Details

sample157.0ms

Algorithm

intervals

Results

96.0ms	96×	body	10240	exit
21.0ms	270×	body	80	valid
7.0ms	14×	body	640	valid
6.0ms	6×	body	1280	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify17.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.5b	(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` `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:

25.0ms	(- (log (+ 1.0 (exp x))) (* x y))
13.0ms	(+ 1.0 (exp x))
10.0ms	(log (+ 1.0 (exp x)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(- (log (+ 1.0 (exp x))) (* x y))
14.0ms	(+ 1.0 (exp x))
128.0ms	(log (+ 1.0 (exp x)))

simplify733.0ms

Counts: 54 → 54

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
7.0ms	(+ 1.0 (exp x))
7.0ms	(log (sqrt (+ 1.0 (exp x))))
12.0ms	(log (sqrt (+ 1.0 (exp x))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (exp x))
9.0ms	(+ 1.0 (exp x))
145.0ms	(log (sqrt (+ 1.0 (exp x))))
149.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.5s

Counts: 76 → 76

prune348.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
8.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite94.0ms

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:

24.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
41.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
28.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series213.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
29.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
77.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify2.1s

Counts: 53 → 53

prune233.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

1.3b	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
8.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
8.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
8.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite107.0ms

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:

1.0ms	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
19.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
46.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
39.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))
67.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
72.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))
68.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify686.0ms

Counts: 66 → 66

prune414.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes54.0ms

Accuracy

0.6% (0.8b remaining)

Error of 1.1b against oracle of 0.2b and baseline of 1.1b

bsearch0.0ms

simplify806.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.9s	2547×	body	10240	exit
731.0ms	8400×	body	80	valid
434.0ms	178×	body	320	valid
152.0ms	270×	body	640	valid
105.0ms	138×	body	1280	valid
17.0ms	110×	body	160	valid