Details

sample78.0ms

Algorithm

intervals

Results

39.0ms	99×	body	1280	valid
10.0ms	36×	body	640	valid
10.0ms	166×	body	80	valid
4.0ms	21×	body	320	valid
2.0ms	13×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5011
7	1930
6	441
5	156
4	64
3	32
2	20
1	14
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize8.0ms

Local error

Found 1 expressions with local error:

4.3b	(- (exp (* a x)) 1)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
4×	`*-un-lft-identity`
3×	`add-log-exp`
2×	`difference-of-squares`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `difference-of-sqr-1` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--`

Counts

1 → 17

Calls

1 calls:

15.0ms

(- (exp (* a x)) 1)

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(- (exp (* a x)) 1)

simplify2.8s

Counts

20 → 20

Iterations

Iter	Nodes
done	5007
4	3741
3	1136
2	321
1	113
0	48

prune123.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (* x a) (* x a)) (* x a)) 1/6)
0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* (* x a) 1/2))
12.8b	(+ (* (* (* (* x a) (* x a)) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))

rewrite807.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
90×	`add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down`
65×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`associate-l` `*-commutative`
2×	`pow-plus`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 122

Calls

4 calls:

343.0ms	(* (* (* (* x a) (* x a)) (* x a)) 1/6)
22.0ms	(* (* x a) (* x a))
71.0ms	(* (* x a) (* (* x a) 1/2))
367.0ms	(+ (* (* (* (* x a) (* x a)) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (* (* (* x a) (* x a)) (* x a)) 1/6)
39.0ms	(* (* x a) (* x a))
53.0ms	(* (* x a) (* (* x a) 1/2))
192.0ms	(+ (* (* (* (* x a) (* x a)) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))

simplify2.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5009
2	2553
1	515
0	161

prune338.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* (* x a) 1/2))
2.4b	(log (exp (* (* x a) (* x a))))
12.8b	(+ (* (* (log (exp (* (* x a) (* x a)))) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

65×	`pow1`
37×	`add-cbrt-cube` `add-exp-log`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
7×	`add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`log-prod` `log-pow`
2×	`pow-plus` `associate-r` `associate-l` `*-commutative`
1×	`pow2` `+-commutative` `exp-prod` `sum-log` `flip3-+` `exp-to-pow` `swap-sqr` `rem-log-exp` `flip-+`

Counts

4 → 91

Calls

4 calls:

34.0ms	(* (* x a) (* x a))
68.0ms	(* (* x a) (* (* x a) 1/2))
11.0ms	(log (exp (* (* x a) (* x a))))
76.0ms	(+ (* (* (log (exp (* (* x a) (* x a)))) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x a) (* x a))
48.0ms	(* (* x a) (* (* x a) 1/2))
54.0ms	(log (exp (* (* x a) (* x a))))
173.0ms	(+ (* (* (log (exp (* (* x a) (* x a)))) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))

simplify2.1s

Counts

103 → 103

Iterations

Iter	Nodes
done	5009
2	1718
1	374
0	122

prune382.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* x a)) 1)
0.0b	(/ (- (exp (* (* 3 x) a)) 1) (+ 1 (* (exp (* x a)) (+ (exp (* x a)) 1))))
0.2b	(* (* 3 x) a)
4.3b	(- (exp (* (* 3 x) a)) 1)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`difference-of-squares`
9×	`pow1`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-l` `*-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

17.0ms	(+ (exp (* x a)) 1)
46.0ms	(/ (- (exp (* (* 3 x) a)) 1) (+ 1 (* (exp (* x a)) (+ (exp (* x a)) 1))))
14.0ms	(* (* 3 x) a)
24.0ms	(- (exp (* (* 3 x) a)) 1)

series189.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (exp (* x a)) 1)
95.0ms	(/ (- (exp (* (* 3 x) a)) 1) (+ 1 (* (exp (* x a)) (+ (exp (* x a)) 1))))
19.0ms	(* (* 3 x) a)
55.0ms	(- (exp (* (* 3 x) a)) 1)

simplify1.8s

Counts

110 → 110

Iterations

Iter	Nodes
done	5006
2	1833
1	487
0	183

prune509.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

36.9% (13.6b remaining)

Error of 13.7b against oracle of 0.1b and baseline of 21.7b

bsearch183.0ms

Steps

Iters	Range		Point
4	3.73373204307318e+54	5.3335735992532233e+54	4.1836874807488166e+54
8	-3.5498477693853334e+107	-1.65227804131582e+103	-5.0289586708105234e+104

simplify20.0ms

Iterations

Iter	Nodes
done	59
1	59
0	38

end1.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	2702×	body	1280	valid
427.0ms	5541×	body	80	valid
355.0ms	1244×	body	640	valid
138.0ms	788×	body	320	valid
45.0ms	387×	body	160	valid