Details

sample121.0ms

Algorithm

intervals

Results

73.0ms	83×	body	1280	valid
19.0ms	45×	body	640	valid
5.0ms	24×	body	320	valid
4.0ms	84×	body	80	valid
3.0ms	80×	body	80	nan
3.0ms	20×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize4.0ms

Local error

Found 1 expressions with local error:

5.8b	(log (+ 1.0 x))

rewrite5.0ms

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:

5.0ms

(log (+ 1.0 x))

series62.0ms

Counts

1 → 3

Calls

1 calls:

62.0ms

(log (+ 1.0 x))

simplify1.7s

Counts

20 → 20

Iterations

Useful iterations: done (1.7s)

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

prune74.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

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:

0.0ms

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

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

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

simplify504.0ms

Counts

13 → 13

Iterations

Useful iterations: done (503.0ms)

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

prune63.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) (cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))))
9.4b	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
9.4b	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
9.4b	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

rewrite30.0ms

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:

21.0ms	(* (cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) (cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))))
2.0ms	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
2.0ms	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
2.0ms	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

340.0ms	(* (cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))) (cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))))
309.0ms	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
326.0ms	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
326.0ms	(cbrt (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	179	3398
1	479	3172
2	1840	2954
done	5001	2454

prune608.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (log (+ 1.0 x)))
5.8b	(log (+ 1.0 x))
5.8b	(log (+ 1.0 x))
5.8b	(log (+ 1.0 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt (log (+ 1.0 x)))
6.0ms	(log (+ 1.0 x))
9.0ms	(log (+ 1.0 x))
9.0ms	(log (+ 1.0 x))

series334.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt (log (+ 1.0 x)))
53.0ms	(log (+ 1.0 x))
44.0ms	(log (+ 1.0 x))
48.0ms	(log (+ 1.0 x))

simplify763.0ms

Counts

77 → 77

Iterations

Useful iterations: done (760.0ms)

Iter	Nodes	Cost
0	127	866
1	324	811
2	1113	731
done	5000	683

prune269.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes164.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 21.1b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	24
1	16	24
done	16	24

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	2322×	body	1280	valid
528.0ms	1687×	body	640	valid
134.0ms	2740×	body	80	valid
122.0ms	811×	body	320	valid
61.0ms	2687×	body	80	nan
40.0ms	440×	body	160	valid