Details

sample75.0ms

Algorithm

intervals

Results

29.0ms	86×	body	1280	valid
12.0ms	179×	body	80	valid
9.0ms	43×	body	640	valid
4.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify567.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
3.9b	(- (exp (* a x)) 1.0)

rewrite33.0ms

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:

8.0ms	(exp (* a x))
24.0ms	(- (exp (* a x)) 1.0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(exp (* a x))
61.0ms	(- (exp (* a x)) 1.0)

simplify609.0ms

Counts: 30 → 30

prune127.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize32.0ms

Local error

Found 4 expressions with local error:

1.7b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.2b	(* (* 1/2 (pow a 2)) x)
11.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
19.2b	(* (pow a 3) (pow x 3))

rewrite141.0ms

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:

21.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
46.0ms	(* (* 1/2 (pow a 2)) x)
39.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
32.0ms	(* (pow a 3) (pow x 3))

series332.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
26.0ms	(* (* 1/2 (pow a 2)) x)
121.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
90.0ms	(* (pow a 3) (pow x 3))

simplify2.0s

Counts: 125 → 125

prune468.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
1.7b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
9.2b	(* (* 1/2 (pow a 2)) x)
11.1b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite101.0ms

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:

8.0ms	(pow (* a x) 3)
20.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
37.0ms	(* (* 1/2 (pow a 2)) x)
31.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(pow (* a x) 3)
77.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
23.0ms	(* (* 1/2 (pow a 2)) x)
139.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify1.4s

Counts: 88 → 88

prune304.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 2)
0.2b	(pow (* a x) 3)
4.8b	(+ (* a x) (* 1/2 (pow (* a x) 2)))
11.1b	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite103.0ms

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) 2)
6.0ms	(pow (* a x) 3)
15.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
74.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (* a x) 2)
85.0ms	(pow (* a x) 3)
100.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
148.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify1.1s

Counts: 76 → 76

prune213.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes306.0ms

Accuracy

98.6% (0.3b remaining)

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

bsearch1.0ms

simplify1.3s

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2694×	body	1280	valid
284.0ms	5524×	body	80	valid
283.0ms	1340×	body	640	valid
91.0ms	730×	body	320	valid
30.0ms	371×	body	160	valid