Details

sample59.0ms

Algorithm

intervals

Results

23.0ms	84×	body	1280	valid
8.0ms	49×	body	640	valid
7.0ms	186×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

simplify591.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize6.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (exp (* a x)) 1.0)

rewrite22.0ms

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:

21.0ms

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

series64.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

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

simplify830.0ms

Counts: 17 → 17

prune87.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* x (+ a (* (* (/ 1 2) (pow a 2)) x)))
6.0b	(* (* (/ 1 2) (pow a 2)) x)
12.6b	(+ (* x (+ a (* (* (/ 1 2) (pow a 2)) x))) (/ (* (pow a 3) (pow x 3)) 6))
14.7b	(* (pow a 3) (pow x 3))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

18.0ms	(* x (+ a (* (* (/ 1 2) (pow a 2)) x)))
78.0ms	(* (* (/ 1 2) (pow a 2)) x)
21.0ms	(+ (* x (+ a (* (* (/ 1 2) (pow a 2)) x))) (/ (* (pow a 3) (pow x 3)) 6))
33.0ms	(* (pow a 3) (pow x 3))

series348.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* x (+ a (* (* (/ 1 2) (pow a 2)) x)))
36.0ms	(* (* (/ 1 2) (pow a 2)) x)
134.0ms	(+ (* x (+ a (* (* (/ 1 2) (pow a 2)) x))) (/ (* (pow a 3) (pow x 3)) 6))
87.0ms	(* (pow a 3) (pow x 3))

simplify2.2s

Counts: 138 → 138

prune559.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
0.5b	(* x (+ a (* (* (/ 1 2) (pow a 2)) x)))
6.0b	(* (* (/ 1 2) (pow a 2)) x)
12.6b	(+ (* x (+ a (* (* (/ 1 2) (pow a 2)) x))) (/ (pow (* a x) 3) 6))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

13.0ms	(pow (* a x) 3)
25.0ms	(* x (+ a (* (* (/ 1 2) (pow a 2)) x)))
58.0ms	(* (* (/ 1 2) (pow a 2)) x)
38.0ms	(+ (* x (+ a (* (* (/ 1 2) (pow a 2)) x))) (/ (pow (* a x) 3) 6))

series382.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (* a x) 3)
107.0ms	(* x (+ a (* (* (/ 1 2) (pow a 2)) x)))
47.0ms	(* (* (/ 1 2) (pow a 2)) x)
161.0ms	(+ (* x (+ a (* (* (/ 1 2) (pow a 2)) x))) (/ (pow (* a x) 3) 6))

simplify1.5s

Counts: 101 → 101

prune371.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 2)
0.2b	(pow (* a x) 3)
5.4b	(+ (* a x) (/ (pow (* a x) 2) 2))
12.6b	(+ (+ (* a x) (/ (pow (* a x) 2) 2)) (/ (pow (* a x) 3) 6))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

7.0ms	(pow (* a x) 2)
7.0ms	(pow (* a x) 3)
33.0ms	(+ (* a x) (/ (pow (* a x) 2) 2))
178.0ms	(+ (+ (* a x) (/ (pow (* a x) 2) 2)) (/ (pow (* a x) 3) 6))

series290.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (* a x) 2)
49.0ms	(pow (* a x) 3)
75.0ms	(+ (* a x) (/ (pow (* a x) 2) 2))
131.0ms	(+ (+ (* a x) (/ (pow (* a x) 2) 2)) (/ (pow (* a x) 3) 6))

simplify1.0s

Counts: 79 → 79

prune238.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch53.0ms

Steps

Iters	Range		Point
11	-2847.8168594635854	-1.1490692009393396e-20	-0.00019349601127565674

simplify912.0ms

end0.0ms

sample2.4s

Algorithm

intervals

Results

850.0ms	2746×	body	1280	valid
779.0ms	5371×	body	80	valid
241.0ms	1330×	body	640	valid
91.0ms	749×	body	320	valid
30.0ms	367×	body	160	valid