Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	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

simplify2.1s

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	2426	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)

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

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

simplify1.0s

Counts

17 → 17

Iterations

Useful iterations: 4 (306.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	297	167
3	715	165
4	2060	163
done	5000	163

prune48.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

2.1b	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
4.6b	(* (* 1/6 (pow a 3)) x)
5.4b	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
10.7b	(+ (* 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)
11.0ms	(* 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))

series305.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* x (+ a (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))))
26.0ms	(* (* 1/6 (pow a 3)) x)
119.0ms	(* 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))

simplify713.0ms

Counts

86 → 86

Iterations

Useful iterations: done (711.0ms)

Iter	Nodes	Cost
0	137	1638
1	404	1524
2	1697	1362
done	5001	1360

prune224.0ms

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))

rewrite21.0ms

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:

10.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
9.0ms	(* (pow a 2) (pow x 2))

series94.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(+ (* 1/2 (* (pow a 2) (pow x 2))) (* a x))
35.0ms	(* (pow a 2) (pow x 2))

simplify724.0ms

Counts

68 → 68

Iterations

Useful iterations: 2 (220.0ms)

Iter	Nodes	Cost
0	101	872
1	258	768
2	1153	596
done	5000	596

prune120.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* a x))
3.8b	(* (pow a (/ 2 2)) (* x (* a x)))
4.0b	(+ (* 1/2 (* (pow a (/ 2 2)) (* x (* a x)))) (* a x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

8.0ms	(* x (* a x))
17.0ms	(* (pow a (/ 2 2)) (* x (* a x)))
40.0ms	(+ (* 1/2 (* (pow a (/ 2 2)) (* x (* a x)))) (* a x))

series111.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(* x (* a x))
36.0ms	(* (pow a (/ 2 2)) (* x (* a x)))
59.0ms	(+ (* 1/2 (* (pow a (/ 2 2)) (* x (* a x)))) (* a x))

simplify3.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (765.0ms)

Iter	Nodes	Cost
0	98	970
1	282	794
2	1012	597
3	4877	538
done	5000	538

prune122.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.8b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	40
1	28	40
done	28	40

end0.0ms

sample936.0ms

Algorithm

intervals

Results

425.0ms	2708×	body	1280	valid
126.0ms	1309×	body	640	valid
111.0ms	5401×	body	80	valid
48.0ms	756×	body	320	valid
21.0ms	409×	body	160	valid