Details

sample80.0ms

Algorithm

intervals

Results

36.0ms	61×	body	10240	exit
15.0ms	260×	body	80	valid
6.0ms	9×	body	1280	valid
3.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	263
1	12	263
2	19	263
done	19	263

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.3b	(log (+ 1.0 (exp x)))

rewrite50.0ms

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` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

11.0ms	(+ 1.0 (exp x))
28.0ms	(- (log (+ 1.0 (exp x))) (* x y))
8.0ms	(log (+ 1.0 (exp x)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ 1.0 (exp x))
81.0ms	(- (log (+ 1.0 (exp x))) (* x y))
81.0ms	(log (+ 1.0 (exp x)))

simplify1.8s

Counts

54 → 54

Iterations

Useful iterations: 3 (730.0ms)

Iter	Nodes	Cost
0	92	16624
1	211	14578
2	648	14578
3	3089	14420
done	5000	14420

prune272.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
81.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
5.0ms	(log (sqrt (+ 1.0 (exp x))))
6.0ms	(log (sqrt (+ 1.0 (exp x))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (exp x))
168.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
109.0ms	(log (sqrt (+ 1.0 (exp x))))
144.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify970.0ms

Counts

82 → 82

Iterations

Useful iterations: done (955.0ms)

Iter	Nodes	Cost
0	122	31315
1	277	26863
2	964	25743
done	5000	25623

prune492.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
8.0ms	(+ 1.0 (exp x))
5.0ms	(log (sqrt (+ 1.0 (exp x))))
9.0ms	(log (sqrt (+ 1.0 (exp x))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (exp x))
9.0ms	(+ 1.0 (exp x))
139.0ms	(log (sqrt (+ 1.0 (exp x))))
140.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.2s

Counts

76 → 76

Iterations

Useful iterations: 3 (434.0ms)

Iter	Nodes	Cost
0	80	24698
1	156	21048
2	435	20968
3	1885	20732
done	5000	20732

prune355.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (* x x))
0.0b	(- (log (+ x (+ (* 1/2 (* x x)) 2.0))) (* x y))
5.8b	(log (+ x (+ (* 1/2 (* x x)) 2.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

14.0ms	(* 1/2 (* x x))
38.0ms	(- (log (+ x (+ (* 1/2 (* x x)) 2.0))) (* x y))
49.0ms	(log (+ x (+ (* 1/2 (* x x)) 2.0)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 1/2 (* x x))
86.0ms	(- (log (+ x (+ (* 1/2 (* x x)) 2.0))) (* x y))
59.0ms	(log (+ x (+ (* 1/2 (* x x)) 2.0)))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	127	19914
1	338	17135
2	1444	17053
done	5001	16892

prune274.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes109.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	343
1	12	343
done	12	343

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	2501×	body	10240	exit
857.0ms	8406×	body	80	valid
122.0ms	139×	body	1280	valid
97.0ms	264×	body	640	valid
45.0ms	202×	body	320	valid
14.0ms	104×	body	160	valid