Details

sample119.0ms

Algorithm

intervals

Results

66.0ms	79×	body	10240	exit
22.0ms	278×	body	80	valid
4.0ms	8×	body	640	valid
2.0ms	1×	body	1280	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.6b	(log (+ 1.0 (exp x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

8.0ms	(+ 1.0 (exp x))
6.0ms	(log (+ 1.0 (exp x)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(+ 1.0 (exp x))
100.0ms	(log (+ 1.0 (exp x)))

simplify1.2s

Counts

33 → 33

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	61	292
1	132	279
2	381	257
3	1493	255
done	5001	253

prune136.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (+ 1.0 (exp x)))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
30×	`pow1`
29×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`swap-sqr`
10×	`sqrt-pow1` `pow1/2`
9×	`log-pow`
7×	`add-exp-log` `associate-r` `associate-l`
6×	`add-cbrt-cube`
5×	`pow-prod-up`
4×	`log-prod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `log-div`
1×	`pow2` `flip3-+` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

19.0ms	(log (+ 1.0 (exp x)))
3.0ms	(sqrt (log (+ 1.0 (exp x))))
3.0ms	(sqrt (log (+ 1.0 (exp x))))
31.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log (+ 1.0 (exp x)))
149.0ms	(sqrt (log (+ 1.0 (exp x))))
123.0ms	(sqrt (log (+ 1.0 (exp x))))
82.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

simplify1.4s

Counts

109 → 109

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	116	1483
1	256	1028
2	893	944
done	5000	913

prune363.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))))
0.7b	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x)))))))
1.3b	(log (sqrt (+ 1.0 (exp x))))
1.3b	(log (sqrt (+ 1.0 (exp x))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

68×	`sqrt-prod`
51×	`log-pow`
46×	`pow1`
37×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
29×	`associate-r`
21×	`add-cube-cbrt`
20×	`distribute-rgt-out`
18×	`distribute-lft-out`
17×	`sqrt-pow1` `pow1/2`
14×	`log-prod`
8×	`add-exp-log` `sqrt-div`
7×	`associate-l`
6×	`add-cbrt-cube`
4×	`log-div` `distribute-lft1-in` `flip3-+` `distribute-rgt1-in` `flip-+` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`count-2` `associate-*r/` `rem-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

30.0ms	(sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))))
57.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x)))))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

308.0ms	(sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))))
609.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x)))))))
105.0ms	(log (sqrt (+ 1.0 (exp x))))
146.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify969.0ms

Counts

146 → 146

Iterations

Useful iterations: done (963.0ms)

Iter	Nodes	Cost
0	239	2784
1	514	2102
2	1933	1982
done	5002	1975

prune484.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(* 1/2 (pow x 2))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
5.6b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

22.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
12.0ms	(* 1/2 (pow x 2))
24.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
18.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
33.0ms	(* 1/2 (pow x 2))
19.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
55.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify896.0ms

Counts

83 → 83

Iterations

Useful iterations: done (892.0ms)

Iter	Nodes	Cost
0	152	1207
1	384	1091
2	1492	1009
done	5001	999

prune239.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	17	25
done	17	25

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.1s	2539×	body	10240	exit
666.0ms	8426×	body	80	valid
105.0ms	273×	body	640	valid
91.0ms	128×	body	1280	valid
40.0ms	171×	body	320	valid
15.0ms	107×	body	160	valid