Details

sample128.0ms

Algorithm

intervals

Results

67.0ms	74×	body	10240	exit
23.0ms	277×	body	80	valid
4.0ms	8×	body	640	valid
3.0ms	2×	body	1280	valid
2.0ms	6×	body	320	valid
0.0ms	2×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.6b	(log (+ 1.0 (exp x)))

rewrite74.0ms

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:

35.0ms	(+ 1.0 (exp x))
25.0ms	(- (log (+ 1.0 (exp x))) (* x y))
12.0ms	(log (+ 1.0 (exp x)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ 1.0 (exp x))
127.0ms	(- (log (+ 1.0 (exp x))) (* x y))
122.0ms	(log (+ 1.0 (exp x)))

simplify2.5s

Counts

54 → 54

Iterations

Useful iterations: 3 (926.0ms)

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

prune363.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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

rewrite221.0ms

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:

13.0ms	(+ 1.0 (exp x))
176.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
14.0ms	(log (sqrt (+ 1.0 (exp x))))
14.0ms	(log (sqrt (+ 1.0 (exp x))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ 1.0 (exp x))
279.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
191.0ms	(log (sqrt (+ 1.0 (exp x))))
209.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify956.0ms

Counts

82 → 82

Iterations

Useful iterations: done (952.0ms)

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

prune554.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.0b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

37.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
39.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
32.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series246.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
131.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
84.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify903.0ms

Counts

53 → 53

Iterations

Useful iterations: done (900.0ms)

Iter	Nodes	Cost
0	110	975
1	298	912
2	1171	833
done	5001	824

prune363.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

1.2b	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
8.0b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
8.0b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
8.0b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log`
6×	`log-div`
4×	`cbrt-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
1×	`pow1/3`

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
31.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
31.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
40.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
94.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
91.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
95.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify1.6s

Counts

66 → 66

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	136	1421
1	367	1354
2	1396	1197
done	5000	1145

prune613.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes143.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.5s	2497×	body	10240	exit
911.0ms	8411×	body	80	valid
190.0ms	111×	body	1280	valid
151.0ms	299×	body	640	valid
56.0ms	188×	body	320	valid
21.0ms	112×	body	160	valid