Details

sample90.0ms

Algorithm

intervals

Results

27.0ms	40×	body	1280	valid
19.0ms	49×	body	640	valid
11.0ms	170×	body	80	valid
5.0ms	25×	body	320	valid
5.0ms	98×	body	80	nan
2.0ms	16×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	150	9
5	501	9
6	2070	9
done	5000	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
7.8b	(pow (/ x (+ x y)) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

12.0ms	(/ x (+ x y))
14.0ms	(pow (/ x (+ x y)) x)

series409.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ x (+ x y))
352.0ms	(pow (/ x (+ x y)) x)

simplify959.0ms

Counts

76 → 76

Iterations

Useful iterations: done (957.0ms)

Iter	Nodes	Cost
0	133	864
1	423	808
2	1598	782
done	5001	781

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
39.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
29.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

234.0ms	(cbrt x)
248.0ms	(cbrt x)
356.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
368.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.9s

Counts

136 → 136

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	301	2387
1	981	2215
2	3139	2077
done	5002	2023

prune528.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
4.3b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
85×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `log-prod`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `pow1/3` `div-exp` `rem-log-exp` `pow-exp` `flip-+` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
20.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
23.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series1.0s

Counts

4 → 12

Calls

4 calls:

294.0ms	(cbrt x)
269.0ms	(cbrt x)
372.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
98.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.5s

Counts

164 → 164

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	280	2535
1	808	2361
2	2494	2285
done	5000	2279

prune669.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
4.3b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

180×	`cbrt-prod`
168×	`times-frac`
163×	`*-un-lft-identity`
144×	`unpow-prod-down`
115×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`log-prod`
24×	`distribute-lft-out`
16×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1` `cbrt-div` `associate-/r/`
6×	`pow-exp`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`rem-log-exp`
1×	`log-div` `log-pow`

Counts

4 → 256

Calls

4 calls:

31.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
24.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
19.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series1.2s

Counts

4 → 12

Calls

4 calls:

369.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
419.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
339.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
102.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.2s

Counts

268 → 268

Iterations

Useful iterations: 2 (432.0ms)

Iter	Nodes	Cost
0	268	5015
1	777	4669
2	2372	4616
done	5002	4616

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes71.0ms

Accuracy

92.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 5.4b

bsearch192.0ms

Steps

Iters	Range		Point
9	0.0002573389159119229	174.92574374341007	2.625152943905099
10	-2.850986015083103e+120	-1.3460544100055364e+107	-1.3619189728089349e+107

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	43
1	30	39
done	30	39

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	1519×	body	1280	valid
565.0ms	1536×	body	640	valid
440.0ms	4792×	body	80	valid
240.0ms	883×	body	320	valid
162.0ms	3079×	body	80	nan
64.0ms	426×	body	160	valid