Details

sample116.0ms

Algorithm

intervals

Results

66.0ms	92×	body	10240	exit
20.0ms	272×	body	80	valid
4.0ms	4×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	19	9
done	19	9

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.8b	(log (+ 1.0 (exp x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

12.0ms	(- (log (+ 1.0 (exp x))) (* x y))
12.0ms	(+ 1.0 (exp x))
11.0ms	(log (+ 1.0 (exp x)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(- (log (+ 1.0 (exp x))) (* x y))
13.0ms	(+ 1.0 (exp x))
90.0ms	(log (+ 1.0 (exp x)))

simplify2.5s

Counts

54 → 54

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	92	575
1	208	544
2	499	514
3	1201	508
4	2613	506
done	5000	506

prune178.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(exp (log (log (+ 1.0 (exp x)))))
0.0b	(log (log (+ 1.0 (exp x))))
0.8b	(log (+ 1.0 (exp x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `*-un-lft-identity`
9×	`pow1`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-exp-log` `add-log-exp`
5×	`log-pow`
4×	`exp-prod` `exp-sum` `add-cbrt-cube`
2×	`log-div` `flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`+-commutative` `sum-log` `rem-exp-log`

Counts

4 → 56

Calls

4 calls:

11.0ms	(+ 1.0 (exp x))
7.0ms	(exp (log (log (+ 1.0 (exp x)))))
2.0ms	(log (log (+ 1.0 (exp x))))
10.0ms	(log (+ 1.0 (exp x)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
119.0ms	(exp (log (log (+ 1.0 (exp x)))))
201.0ms	(log (log (+ 1.0 (exp x))))
89.0ms	(log (+ 1.0 (exp x)))

simplify3.1s

Counts

68 → 68

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	102	673
1	202	616
2	464	558
3	1239	548
4	3859	531
done	5000	531

prune331.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (+ (log (log 2.0)) (* 0.5 (/ x (log 2.0)))) (* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))))
0.2b	(* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))
0.2b	(/ (pow x 2) (log 2.0))
0.2b	(/ x (log 2.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
65×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
51×	`add-cube-cbrt`
36×	`associate-l`
28×	`unpow-prod-down`
27×	`pow1`
21×	`add-exp-log` `log-pow`
13×	`add-cbrt-cube`
11×	`associate-/l*`
10×	`unpow2` `sqr-pow`
9×	`add-log-exp`
8×	`associate-/r*`
7×	`div-exp`
6×	`associate-r`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `exp-prod` `distribute-lft-in` `exp-sum` `associate--l+` `div-inv` `rem-exp-log`
2×	`frac-times` `pow-to-exp` `flip3--` `frac-2neg` `diff-log` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `distribute-lft-out--`
1×	`exp-diff` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `distribute-lft-out` `difference-of-squares`

Counts

4 → 179

Calls

4 calls:

151.0ms	(exp (- (+ (log (log 2.0)) (* 0.5 (/ x (log 2.0)))) (* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))))
1.0s	(* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))
11.0ms	(/ (pow x 2) (log 2.0))
6.0ms	(/ x (log 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

382.0ms	(exp (- (+ (log (log 2.0)) (* 0.5 (/ x (log 2.0)))) (* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))))
660.0ms	(* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25))
260.0ms	(/ (pow x 2) (log 2.0))
349.0ms	(/ x (log 2.0))

simplify1.9s

Counts

191 → 191

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	250	3460
1	586	3323
2	2015	2977
done	5000	2966

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.5b	(log (sqrt (+ 1.0 (exp x))))
1.5b	(log (sqrt (+ 1.0 (exp x))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

12.0ms	(+ 1.0 (exp x))
14.0ms	(+ 1.0 (exp x))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
18.0ms	(log (sqrt (+ 1.0 (exp x))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp x))
13.0ms	(+ 1.0 (exp x))
172.0ms	(log (sqrt (+ 1.0 (exp x))))
169.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify2.0s

Counts

76 → 76

Iterations

Useful iterations: 3 (190.0ms)

Iter	Nodes	Cost
0	80	764
1	156	720
2	327	656
3	732	644
4	2329	644
done	5001	644

prune287.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.4b

regimes59.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	12	11
done	12	11

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.1s	2410×	body	10240	exit
607.0ms	8459×	body	80	valid
99.0ms	255×	body	640	valid
98.0ms	136×	body	1280	valid
58.0ms	99×	body	160	valid
44.0ms	178×	body	320	valid