Details

sample116.0ms

Algorithm

intervals

Results

62.0ms	73×	body	1280	valid
23.0ms	57×	body	640	valid
6.0ms	28×	body	320	valid
3.0ms	74×	body	80	valid
3.0ms	24×	body	160	valid
3.0ms	90×	body	80	nan

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: 42.5b

localize8.0ms

Local error

Found 1 expressions with local error:

6.5b	(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))

series72.0ms

Counts

1 → 3

Calls

1 calls:

72.0ms

(log (+ 1.0 x))

simplify5.7s

Counts

20 → 20

Iterations

Useful iterations: done (5.7s)

Iter	Nodes	Cost
0	60	188
1	132	177
2	293	159
3	601	158
4	1413	151
5	3597	149
done	5001	147

prune105.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 1 expressions with local error:

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

series71.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

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

simplify1.0s

Counts

13 → 13

Iterations

Useful iterations: 4 (278.0ms)

Iter	Nodes	Cost
0	25	202
1	45	199
2	103	175
3	276	172
4	918	169
done	5000	169

prune86.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0))) (cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0))))
7.8b	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
7.8b	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
7.8b	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

12.0ms	(* (cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0))) (cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0))))
1.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
1.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
2.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

351.0ms	(* (cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0))) (cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0))))
314.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
387.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
309.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))

simplify2.4s

Counts

93 → 93

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	179	3098
1	446	2888
2	1307	2698
3	4365	2120
done	5000	2115

prune549.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
6.6b	(log (sqrt (+ 1.0 x)))
6.6b	(log (sqrt (+ 1.0 x)))

rewrite31.0ms

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)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 1.0 x))
53.0ms	(sqrt (+ 1.0 x))
123.0ms	(log (sqrt (+ 1.0 x)))
115.0ms	(log (sqrt (+ 1.0 x)))

simplify3.1s

Counts

94 → 94

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	93	896
1	188	816
2	420	738
3	1015	730
4	4040	708
done	5000	700

prune344.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes96.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	36
1	23	36
done	23	36

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	2227×	body	1280	valid
540.0ms	1661×	body	640	valid
180.0ms	843×	body	320	valid
93.0ms	2807×	body	80	valid
61.0ms	2659×	body	80	nan
43.0ms	462×	body	160	valid