Details

sample97.0ms

Algorithm

intervals

Results

33.0ms	52×	body	1280	valid
17.0ms	42×	body	640	valid
10.0ms	160×	body	80	valid
10.0ms	27×	body	320	valid
4.0ms	90×	body	80	nan
3.0ms	17×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	49	9
4	107	9
5	245	9
6	580	9
7	1850	9
done	5000	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
5.1b	(pow (/ x (+ x y)) x)

rewrite155.0ms

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×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

81.0ms	(/ (pow (/ x (+ x y)) x) x)
21.0ms	(/ x (+ x y))
35.0ms	(pow (/ x (+ x y)) x)

series633.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(/ (pow (/ x (+ x y)) x) x)
71.0ms	(/ x (+ x y))
366.0ms	(pow (/ x (+ x y)) x)

simplify1.5s

Counts

187 → 187

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	282	2929
1	545	2745
2	1552	2688
done	5000	2684

prune579.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite49.0ms

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×	`expm1-log1p-u` `frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 72

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
44.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt x)
241.0ms	(cbrt x)
262.0ms	(cbrt x)
418.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify2.4s

Counts

84 → 84

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	154	1147
1	370	1061
2	850	939
3	2548	921
done	5000	918

prune460.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
3.7b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

55×	`cbrt-prod`
48×	`log-prod` `*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`flip3-+` `rem-log-exp` `associate-/r/` `flip-+`
1×	`log-div` `div-exp` `log-pow` `div-inv`

Counts

4 → 103

Calls

4 calls:

4.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (+ x y))
248.0ms	(cbrt x)
269.0ms	(cbrt x)
116.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify3.1s

Counts

115 → 115

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	198	1395
1	374	1300
2	728	1243
3	1520	1199
4	3798	1197
done	5001	1192

prune729.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `expm1-log1p-u` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

18.0ms

(/ (exp (- y)) x)

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(/ (exp (- y)) x)

simplify2.8s

Counts

34 → 34

Iterations

Useful iterations: 3 (284.0ms)

Iter	Nodes	Cost
0	66	311
1	120	300
2	293	280
3	709	278
4	2815	278
done	5002	278

prune105.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes90.0ms

Accuracy

98.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.7b

bsearch116.0ms

Steps

Iters	Range		Point
10	7.644017251437775e-11	110.15968793260775	2.6696508553050338
7	-1.5126856462889343e+40	-7.247257622710332e+38	-8.28189259607922e+38

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	44
1	34	44
done	34	44

end0.0ms

sample2.4s

Algorithm

intervals

Results

830.0ms	1531×	body	1280	valid
464.0ms	1424×	body	640	valid
274.0ms	4864×	body	80	valid
175.0ms	845×	body	320	valid
137.0ms	3124×	body	80	nan
58.0ms	438×	body	160	valid