Details

sample98.0ms

Algorithm

intervals

Results

56.0ms	74×	body	10240	exit
16.0ms	282×	body	80	valid
3.0ms	9×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

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)))

rewrite51.0ms

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))
24.0ms	(- (log (+ 1.0 (exp x))) (* x y))
12.0ms	(log (+ 1.0 (exp x)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1.0 (exp x))
106.0ms	(- (log (+ 1.0 (exp x))) (* x y))
121.0ms	(log (+ 1.0 (exp x)))

simplify1.7s

Counts

54 → 54

Iterations

Useful iterations: 3 (551.0ms)

Iter	Nodes	Cost
0	92	575
1	211	544
2	643	514
3	3055	508
done	5000	508

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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))))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

6.0ms	(+ 1.0 (exp x))
403.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
7.0ms	(log (sqrt (+ 1.0 (exp x))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (exp x))
193.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
104.0ms	(log (sqrt (+ 1.0 (exp x))))
116.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify533.0ms

Counts

82 → 82

Iterations

Useful iterations: done (529.0ms)

Iter	Nodes	Cost
0	122	1143
1	277	988
2	985	853
done	5001	845

prune442.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.6b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite105.0ms

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:

12.0ms	(* 1/2 (pow x 2))
27.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
35.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
28.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* 1/2 (pow x 2))
25.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
121.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
98.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify861.0ms

Counts

83 → 83

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	152	1207
1	385	1093
2	1465	1009
done	5002	999

prune292.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2))))
6.6b	(log (+ (* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2)))) (+ x 2.0)))
26.8b	(sqrt (* 1/2 (pow x 2)))
26.8b	(sqrt (* 1/2 (pow x 2)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

68.0ms	(* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2))))
99.0ms	(log (+ (* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2)))) (+ x 2.0)))
10.0ms	(sqrt (* 1/2 (pow x 2)))
9.0ms	(sqrt (* 1/2 (pow x 2)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2))))
186.0ms	(log (+ (* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2)))) (+ x 2.0)))
46.0ms	(sqrt (* 1/2 (pow x 2)))
52.0ms	(sqrt (* 1/2 (pow x 2)))

simplify864.0ms

Counts

84 → 84

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	116	1304
1	306	811
2	1404	696
done	5000	682

prune291.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes76.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
done	12	17

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	2535×	body	10240	exit
729.0ms	8360×	body	80	valid
500.0ms	249×	body	640	valid
96.0ms	127×	body	1280	valid
64.0ms	189×	body	320	valid
16.0ms	108×	body	160	valid