Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	39×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	18×	body	320	valid
0.0ms	9×	body	160	valid

simplify122.0ms

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	60	13
8	78	13
9	99	13
10	147	13
11	190	13
12	205	13
done	205	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite80.0ms

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

series196.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
124.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify488.0ms

Counts

113 → 113

Iterations

Useful iterations: done (485.0ms)

Iter	Nodes	Cost
0	176	1584
1	399	1503
2	1294	1427
done	5000	1425

prune203.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.1b	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
0.1b	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

257×	`*-un-lft-identity`
112×	`times-frac`
79×	`add-sqr-sqrt`
65×	`distribute-lft-out--`
44×	`distribute-lft-out`
38×	`cbrt-prod`
32×	`unpow-prod-down` `cube-prod`
20×	`difference-of-squares`
19×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`pow-unpow` `cbrt-div` `flip3--` `frac-sub` `flip--` `associate-/l*`
2×	`cube-mult` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 161

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
90.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
87.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
57.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ x (+ x 1.0))
170.0ms	(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
125.0ms	(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
126.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify766.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (171.0ms)

Iter	Nodes	Cost
0	204	3801
1	512	3273
2	1865	3069
done	5000	3069

prune248.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (* (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)) (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
0.1b	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

144×	`*-un-lft-identity`
60×	`times-frac`
42×	`add-sqr-sqrt`
39×	`distribute-lft-out--`
24×	`cbrt-prod` `distribute-lft-out`
12×	`difference-of-squares`
9×	`cbrt-div`
8×	`add-log-exp`
6×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `frac-sub` `add-cbrt-cube` `flip--`
3×	`cube-div` `associate-*r/`
2×	`sub-neg` `pow1/3` `diff-log`
1×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 99

Calls

4 calls:

3.0ms	(cbrt (pow (* (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)) (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
42.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
57.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
57.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (pow (* (cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 2)) (cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))) 3))
273.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
125.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
126.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify462.0ms

Counts

111 → 111

Iterations

Useful iterations: done (458.0ms)

Iter	Nodes	Cost
0	187	3149
1	457	2844
2	1412	2474
done	5002	2423

prune318.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

188×	`*-un-lft-identity`
80×	`times-frac`
52×	`add-sqr-sqrt` `distribute-lft-out--`
32×	`distribute-lft-out`
16×	`difference-of-squares`
12×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--`

Counts

4 → 104

Calls

4 calls:

56.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
57.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
58.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
58.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
127.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify688.0ms

Counts

116 → 116

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	66	2356
1	164	2304
2	424	2168
3	1647	2160
done	5000	2160

prune371.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch81.0ms

Steps

Iters	Range		Point
6	2942.2625356967415	22276.40736340321	9789.556568540302
10	-155084744.97222546	-0.0009113054925467739	-10645.547231578275

simplify7.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	34	72
1	47	57
2	54	57
3	57	57
done	57	57

end0.0ms

sample519.0ms

Algorithm

intervals

Results

174.0ms	1656×	body	1280	valid
97.0ms	4102×	body	80	valid
97.0ms	1212×	body	640	valid
42.0ms	663×	body	320	valid
16.0ms	367×	body	160	valid