Details

sample119.0ms

Algorithm

intervals

Results

60.0ms	66×	body	1280	valid
27.0ms	65×	body	640	valid
7.0ms	31×	body	320	valid
4.0ms	83×	body	80	valid
3.0ms	91×	body	80	nan
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4
done	5	4

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize8.0ms

Local error

Found 1 expressions with local error:

3.8b	(log (+ 1.0 x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`expm1-log1p-u` `flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

10.0ms

(log (+ 1.0 x))

series86.0ms

Counts

1 → 3

Calls

1 calls:

86.0ms

(log (+ 1.0 x))

simplify1.6s

Counts

20 → 20

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	60	188
1	133	177
2	429	159
3	1678	158
done	5000	154

prune79.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))

series78.0ms

Counts

1 → 3

Calls

1 calls:

78.0ms

(fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))

simplify567.0ms

Counts

13 → 13

Iterations

Useful iterations: done (566.0ms)

Iter	Nodes	Cost
0	25	225
1	45	222
2	148	194
3	640	191
done	5001	188

prune71.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
3.6b	(log (sqrt (+ 1.0 x)))
3.6b	(log (sqrt (+ 1.0 x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-def`

Counts

4 → 82

Calls

4 calls:

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

series371.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (+ 1.0 x))
52.0ms	(sqrt (+ 1.0 x))
119.0ms	(log (sqrt (+ 1.0 x)))
146.0ms	(log (sqrt (+ 1.0 x)))

simplify2.2s

Counts

94 → 94

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	93	896
1	192	816
2	668	738
3	3524	730
done	5000	730

prune366.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (sqrt (+ 1.0 x)))
3.8b	(log (sqrt (fma 1.0 1.0 (* x (- x 1.0)))))
8.1b	(log (hypot (pow 1.0 3/2) (pow x 3/2)))
9.8b	(sqrt (fma 1.0 1.0 (* x (- x 1.0))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `sqrt-prod`
7×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `rem-log-exp`
2×	`log-div` `sqrt-div`
1×	`rem-sqrt-square` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

6.0ms	(log (sqrt (+ 1.0 x)))
8.0ms	(log (sqrt (fma 1.0 1.0 (* x (- x 1.0)))))
1.0ms	(log (hypot (pow 1.0 3/2) (pow x 3/2)))
2.0ms	(sqrt (fma 1.0 1.0 (* x (- x 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

108.0ms	(log (sqrt (+ 1.0 x)))
147.0ms	(log (sqrt (fma 1.0 1.0 (* x (- x 1.0)))))
1.2s	(log (hypot (pow 1.0 3/2) (pow x 3/2)))
85.0ms	(sqrt (fma 1.0 1.0 (* x (- x 1.0))))

simplify712.0ms

Counts

82 → 82

Iterations

Useful iterations: done (710.0ms)

Iter	Nodes	Cost
0	173	1056
1	344	991
2	1066	885
done	5000	881

prune452.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes75.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.0b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	18	31
done	18	31

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	2183×	body	1280	valid
595.0ms	1738×	body	640	valid
170.0ms	812×	body	320	valid
139.0ms	2863×	body	80	valid
69.0ms	2641×	body	80	nan
40.0ms	404×	body	160	valid