Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	85×	body	1280	valid
6.0ms	49×	body	640	valid
5.0ms	195×	body	80	valid
2.0ms	31×	body	320	valid
1.0ms	10×	body	160	valid

simplify52.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.4b	(- (exp (* a x)) 1.0)

rewrite18.0ms

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:

4.0ms	(exp (* a x))
13.0ms	(- (exp (* a x)) 1.0)

series63.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
49.0ms	(- (exp (* a x)) 1.0)

simplify35.0ms

Counts: 30 → 30

prune74.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.8b

localize18.0ms

Local error

Found 4 expressions with local error:

2.2b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.3b	(* (* 1/2 (pow a 2)) x)
9.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
18.8b	(* (pow a 3) (pow x 3))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `cube-mult` `associate-+l+` `distribute-lft-in` `flip3-+` `unpow3` `associate-*r/` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 113

Calls

4 calls:

19.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
24.0ms	(* (* 1/2 (pow a 2)) x)
20.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
27.0ms	(* (pow a 3) (pow x 3))

series255.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
27.0ms	(* (* 1/2 (pow a 2)) x)
103.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
64.0ms	(* (pow a 3) (pow x 3))

simplify96.0ms

Counts: 125 → 125

prune330.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* a x) 3)
2.2b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.3b	(* (* 1/2 (pow a 2)) x)
9.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`prod-exp`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
5×	`cbrt-unprod`
4×	`associate-l`
3×	`pow-unpow` `pow-prod-down` `pow-exp`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `pow-pow` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `rem-cube-cbrt`
1×	`+-commutative` `cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sum-log` `unswap-sqr` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

6.0ms	(pow (* a x) 3)
22.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
24.0ms	(* (* 1/2 (pow a 2)) x)
17.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (* a x) 3)
66.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
25.0ms	(* (* 1/2 (pow a 2)) x)
106.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify75.0ms

Counts: 88 → 88

prune231.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* a x) 3)
0.3b	(pow (* a x) 2)
3.4b	(+ (* a x) (* 1/2 (pow (* a x) 2)))
9.1b	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
10×	`pow1` `add-exp-log`
7×	`add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`pow-pow` `pow-exp` `sum-log`
2×	`+-commutative` `pow-to-exp` `unpow-prod-down` `flip3-+` `pow-prod-down` `prod-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`cube-mult` `associate-+l+` `unpow3` `cube-prod` `cbrt-unprod` `unpow2`

Counts

4 → 64

Calls

4 calls:

6.0ms	(pow (* a x) 3)
6.0ms	(pow (* a x) 2)
9.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
41.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (* a x) 3)
28.0ms	(pow (* a x) 2)
65.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
107.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify60.0ms

Counts: 76 → 76

prune170.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes172.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.6b

bsearch31.0ms

Steps

Iters	Range		Point
10	-0.017184274846981436	-1.270469882958216e-12	-0.00017516040291641713

simplify1.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

547.0ms	2594×	body	1280	valid
530.0ms	5585×	body	80	valid
198.0ms	1341×	body	640	valid
65.0ms	782×	body	320	valid
24.0ms	421×	body	160	valid