Details

sample22.0ms

Algorithm

intervals

Results

8.0ms	54×	body	1280	valid
4.0ms	49×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	27×	body	320	valid
0.0ms	3×	body	160	valid

simplify83.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	76	13
9	97	13
10	127	13
11	143	13
12	151	13
done	151	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

7.0ms	(/ x (+ x 1.0))
11.0ms	(/ (+ x 1.0) (- x 1.0))
57.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.5s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	176	1584
1	390	1503
2	1112	1427
3	4847	1416
done	5000	1416

prune211.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.2b	(/ 1.0 (* x x))
0.3b	(/ 3.0 (pow x 3))
8.0b	(+ (/ 1.0 (* x x)) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
53×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
9×	`unpow3`
8×	`distribute-lft-out`
6×	`associate-/l*`
5×	`div-exp` `frac-add`
4×	`pow1` `cube-mult` `distribute-rgt-out` `sum-log` `div-inv` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+`
2×	`+-commutative` `frac-2neg` `clear-num`
1×	`pow-to-exp` `associate-+r+` `distribute-lft1-in` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

40.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
4.0ms	(/ 1.0 (* x x))
4.0ms	(/ 3.0 (pow x 3))
121.0ms	(+ (/ 1.0 (* x x)) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
26.0ms	(/ 1.0 (* x x))
36.0ms	(/ 3.0 (pow x 3))
31.0ms	(+ (/ 1.0 (* x x)) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify1.1s

Counts

138 → 138

Iterations

Useful iterations: 2 (248.0ms)

Iter	Nodes	Cost
0	201	1818
1	506	1563
2	2404	1473
done	5001	1473

prune247.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
31.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
117.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
45.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
349.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
210.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify475.0ms

Counts

341 → 341

Iterations

Useful iterations: done (461.0ms)

Iter	Nodes	Cost
0	410	10805
1	1269	9795
done	5001	9689

prune488.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
1.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

814×	`*-un-lft-identity`
294×	`distribute-lft-out`
288×	`times-frac`
72×	`distribute-lft-out--`
70×	`swap-sqr`
27×	`frac-times` `frac-sub`
21×	`associate-r/` `associate-l/`
12×	`associate-r` `associate-l`
11×	`pow1`
10×	`add-sqr-sqrt` `add-log-exp`
8×	`add-cube-cbrt` `flip3-+` `frac-add` `flip-+`
6×	`add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 193

Calls

4 calls:

351.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
207.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
208.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))
206.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify654.0ms

Counts

205 → 205

Iterations

Useful iterations: 2 (169.0ms)

Iter	Nodes	Cost
0	161	7383
1	493	6541
2	2099	5947
done	5000	5947

prune290.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch98.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	12679.85899306799
8	-14583263.309321204	-1162.6651869185068	-11931.41196902016

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	97
1	44	82
2	51	82
3	54	82
done	54	82

end0.0ms

sample518.0ms

Algorithm

intervals

Results

178.0ms	1731×	body	1280	valid
108.0ms	1265×	body	640	valid
91.0ms	4084×	body	80	valid
37.0ms	618×	body	320	valid
12.0ms	302×	body	160	valid