Details

sample60.0ms

Algorithm

intervals

Results

22.0ms	49×	body	1280	valid
11.0ms	44×	body	640	valid
7.0ms	162×	body	80	valid
4.0ms	24×	body	320	valid
3.0ms	90×	body	80	nan
1.0ms	12×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	100	9
5	235	9
6	543	9
7	1636	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ (pow (/ x (+ x y)) x) x)
7.9b	(pow (/ x (+ x y)) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

5.0ms	(/ x (+ x y))
26.0ms	(/ (pow (/ x (+ x y)) x) x)
7.0ms	(pow (/ x (+ x y)) x)

series453.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ x (+ x y))
149.0ms	(/ (pow (/ x (+ x y)) x) x)
256.0ms	(pow (/ x (+ x y)) x)

simplify818.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (269.0ms)

Iter	Nodes	Cost
0	276	2881
1	536	2708
2	1561	2650
done	5000	2650

prune428.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.5b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
13×	`unpow-prod-down`
12×	`cbrt-div`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/r/`
6×	`flip3-+` `flip-+`
5×	`pow1` `pow-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-pow` `times-frac` `div-inv` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
14.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series900.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt x)
194.0ms	(cbrt x)
201.0ms	(cbrt x)
312.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.2s

Counts

76 → 76

Iterations

Useful iterations: 3 (447.0ms)

Iter	Nodes	Cost
0	150	1093
1	357	1017
2	856	899
3	2455	878
done	5000	878

prune268.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
48×	`log-prod`
46×	`*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-div` `rem-log-exp` `associate-/r/`
1×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 92

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt x)
195.0ms	(cbrt x)
194.0ms	(cbrt x)
84.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: 4 (588.0ms)

Iter	Nodes	Cost
0	173	1259
1	309	1172
2	558	1117
3	1206	1074
4	2543	1072
done	5000	1072

prune367.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
1.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

72×	`cbrt-prod`
49×	`*-un-lft-identity`
48×	`log-prod`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-div` `rem-log-exp` `associate-/r/`
1×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
1.0ms	(cbrt (cbrt x))
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series883.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt (cbrt x))
268.0ms	(cbrt (cbrt x))
270.0ms	(cbrt (cbrt x))
78.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	184	1388
1	323	1298
2	558	1257
3	1133	1214
4	2199	1212
done	5000	1206

prune440.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

88% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 7.3b

bsearch113.0ms

Steps

Iters	Range		Point
8	0.44834868164545755	179.5191949529741	6.441277885744034
10	-3540160029299381.0	-1.204215327568116	-7.1506444135661775

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	59
1	37	55
done	37	55

end0.0ms

sample1.8s

Algorithm

intervals

Results

655.0ms	1491×	body	1280	valid
379.0ms	1472×	body	640	valid
208.0ms	4795×	body	80	valid
150.0ms	889×	body	320	valid
99.0ms	3040×	body	80	nan
51.0ms	497×	body	160	valid