Details

sample98.0ms

Algorithm

intervals

Results

50.0ms	72×	body	10240	exit
18.0ms	278×	body	80	valid
4.0ms	8×	body	640	valid
2.0ms	7×	body	320	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
1.2b	(log (+ 1.0 (exp x)))

rewrite35.0ms

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:

13.0ms	(+ 1.0 (exp x))
14.0ms	(- (log (+ 1.0 (exp x))) (* x y))
6.0ms	(log (+ 1.0 (exp x)))

series230.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1.0 (exp x))
97.0ms	(- (log (+ 1.0 (exp x))) (* x y))
114.0ms	(log (+ 1.0 (exp x)))

simplify2.4s

Counts

54 → 54

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	92	575
1	208	544
2	499	514
3	1195	508
4	2600	506
done	5000	506

prune169.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
1.2b	(log (+ (pow 1.0 3) (pow (exp x) 3)))
4.6b	(- (exp x) 1.0)
5.8b	(log (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `log-prod`
10×	`add-cube-cbrt`
7×	`pow1` `unpow-prod-down` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`add-cbrt-cube` `distribute-lft-out`
4×	`log-div` `pow-pow`
3×	`pow-unpow` `exp-prod`
2×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `sum-cubes` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

5.0ms	(pow (exp x) 3)
22.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
18.0ms	(- (exp x) 1.0)
25.0ms	(log (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (exp x) 3)
126.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
26.0ms	(- (exp x) 1.0)
157.0ms	(log (+ (* (exp x) (- (exp x) 1.0)) (* 1.0 1.0)))

simplify1.1s

Counts

86 → 86

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	163	1025
1	343	918
2	1005	841
done	5000	828

prune410.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1.0 (exp x)))
0.2b	(sqrt (+ 1.0 (exp x)))
1.7b	(log (sqrt (+ 1.0 (exp x))))
1.7b	(log (sqrt (+ 1.0 (exp x))))

rewrite60.0ms

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-+` `pow1/2` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

18.0ms	(sqrt (+ 1.0 (exp x)))
18.0ms	(sqrt (+ 1.0 (exp x)))
13.0ms	(log (sqrt (+ 1.0 (exp x))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ 1.0 (exp x)))
58.0ms	(sqrt (+ 1.0 (exp x)))
177.0ms	(log (sqrt (+ 1.0 (exp x))))
154.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify2.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (276.0ms)

Iter	Nodes	Cost
0	86	910
1	163	834
2	359	780
3	963	754
4	3837	754
done	5000	754

prune348.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1.0 (exp x)))
0.7b	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
1.7b	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
1.7b	(log (sqrt (+ 1.0 (exp x))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

90×	`sqrt-prod`
66×	`sqrt-pow1`
54×	`pow1`
52×	`sqrt-div`
50×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
34×	`pow1/2`
25×	`log-pow`
19×	`add-cube-cbrt`
18×	`swap-sqr` `pow-prod-up`
14×	`flip3-+` `flip-+`
10×	`add-exp-log` `log-div` `associate-r` `associate-l` `pow-prod-down` `pow-sqr`
9×	`unswap-sqr`
8×	`frac-times` `log-prod` `distribute-lft-out`
6×	`add-cbrt-cube`
4×	`associate-r/` `associate-l/` `add-log-exp`
3×	`rem-log-exp`
2×	`pow2` `pow-plus` `prod-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 164

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (exp x)))
84.0ms	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
31.0ms	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ 1.0 (exp x)))
42.0ms	(* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x)))))
130.0ms	(log (* (sqrt (sqrt (+ 1.0 (exp x)))) (sqrt (sqrt (+ 1.0 (exp x))))))
165.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.7s

Counts

176 → 176

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	181	2839
1	315	1812
2	746	1710
3	2140	1662
done	5000	1642

prune603.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes56.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	21	26
done	21	26

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.7s	2339×	body	10240	exit
1.0s	8438×	body	80	valid
95.0ms	246×	body	640	valid
82.0ms	112×	body	1280	valid
46.0ms	193×	body	320	valid
13.0ms	89×	body	160	valid