Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify291.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	35	19
3	67	19
4	114	19
5	166	19
6	195	19
7	199	19
done	199	19

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize17.0ms

Local error

Found 2 expressions with local error:

2.9b	(- (* x x) (* (* y 4.0) y))
28.6b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

8.0ms	(- (* x x) (* (* y 4.0) y))
45.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series110.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (* x x) (* (* y 4.0) y))
68.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify661.0ms

Counts

50 → 50

Iterations

Useful iterations: done (659.0ms)

Iter	Nodes	Cost
0	82	1196
1	237	1174
2	1163	1062
done	5001	1060

prune134.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune10.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

28.2b	(cbrt (+ (* x x) (* (* y 4.0) y)))
28.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
28.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
28.2b	(cbrt (- (* x x) (* (* y 4.0) y)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `flip--`
1×	`flip3-+` `flip-+`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))
6.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
6.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
6.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (+ (* x x) (* (* y 4.0) y)))
146.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
173.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
195.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))

simplify2.0s

Counts

64 → 64

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	87	1155
1	196	1127
2	608	1007
3	2927	971
done	5002	955

prune294.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

28.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
28.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
28.2b	(cbrt (- (* x x) (* (* y 4.0) y)))
30.5b	(pow (+ (* x x) (* (* y 4.0) y)) 1/3)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `flip3--` `pow1/3` `flip--`
1×	`pow-to-exp` `pow-pow` `unpow1/3` `pow-exp` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

6.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
6.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
6.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
10.0ms	(pow (+ (* x x) (* (* y 4.0) y)) 1/3)

series565.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
125.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
161.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
147.0ms	(pow (+ (* x x) (* (* y 4.0) y)) 1/3)

simplify2.2s

Counts

69 → 69

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	97	1188
1	257	1122
2	867	1009
3	3562	975
done	5001	959

prune305.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes213.0ms

Accuracy

58% (13.4b remaining)

Error of 13.7b against oracle of 0.3b and baseline of 32.2b

bsearch180.0ms

Steps

Iters	Range		Point
10	1.503577332120078e+256	2.5568038148222018e+269	3.58449778291976e+266
6	1.6216757725262435e+246	1.013111312691819e+247	4.382319121848211e+246
8	8.887721620252314e+213	1.30845433272084e+217	1.2403526691053074e+217
9	2.160548729551366e-40	1.3358342402894081e-34	5.402861320094047e-40
9	4.2563582767693984e-94	1.0719414909580075e-87	1.0092312166797807e-87
9	7.563253502523516e-165	7.647977024157378e-157	9.276635314362871e-162

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	109
1	34	109
done	34	109

end0.0ms

sample810.0ms

Algorithm

intervals

Results

525.0ms

8000×

body

valid