Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	82×	body	1280	valid
4.0ms	48×	body	640	valid
3.0ms	175×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	26	6
4	49	6
5	107	6
6	246	6
7	702	6
8	2429	6
done	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series49.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
37.0ms	(- (exp (* a x)) 1.0)

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	53	263
1	116	248
2	312	232
3	1006	228
4	4632	226
done	5000	226

prune69.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
5.7b	(* (* 1/6 (pow a 3)) x)
6.7b	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
8.6b	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
10.0ms	(* (* 1/6 (pow a 3)) x)
12.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
3.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

series313.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
26.0ms	(* (* 1/6 (pow a 3)) x)
125.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
63.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

simplify856.0ms

Counts

86 → 86

Iterations

Useful iterations: done (854.0ms)

Iter	Nodes	Cost
0	137	1638
1	404	1524
2	1696	1362
done	5000	1360

prune220.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

localize9.0ms

Local error

Found 2 expressions with local error:

4.4b	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
15.5b	(* (pow a 2) (pow x 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`add-exp-log` `unpow-prod-down`
10×	`unpow2` `sqr-pow`
9×	`prod-exp`
8×	`associate-r` `associate-l`
6×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow1`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 62

Calls

2 calls:

9.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
9.0ms	(* (pow a 2) (pow x 2))

series97.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
35.0ms	(* (pow a 2) (pow x 2))

simplify843.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	101	872
1	258	768
2	1153	596
done	5001	596

prune117.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* a x))
4.4b	(+ (* 1/2 (* a (* x (* a x)))) (* a x))
4.6b	(* a (* x (* a x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 50

Calls

3 calls:

6.0ms	(* x (* a x))
42.0ms	(+ (* 1/2 (* a (* x (* a x)))) (* a x))
15.0ms	(* a (* x (* a x)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(* x (* a x))
60.0ms	(+ (* 1/2 (* a (* x (* a x)))) (* a x))
31.0ms	(* a (* x (* a x)))

simplify2.8s

Counts

59 → 59

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	79	683
1	227	651
2	906	523
3	4119	475
done	5000	475

prune86.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.9b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	34
1	27	34
done	27	34

end0.0ms

sample932.0ms

Algorithm

intervals

Results

427.0ms	2638×	body	1280	valid
136.0ms	1335×	body	640	valid
105.0ms	5515×	body	80	valid
49.0ms	743×	body	320	valid
19.0ms	440×	body	160	valid