Details

sample83.0ms

Algorithm

intervals

Results

41.0ms	76×	body	10240	exit
17.0ms	270×	body	80	valid
3.0ms	8×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`log-prod` `*-un-lft-identity`
4×	`add-sqr-sqrt` `log-div` `associate--l+` `add-cube-cbrt`
3×	`pow1` `add-exp-log` `add-log-exp`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

2 → 33

Calls

2 calls:

9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
4.0ms	(log (+ 1.0 (exp x)))

series208.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (log (+ 1.0 (exp x))) (* x y))
128.0ms	(log (+ 1.0 (exp x)))

simplify3.5s

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
4	4203
3	1272
2	432
1	181
0	83

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(sqrt (+ 1.0 (exp x)))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 (exp x)))
10.0ms	(sqrt (+ 1.0 (exp x)))
10.0ms	(log (sqrt (+ 1.0 (exp x))))
10.0ms	(log (sqrt (+ 1.0 (exp x))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ 1.0 (exp x)))
58.0ms	(sqrt (+ 1.0 (exp x)))
160.0ms	(log (sqrt (+ 1.0 (exp x))))
156.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	5008
4	3753
3	1118
2	416
1	165
0	86

prune341.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2)))
0.0b	(* (+ 0.5 (* 0.25 x)) x)
0.0b	(- (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x)) (* x y))
4.2b	(+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-log-exp`
9×	`add-sqr-sqrt`
7×	`sum-log` `*-un-lft-identity` `flip3-+` `add-cube-cbrt` `flip-+`
6×	`pow1` `add-cbrt-cube` `associate-*l/` `add-exp-log`
4×	`associate-+l+` `frac-add`
3×	`log-prod` `diff-log` `associate-r` `associate-l`
2×	`+-commutative`
1×	`sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

12.0ms	(+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2)))
23.0ms	(* (+ 0.5 (* 0.25 x)) x)
156.0ms	(- (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x)) (* x y))
49.0ms	(+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))

series507.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2)))
81.0ms	(* (+ 0.5 (* 0.25 x)) x)
59.0ms	(- (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x)) (* x y))
37.0ms	(+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))

simplify1.8s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	1810
1	449
0	150

prune428.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 0.5 (* 0.25 x)) x)
0.8b	(exp (log (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))))
4.2b	(+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))
5.1b	(log (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

16×	`flip3-+` `flip-+`
14×	`associate-*l/`
12×	`log-div` `frac-add`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-log-exp`
7×	`add-exp-log`
6×	`log-prod` `add-cbrt-cube` `exp-diff`
4×	`exp-prod`
3×	`sum-log` `associate-r` `associate-l` `exp-sum`
2×	`log-pow`
1×	`+-commutative` `associate-+l+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 76

Calls

4 calls:

22.0ms	(* (+ 0.5 (* 0.25 x)) x)
27.0ms	(exp (log (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))))
38.0ms	(+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))
30.0ms	(log (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (+ 0.5 (* 0.25 x)) x)
35.0ms	(exp (log (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))))
47.0ms	(+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x))
145.0ms	(log (+ (+ (log 2.0) (* (/ x 2.0) (* (/ x 2.0) -1/2))) (* (+ 0.5 (* 0.25 x)) x)))

simplify2.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1905
1	515
0	194

prune577.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes72.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.6s	2404×	body	10240	exit
589.0ms	8473×	body	80	valid
372.0ms	98×	body	160	valid
129.0ms	129×	body	1280	valid
119.0ms	239×	body	640	valid
41.0ms	178×	body	320	valid