Details

sample85.0ms

Algorithm

intervals

Results

50.0ms	83×	body	1280	valid
13.0ms	45×	body	640	valid
3.0ms	24×	body	320	valid
3.0ms	84×	body	80	valid
2.0ms	20×	body	160	valid
2.0ms	80×	body	80	nan

simplify3.0ms

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: 40.5b

localize8.0ms

Local error

Found 1 expressions with local error:

5.8b	(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×	`flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

10.0ms

(log (+ 1.0 x))

series71.0ms

Counts

1 → 3

Calls

1 calls:

71.0ms

(log (+ 1.0 x))

simplify881.0ms

Counts

18 → 18

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	58	178
1	123	171
2	378	151
3	1338	151
done	5000	146

prune61.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
70×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 126

Calls

2 calls:

88.0ms	(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
70.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

series131.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
75.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

simplify2.0s

Counts

132 → 132

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	268	1979
1	761	1743
2	3668	1459
done	5000	1455

prune441.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite423.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-div`
30×	`associate-*r/`
26×	`frac-sub`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
16×	`frac-times`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`flip3--` `flip3-+` `flip--` `flip-+`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`associate-*l/` `add-cbrt-cube` `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 → 109

Calls

4 calls:

307.0ms	(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
47.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
24.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
39.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
312.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
292.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
287.0ms	(cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.8s

Counts

121 → 121

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	255	6502
1	645	6058
2	2603	5818
done	5001	5455

prune664.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

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))

rewrite17.0ms

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` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (log (+ 1.0 x)))
5.0ms	(log (+ 1.0 x))
5.0ms	(log (+ 1.0 x))
5.0ms	(log (+ 1.0 x))

series379.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (log (+ 1.0 x)))
57.0ms	(log (+ 1.0 x))
56.0ms	(log (+ 1.0 x))
57.0ms	(log (+ 1.0 x))

simplify566.0ms

Counts

69 → 69

Iterations

Useful iterations: done (563.0ms)

Iter	Nodes	Cost
0	123	824
1	308	785
2	1066	701
done	5000	650

prune243.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes129.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	21	26
done	21	26

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	2322×	body	1280	valid
520.0ms	1687×	body	640	valid
164.0ms	811×	body	320	valid
91.0ms	2687×	body	80	nan
90.0ms	2740×	body	80	valid
82.0ms	440×	body	160	valid