Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	45×	body	1280	valid
9.0ms	48×	body	640	valid
7.0ms	137×	body	80	valid
2.0ms	12×	body	320	valid
1.0ms	14×	body	160	valid

simplify161.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

12.0ms	(/ x (+ x 1.0))
28.0ms	(/ (+ x 1.0) (- x 1.0))
195.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series294.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ x (+ x 1.0))
43.0ms	(/ (+ x 1.0) (- x 1.0))
208.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.5s

Counts

605 → 605

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune557.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(exp (/ x (+ x 1.0)))
3.7b	(log (exp (/ x (+ x 1.0))))
3.9b	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

1091×	`*-un-lft-identity`
809×	`times-frac`
687×	`add-sqr-sqrt`
572×	`prod-diff`
533×	`log-pow`
522×	`exp-prod`
496×	`add-cube-cbrt`
203×	`distribute-lft-out`
104×	`associate-/r/`
95×	`distribute-lft-out--` `difference-of-squares`
52×	`div-inv`
33×	`pow1`
30×	`flip3-+` `flip-+`
24×	`flip3--` `flip--`
22×	`fma-neg`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate--l+`
2×	`associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 722

Calls

4 calls:

27.0ms	(/ (+ x 1.0) (- x 1.0))
39.0ms	(exp (/ x (+ x 1.0)))
27.0ms	(log (exp (/ x (+ x 1.0))))
379.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (+ x 1.0) (- x 1.0))
77.0ms	(exp (/ x (+ x 1.0)))
49.0ms	(log (exp (/ x (+ x 1.0))))
146.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify2.7s

Counts

734 → 734

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	621	42672
1	1359	37238
2	2949	26623
done	5000	19606

prune698.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
16.8b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
46×	`associate-*r/`
42×	`add-sqr-sqrt`
37×	`prod-diff`
36×	`add-cube-cbrt` `flip3-+` `flip-+`
32×	`frac-sub`
28×	`frac-times`
24×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`
22×	`associate--l+`
18×	`associate-/l/`
14×	`associate-*l/`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-r`
8×	`associate-l` `associate-/r/`
7×	`distribute-lft-out`
6×	`swap-sqr` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `associate--r+` `unswap-sqr`
1×	`pow2` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 201

Calls

4 calls:

62.0ms	(* (+ x 1.0) (- x 1.0))
60.0ms	(* (+ x 1.0) (+ x 1.0))
107.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
38.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ x 1.0) (- x 1.0))
26.0ms	(* (+ x 1.0) (+ x 1.0))
99.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- x 1.0)))
61.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify3.2s

Counts

213 → 213

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	320	4818
1	976	4215
2	4807	3642
done	5000	3641

prune742.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) (- x 1.0))
0.1b	(fma 3.0 x 1.0)
12.3b	(/ (- (fma 3.0 x 1.0)) (* (+ x 1.0) (- x 1.0)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-exp-log` `times-frac` `add-cbrt-cube` `associate-/l*`
8×	`frac-times` `associate-/r/`
6×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `flip3-+` `flip--` `flip-+`
5×	`pow1` `associate-r`
4×	`associate-r/` `associate-l` `associate-l/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `neg-mul-1` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod`
1×	`neg-sub0` `frac-2neg` `div-sub` `distribute-frac-neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `fma-udef` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 110

Calls

3 calls:

51.0ms	(* (+ x 1.0) (- x 1.0))
0.0ms	(fma 3.0 x 1.0)
26.0ms	(/ (- (fma 3.0 x 1.0)) (* (+ x 1.0) (- x 1.0)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* (+ x 1.0) (- x 1.0))
42.0ms	(fma 3.0 x 1.0)
80.0ms	(/ (- (fma 3.0 x 1.0)) (* (+ x 1.0) (- x 1.0)))

simplify1.7s

Counts

119 → 119

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	209	1976
1	520	1766
2	1834	1562
done	5001	1537

prune282.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes24.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
done	12	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

648.0ms	4143×	body	80	valid
371.0ms	1673×	body	1280	valid
349.0ms	1251×	body	640	valid
123.0ms	612×	body	320	valid
26.0ms	321×	body	160	valid