Details

sample90.0ms

Algorithm

intervals

Results

49.0ms	69×	body	1280	valid
17.0ms	51×	body	640	valid
6.0ms	34×	body	320	valid
3.0ms	88×	body	80	valid
3.0ms	95×	body	80	nan
1.0ms	14×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	112
1	5	112
done	5	112

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize5.0ms

Local error

Found 1 expressions with local error:

3.7b	(log (+ 1.0 x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

4.0ms

(log (+ 1.0 x))

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(log (+ 1.0 x))

simplify1.2s

Counts

20 → 20

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	60	5878
1	131	4564
2	419	4337
3	1662	4312
done	5000	4161

prune90.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

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

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

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

simplify1.0s

Counts

13 → 13

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	25	4482
1	47	3894
2	144	3894
3	601	3849
done	5001	3729

prune69.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
2.5b	(log (- (* 1.0 1.0) (* x x)))
3.7b	(log (- 1.0 x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 87

Calls

3 calls:

14.0ms	(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
7.0ms	(log (- (* 1.0 1.0) (* x x)))
5.0ms	(log (- 1.0 x))

series361.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(- (log (- (* 1.0 1.0) (* x x))) (log (- 1.0 x)))
169.0ms	(log (- (* 1.0 1.0) (* x x)))
50.0ms	(log (- 1.0 x))

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	176	43999
1	449	36683
2	1962	31960
done	5002	31935

prune357.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 x (fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0)))))
0.0b	(fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0))))
0.1b	(* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0))
7.6b	(- (fma 1.0 x (fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0))))) (* 1.0 (* x x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
13×	`cbrt-undiv` `-un-lft-identity` `div-exp` `associate-r*` `add-cube-cbrt`
10×	`times-frac`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff` `pow-prod-down` `associate-*r/` `fma-udef`
2×	`pow2` `pow-sqr` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `associate--l+` `*-commutative` `div-inv` `flip--`

Counts

4 → 105

Calls

4 calls:

0.0ms	(fma 1.0 x (fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0)))))
0.0ms	(fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0))))
51.0ms	(* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0))
5.0ms	(- (fma 1.0 x (fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0))))) (* 1.0 (* x x)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma 1.0 x (fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0)))))
107.0ms	(fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0))))
56.0ms	(* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0))
62.0ms	(- (fma 1.0 x (fma (* (* (/ x 1.0) (/ x 1.0)) (/ x 1.0)) 1/3 (* 1/2 (* (/ x 1.0) (/ x 1.0))))) (* 1.0 (* x x)))

simplify2.1s

Counts

117 → 117

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	167	36289
1	486	29834
2	2830	27242
done	5000	25712

prune474.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes107.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 21.3b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	500
1	19	500
done	19	500

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	2308×	body	1280	valid
606.0ms	1644×	body	640	valid
156.0ms	806×	body	320	valid
95.0ms	2821×	body	80	valid
62.0ms	2729×	body	80	nan
40.0ms	421×	body	160	valid