)) 1.0)
119.0ms	(* b (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify861.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	157	1557
1	421	1477
2	1678	1259
done	5000	1259

prune419.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 49.2b

regimes220.0ms

Accuracy

56.8% (3.4b remaining)

Error of 52.4b against oracle of 49.0b and baseline of 56.8b

bsearch321.0ms

Steps

Iters	Range		Point
11	3.9777289923527025e+45	6.762908678833405e+72	6.364568599760148e+46
5	-2.350670412092924e+26	-9.509086209243448e+25	-2.132327481851413e+26

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	48	125
1	71	87
done	71	87

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2599×	body	2560	valid
1.8s	2102×	body	10240	exit
1.7s	3417×	body	1280	valid
287.0ms	1057×	body	640	valid
174.0ms	10105×	pre	80	true
67.0ms	360×	body	320	valid
23.0ms	439×	body	80	valid
15.0ms	131×	body	160	valid