Details

sample118.0ms

Algorithm

intervals

Results

38.0ms	47×	body	1280	valid
25.0ms	52×	body	640	valid
14.0ms	165×	body	80	valid
7.0ms	110×	body	80	nan
7.0ms	24×	body	320	valid
2.0ms	12×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	49	9
4	105	9
5	241	9
6	578	9
7	1854	9
done	5000	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.4b	(pow (/ x (+ x y)) x)

rewrite88.0ms

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:

51.0ms	(/ (pow (/ x (+ x y)) x) x)
11.0ms	(/ x (+ x y))
17.0ms	(pow (/ x (+ x y)) x)

series570.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(/ (pow (/ x (+ x y)) x) x)
68.0ms	(/ x (+ x y))
334.0ms	(pow (/ x (+ x y)) x)

simplify1.2s

Counts

181 → 181

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	276	2881
1	528	2708
2	1487	2650
done	5000	2646

prune552.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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` `frac-2neg` `exp-diff` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

13.0ms

(/ (exp (- y)) x)

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(/ (exp (- y)) x)

simplify2.9s

Counts

32 → 32

Iterations

Useful iterations: 3 (201.0ms)

Iter	Nodes	Cost
0	64	299
1	117	289
2	281	269
3	680	267
4	2766	267
done	5001	267

prune94.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
2.0b	(pow (/ x (cbrt (+ x y))) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
27×	`unpow-prod-down`
24×	`cbrt-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
8×	`cbrt-div`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-exp` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `div-exp` `div-inv` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
5.0ms	(cbrt (+ x y))
17.0ms	(pow (/ x (cbrt (+ x y))) x)

series761.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (+ x y))
207.0ms	(cbrt (+ x y))
185.0ms	(cbrt (+ x y))
156.0ms	(pow (/ x (cbrt (+ x y))) x)

simplify2.6s

Counts

96 → 96

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	207	1387
1	497	1298
2	1267	1262
3	4150	1249
done	5001	1249

prune478.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-div`
10×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `associate-l/`

Counts

4 → 50

Calls

4 calls:

14.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

361.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
287.0ms	(cbrt x)
296.0ms	(cbrt x)
264.0ms	(cbrt x)

simplify2.0s

Counts

62 → 62

Iterations

Useful iterations: 4 (751.0ms)

Iter	Nodes	Cost
0	104	597
1	193	572
2	385	534
3	853	522
4	2333	520
done	5000	520

prune447.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes89.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 12.3b

bsearch115.0ms

Steps

Iters	Range		Point
8	0.00013312118248051433	0.12160444842987421	0.12040142811151512
7	-123.41774798665298	-0.7718806003288846	-13.811744642352284

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	63
1	36	59
done	36	59

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.3s	1549×	body	1280	valid
769.0ms	1489×	body	640	valid
556.0ms	446×	body	160	valid
445.0ms	4811×	body	80	valid
282.0ms	3131×	body	80	nan
234.0ms	839×	body	320	valid