Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	61×	body	1280	valid
8.0ms	37×	body	640	valid
7.0ms	131×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	13×	body	160	valid

simplify335.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	202
1	12	202
2	16	202
3	19	202
4	21	202
5	27	202
6	39	202
7	58	202
8	75	202
9	96	202
10	222	202
11	329	202
12	340	202
13	346	202
14	350	202
done	350	202

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
40×	`times-frac`
35×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
14×	`distribute-lft-out`
13×	`add-cube-cbrt`
9×	`difference-of-squares`
5×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `frac-sub` `flip-+` `div-inv`

Counts

2 → 71

Calls

2 calls:

20.0ms	(/ (+ x 1.0) (- x 1.0))
107.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series250.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ x 1.0) (- x 1.0))
204.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.3s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	135	24037
1	321	21481
2	912	20919
3	3385	20760
done	5043	20760

prune357.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
80×	`times-frac`
53×	`add-sqr-sqrt`
52×	`distribute-lft-out--`
32×	`distribute-lft-out`
16×	`cbrt-prod` `difference-of-squares`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `frac-sub` `flip--`
3×	`cbrt-div` `sub-neg` `diff-log`
1×	`pow1/3`

Counts

4 → 105

Calls

4 calls:

70.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
147.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
111.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
91.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series992.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
179.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
209.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
189.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.0s

Counts

117 → 117

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	147	48745
1	345	42531
2	963	41725
3	3480	41285
done	5001	40984

prune441.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(log (exp (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite681.0ms

Algorithm

rewrite-expression-head

Rules

191×	`*-un-lft-identity`
80×	`times-frac`
55×	`add-sqr-sqrt`
52×	`distribute-lft-out--`
32×	`distribute-lft-out`
20×	`log-pow`
19×	`exp-prod`
16×	`cbrt-prod` `difference-of-squares`
10×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`rem-log-exp`

Counts

4 → 109

Calls

4 calls:

349.0ms	(log (exp (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
97.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
110.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series965.0ms

Counts

4 → 12

Calls

4 calls:

412.0ms	(log (exp (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
159.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
198.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
195.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.9s

Counts

121 → 121

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	172	48648
1	374	38706
2	997	37939
3	3574	37499
done	5004	37198

prune523.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
4.8b	(/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0))))
12.2b	(- (/ x (+ x 1.0)) (* (/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
17.6b	(* (/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
33×	`times-frac`
31×	`add-sqr-sqrt`
25×	`associate-l` `add-cube-cbrt`
20×	`pow1`
19×	`cube-unmult`
16×	`add-cbrt-cube` `add-exp-log`
9×	`difference-cubes` `distribute-lft-out`
6×	`add-log-exp`
5×	`flip3-+` `prod-exp` `pow-prod-up` `frac-sub` `cbrt-unprod` `flip-+`
4×	`frac-times` `associate-/r` `associate-r` `pow-prod-down` `associate-r/` `associate-/r/` `associate-/l*`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp` `associate-l/` `-commutative` `div-inv` `associate--r+` `associate-/l/`
1×	`pow2` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `pow-sqr`

Counts

4 → 130

Calls

4 calls:

17.0ms	(* x (* x x))
52.0ms	(/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0))))
69.0ms	(- (/ x (+ x 1.0)) (* (/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
165.0ms	(* (/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* x (* x x))
71.0ms	(/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0))))
214.0ms	(- (/ x (+ x 1.0)) (* (/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
103.0ms	(* (/ (+ 1.0 x) (- (* x (* x x)) (* 1.0 (* 1.0 1.0)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify3.8s

Counts

142 → 142

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	253	68700
1	858	59772
2	3991	58292
done	5004	57932

prune521.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.5b

bsearch3.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	29	1054
1	38	1054
done	38	1054

end0.0ms

sample1.6s

Algorithm

intervals

Results

618.0ms	1221×	body	640	valid
459.0ms	1755×	body	1280	valid
237.0ms	4080×	body	80	valid
78.0ms	646×	body	320	valid
28.0ms	298×	body	160	valid