Details

sample117.0ms

Algorithm

intervals

Results

62.0ms	72×	body	1280	valid
27.0ms	65×	body	640	valid
5.0ms	23×	body	320	valid
3.0ms	78×	body	80	valid
3.0ms	91×	body	80	nan
2.0ms	18×	body	160	valid

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: 42.1b

localize5.0ms

Local error

Found 1 expressions with local error:

5.4b	(log (+ 1.0 x))

rewrite8.0ms

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:

7.0ms

(log (+ 1.0 x))

series79.0ms

Counts

1 → 3

Calls

1 calls:

79.0ms

(log (+ 1.0 x))

simplify5.6s

Counts

20 → 20

Iterations

Useful iterations: done (5.6s)

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

prune78.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

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:

0.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify1.2s

Counts

13 → 13

Iterations

Useful iterations: 4 (274.0ms)

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

prune82.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (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))))
10.5b	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
10.5b	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
10.5b	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))

rewrite25.0ms

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:

17.0ms	(* (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))))
2.0ms	(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)))
2.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (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))))
288.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
332.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))
297.0ms	(cbrt (fma x (fma (/ -1/2 (* 1.0 1.0)) x 1.0) (log 1.0)))

simplify2.5s

Counts

93 → 93

Iterations

Useful iterations: done (2.5s)

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

prune426.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b	(- (log (+ (pow 1.0 3) (pow x 3))) (log (fma 1.0 1.0 (* x (- x 1.0)))))
13.9b	(log (+ (pow 1.0 3) (pow x 3)))
15.6b	(log (fma 1.0 1.0 (* x (- x 1.0))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
24×	`log-prod`
18×	`pow1` `add-sqr-sqrt`
16×	`add-cube-cbrt` `prod-diff`
15×	`log-pow`
10×	`distribute-lft-out`
9×	`associate--l+`
8×	`unpow-prod-down` `cube-prod`
5×	`add-exp-log`
4×	`log-div` `fma-neg` `distribute-lft-out--`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `associate--r+` `add-log-exp`
2×	`associate--l-` `flip3-+` `rem-log-exp` `sum-cubes` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

3 → 89

Calls

3 calls:

34.0ms	(- (log (+ (pow 1.0 3) (pow x 3))) (log (fma 1.0 1.0 (* x (- x 1.0)))))
32.0ms	(log (+ (pow 1.0 3) (pow x 3)))
3.0ms	(log (fma 1.0 1.0 (* x (- x 1.0))))

series647.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(- (log (+ (pow 1.0 3) (pow x 3))) (log (fma 1.0 1.0 (* x (- x 1.0)))))
356.0ms	(log (+ (pow 1.0 3) (pow x 3)))
98.0ms	(log (fma 1.0 1.0 (* x (- x 1.0))))

simplify3.1s

Counts

98 → 98

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	177	2730
1	421	2202
2	1178	1872
3	4321	1622
done	5000	1619

prune339.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes132.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	44
1	29	44
done	29	44

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	2311×	body	1280	valid
510.0ms	1637×	body	640	valid
133.0ms	815×	body	320	valid
124.0ms	2707×	body	80	nan
103.0ms	2794×	body	80	valid
41.0ms	443×	body	160	valid