Details

sample39.0ms

Algorithm

intervals

Results

10.0ms	51×	body	1280	valid
7.0ms	41×	body	640	valid
6.0ms	132×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify2.9s

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	79	202
9	183	202
10	535	202
11	1745	202
12	4085	202
done	5000	202

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite148.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `flip-+` `div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

9.0ms	(/ x (+ x 1.0))
20.0ms	(/ (+ x 1.0) (- x 1.0))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series274.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ x (+ x 1.0))
58.0ms	(/ (+ x 1.0) (- x 1.0))
151.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: 2 (429.0ms)

Iter	Nodes	Cost
0	176	32522
1	408	28545
2	1794	27703
done	5002	27703

prune464.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.9b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite799.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
80×	`times-frac`
64×	`add-sqr-sqrt`
44×	`distribute-lft-out--`
32×	`exp-prod`
30×	`distribute-lft-out`
18×	`add-cube-cbrt`
17×	`log-pow` `difference-of-squares`
9×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum` `associate-/l*`
3×	`sub-neg`
2×	`flip3--` `exp-diff` `diff-log` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `frac-sub` `flip-+` `div-inv`

Counts

4 → 130

Calls

4 calls:

294.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
20.0ms	(/ (+ x 1.0) (- x 1.0))
353.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
120.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
50.0ms	(/ (+ x 1.0) (- x 1.0))
198.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
175.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts

142 → 142

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	185	45407
1	429	35553
2	1652	34629
done	5000	34550

prune423.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
8.9b	(log (exp (- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))))
8.9b	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
32×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-l`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-log-exp`
5×	`log-prod` `associate-/r*` `frac-sub`
4×	`frac-times` `flip3-+` `div-exp` `associate-r` `prod-exp` `associate-*r/` `associate-/r/` `log-pow` `flip-+`
3×	`exp-prod` `flip3--` `flip--` `associate-/l*` `unswap-sqr`
2×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `sub-neg` `distribute-lft-in` `1-exp` `exp-sum` `associate-*l/` `cbrt-unprod` `div-inv` `associate--r+`
1×	`log-div` `clear-num` `frac-2neg` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `*-commutative` `pow-flip` `distribute-lft-out` `inv-pow`

Counts

4 → 128

Calls

4 calls:

17.0ms	(/ 1 (- x 1.0))
45.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
180.0ms	(log (exp (- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))))
92.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (- x 1.0))
61.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
193.0ms	(log (exp (- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))))
169.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

simplify873.0ms

Counts

140 → 140

Iterations

Useful iterations: done (848.0ms)

Iter	Nodes	Cost
0	222	46727
1	701	35151
done	5000	32110

prune570.0ms

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 (+ x 1.0))
0.0b	(/ 1 (- x 1.0))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
8.9b	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
44×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-l`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `frac-sub` `flip-+` `distribute-lft-out`
4×	`frac-times` `associate-r` `prod-exp` `associate-*r/`
3×	`cbrt-undiv` `flip3--` `div-inv` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `rec-exp` `clear-num` `frac-2neg` `distribute-lft-in` `1-exp` `associate-*l/` `cbrt-unprod` `associate--r+`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 143

Calls

4 calls:

17.0ms	(/ x (+ x 1.0))
16.0ms	(/ 1 (- x 1.0))
66.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
61.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ x (+ x 1.0))
32.0ms	(/ 1 (- x 1.0))
51.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
180.0ms	(- (/ x (+ x 1.0)) (* (/ 1 (- x 1.0)) (+ x 1.0)))

simplify813.0ms

Counts

155 → 155

Iterations

Useful iterations: done (799.0ms)

Iter	Nodes	Cost
0	240	44714
1	750	35402
done	5000	31780

prune645.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 26.3b

bsearch114.0ms

Steps

Iters	Range		Point
8	160.65039477392645	261980.93535209994	9776.98433563854
10	-83422883652835.42	-0.9341403346610884	-14927.878414639817

simplify17.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	966
1	39	966
2	46	966
3	49	966
done	49	966

end0.0ms

sample1.5s

Algorithm

intervals

Results

523.0ms	4096×	body	80	valid
434.0ms	1667×	body	1280	valid
242.0ms	1320×	body	640	valid
156.0ms	587×	body	320	valid
25.0ms	330×	body	160	valid