Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify283.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	9	19
1	19	18
2	39	18
3	77	18
4	131	18
5	193	18
6	234	18
7	242	18
done	242	18

prune8.0ms

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)))

rewrite55.0ms

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` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

11.0ms	(- (* x x) (* (* y 4.0) y))
43.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series128.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (* x x) (* (* y 4.0) y))
72.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify1.1s

Counts

56 → 56

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	91	1282
1	255	1209
2	1493	1096
done	5000	1090

prune250.0ms

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

localize27.0ms

Local error

Found 4 expressions with local error:

28.2b	(cbrt (fma 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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt (fma 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)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (fma x x (* (* y 4.0) y)))
170.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
141.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
137.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))

simplify2.0s

Counts

70 → 70

Iterations

Useful iterations: 3 (729.0ms)

Iter	Nodes	Cost
0	88	1151
1	198	1122
2	627	1007
3	3004	973
done	5001	973

prune329.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize34.0ms

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 (fma x x (* (* y 4.0) y)) 1/3)

rewrite22.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 65

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)))
3.0ms	(pow (fma x x (* (* y 4.0) y)) 1/3)

series679.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
171.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
180.0ms	(cbrt (- (* x x) (* (* y 4.0) y)))
156.0ms	(pow (fma x x (* (* y 4.0) y)) 1/3)

simplify3.1s

Counts

77 → 77

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	103	1253
1	268	1189
2	904	1083
3	4270	1047
done	5000	1047

prune313.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes191.0ms

Accuracy

58% (13.4b remaining)

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

bsearch184.0ms

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample785.0ms

Algorithm

intervals

Results

521.0ms

8000×

body

valid