Details

sample77.0ms

Algorithm

intervals

Results

28.0ms	57×	body	1280	valid
14.0ms	48×	body	640	valid
8.0ms	161×	body	80	valid
5.0ms	27×	body	320	valid
4.0ms	103×	body	80	nan
2.0ms	15×	body	160	valid

simplify2.4s

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	105	9
5	241	9
6	578	9
7	1854	9
done	5000	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.1b	(pow (/ x (+ x y)) x)

rewrite28.0ms

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×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

11.0ms	(/ x (+ x y))
14.0ms	(pow (/ x (+ x y)) x)

series429.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ x (+ x y))
367.0ms	(pow (/ x (+ x y)) x)

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	129	836
1	305	785
2	738	756
3	1992	754
done	5001	749

prune288.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(* (cbrt x) (cbrt x))
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.2b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

65×	`cbrt-prod`
61×	`unpow-prod-down`
57×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
43×	`add-cube-cbrt` `times-frac`
22×	`add-exp-log`
16×	`cbrt-div`
13×	`pow1`
10×	`associate-/r/`
8×	`flip3-+` `flip-+`
7×	`pow1/3` `pow-exp` `distribute-lft-out`
6×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
5×	`div-exp` `prod-exp`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `div-inv` `sqr-pow`
1×	`pow2` `pow-plus` `*-commutative` `cbrt-unprod`

Counts

4 → 148

Calls

4 calls:

10.0ms	(cbrt (+ x y))
27.0ms	(* (cbrt x) (cbrt x))
38.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
57.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (+ x y))
305.0ms	(* (cbrt x) (cbrt x))
377.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
465.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.5s

Counts

160 → 160

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	338	2679
1	782	2470
2	1831	2219
done	5000	2200

prune724.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.8b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
33.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series872.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (+ x y))
209.0ms	(cbrt (+ x y))
375.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
109.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify2.0s

Counts

162 → 162

Iterations

Useful iterations: 3 (835.0ms)

Iter	Nodes	Cost
0	287	2677
1	636	2499
2	1275	2450
3	3161	2405
done	5000	2405

prune797.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite31.0ms

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:

29.0ms

(/ (exp (- y)) x)

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(/ (exp (- y)) x)

simplify2.7s

Counts

32 → 32

Iterations

Useful iterations: 3 (208.0ms)

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

prune91.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes77.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.5b

bsearch216.0ms

Steps

Iters	Range		Point
9	2.9210494299769893e-08	3.811728419345326	3.548587978717038
10	-2.4955120319962723e+20	-128623.8930200133	-2375445713.2073126

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	25	47
1	34	40
done	34	40

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	1538×	body	1280	valid
705.0ms	1492×	body	640	valid
424.0ms	4916×	body	80	valid
322.0ms	2973×	body	80	nan
251.0ms	805×	body	320	valid
76.0ms	418×	body	160	valid