Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	97×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	158×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	16×	body	160	valid

simplify4.7s

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	263	6
7	1146	6
8	4071	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize5.0ms

Local error

Found 1 expressions with local error:

3.5b	(- (exp (* a x)) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

4.0ms

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

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

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

simplify2.5s

Counts

17 → 17

Iterations

Useful iterations: 4 (500.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	303	167
3	995	165
4	4348	163
done	5000	163

prune48.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

localize14.0ms

Local error

Found 4 expressions with local error:

2.1b	(* x (+ (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))) a))
4.6b	(* (* 1/6 (pow a 3)) x)
5.4b	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
10.7b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

rewrite102.0ms

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:

46.0ms	(* x (+ (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))) a))
12.0ms	(* (* 1/6 (pow a 3)) x)
33.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
9.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* x (+ (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))) a))
33.0ms	(* (* 1/6 (pow a 3)) x)
158.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
69.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

simplify849.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	137	1638
1	413	1522
2	2069	1362
done	5001	1362

prune223.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.7b

localize9.0ms

Local error

Found 2 expressions with local error:

4.0b	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
14.3b	(* (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))

series96.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
32.0ms	(* (pow a 2) (pow x 2))

simplify851.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	101	872
1	260	768
2	1292	596
done	5000	596

prune118.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* (fabs a) (fabs x)) (* (fabs a) (fabs x)))
4.0b	(+ (* 1/2 (* (* (fabs a) (fabs x)) (* (fabs a) (fabs x)))) (* a x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
17×	`pow-prod-down`
14×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-plus`
1×	`+-commutative` `pow2` `flip3-+` `swap-sqr` `associate-r` `associate-l` `sum-log` `*-commutative` `flip-+`

Counts

2 → 45

Calls

2 calls:

10.0ms	(* (* (fabs a) (fabs x)) (* (fabs a) (fabs x)))
26.0ms	(+ (* 1/2 (* (* (fabs a) (fabs x)) (* (fabs a) (fabs x)))) (* a x))

series80.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* (* (fabs a) (fabs x)) (* (fabs a) (fabs x)))
59.0ms	(+ (* 1/2 (* (* (fabs a) (fabs x)) (* (fabs a) (fabs x)))) (* a x))

simplify475.0ms

Counts

51 → 51

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	67	813
1	205	666
2	959	526
done	5001	526

prune81.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.7b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	26	40
done	26	40

end0.0ms

sample919.0ms

Algorithm

intervals

Results

427.0ms	2708×	body	1280	valid
134.0ms	1309×	body	640	valid
106.0ms	5401×	body	80	valid
49.0ms	756×	body	320	valid
18.0ms	409×	body	160	valid