Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	58×	body	640	valid
8.0ms	126×	body	80	valid
7.0ms	39×	body	320	valid
6.0ms	18×	body	1280	valid
2.0ms	15×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.8b	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `associate-+r+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+r-`

Counts

4 → 114

Calls

4 calls:

9.0ms	(/ 1.0 (+ x 1.0))
9.0ms	(/ 1.0 (- x 1.0))
76.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
176.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (+ x 1.0))
29.0ms	(/ 1.0 (- x 1.0))
70.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
314.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	2093
1	537
0	211

prune560.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
2.9b	(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
5.6b	(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
16.2b	(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

370×	`*-un-lft-identity`
239×	`times-frac`
150×	`add-sqr-sqrt`
87×	`distribute-lft-out--`
68×	`distribute-lft-out`
56×	`frac-sub`
53×	`difference-of-squares`
33×	`add-cube-cbrt`
28×	`flip3--` `flip--`
27×	`frac-times`
17×	`associate-/l/`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`associate-/r` `associate-l/` `associate-*r/`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`sub-neg` `associate-/l*`
5×	`associate-/r/`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
3×	`frac-add` `div-inv`
2×	`diff-log`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 238

Calls

4 calls:

351.0ms	(* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
70.0ms	(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
215.0ms	(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
902.0ms	(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x)))

series1.8s

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
295.0ms	(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
396.0ms	(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
974.0ms	(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x)))

simplify560.0ms

Counts

250 → 250

Iterations

Iter	Nodes
done	5001
1	1216
0	406

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0))) (* (* (- x 1.0) x) (+ 1.0 x)))
0.0b	(- (* x 1.0) (* 2.0 (+ 1.0 x)))
0.0b	(* (* (- x 1.0) x) (+ 1.0 x))
18.5b	(+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

56×	`associate-*l/`
44×	`associate-*r/`
32×	`frac-add`
31×	`flip3--` `flip--`
24×	`frac-times` `flip3-+` `flip-+`
18×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
9×	`pow1` `*-un-lft-identity`
8×	`associate-/r/` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-r`
3×	`cbrt-undiv` `sub-neg` `times-frac` `div-exp` `pow-prod-down` `associate-/l*`
2×	`associate--r+`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `diff-log` `associate-l` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 123

Calls

4 calls:

132.0ms	(/ (+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0))) (* (* (- x 1.0) x) (+ 1.0 x)))
12.0ms	(- (* x 1.0) (* 2.0 (+ 1.0 x)))
70.0ms	(* (* (- x 1.0) x) (+ 1.0 x))
55.0ms	(+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0))) (* (* (- x 1.0) x) (+ 1.0 x)))
63.0ms	(- (* x 1.0) (* 2.0 (+ 1.0 x)))
142.0ms	(* (* (- x 1.0) x) (+ 1.0 x))
3.0ms	(+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0)))

simplify473.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
1	1030
0	280

prune936.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x 1.0) x)
0.0b	(* (* (- x 1.0) x) (+ 1.0 x))
0.1b	(/ 2.0 (* (* (- x 1.0) x) (+ 1.0 x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-*l/`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`pow1`
8×	`frac-times` `associate-/r/` `add-cube-cbrt`
7×	`flip3--` `associate-r` `prod-exp` `cbrt-unprod` `flip--`
6×	`flip3-+` `associate-l` `flip-+`
4×	`pow-prod-down` `associate-*r/`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*` `add-log-exp`
2×	`*-commutative`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 82

Calls

3 calls:

21.0ms	(* (- x 1.0) x)
54.0ms	(* (* (- x 1.0) x) (+ 1.0 x))
32.0ms	(/ 2.0 (* (* (- x 1.0) x) (+ 1.0 x)))

series373.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (- x 1.0) x)
166.0ms	(* (* (- x 1.0) x) (+ 1.0 x))
140.0ms	(/ 2.0 (* (* (- x 1.0) x) (+ 1.0 x)))

simplify1.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	3388
1	470
0	156

prune352.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

467.0ms	1834×	body	640	valid
370.0ms	4158×	body	80	valid
265.0ms	959×	body	320	valid
168.0ms	610×	body	1280	valid
84.0ms	442×	body	160	valid