Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	59×	body	640	valid
5.0ms	52×	body	320	valid
4.0ms	134×	body	80	valid
1.0ms	11×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	15	11
done	15	11

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.0b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
3.1b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
55×	`times-frac`
50×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
25×	`distribute-lft-out--`
10×	`distribute-lft-out`
9×	`associate-/r*`
8×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/` `associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1` `flip--`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip-+`
1×	`sub-neg` `flip3-+` `diff-log` `frac-sub`

Counts

3 → 102

Calls

3 calls:

6.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ 1.0 (+ x 1.0))
30.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))
9.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify621.0ms

Counts

111 → 111

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	174	1402
1	396	1323
2	1092	1257
3	2883	1255
done	5000	1254

prune191.0ms

Filtered

78 candidates to 111 candidates (-42.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	2	112

Merged error: 0.2b

Counts

112 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.5b	(/ 1.0 (- (pow x 3) (pow 1.0 3)))
12.6b	(- (/ 1.0 (+ x 1.0)) (* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
20.8b	(* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

246×	`add-sqr-sqrt`
163×	`times-frac`
151×	`*-un-lft-identity`
112×	`difference-of-squares`
84×	`unpow-prod-down` `cube-prod`
81×	`associate-l`
73×	`add-cube-cbrt`
56×	`sqr-pow`
35×	`distribute-lft-out--`
29×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
7×	`difference-cubes`
6×	`pow1` `associate-/r/` `associate-/l*` `add-log-exp`
5×	`flip3-+` `frac-sub` `flip-+`
4×	`frac-times` `associate-*r/` `distribute-lft-out`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `flip--` `div-inv`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 275

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
20.0ms	(/ 1.0 (- (pow x 3) (pow 1.0 3)))
11.0ms	(- (/ 1.0 (+ x 1.0)) (* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
33.0ms	(* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (+ x 1.0))
6.0ms	(/ 1.0 (- (pow x 3) (pow 1.0 3)))
19.0ms	(- (/ 1.0 (+ x 1.0)) (* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
6.0ms	(* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify418.0ms

Counts

287 → 287

Iterations

Useful iterations: done (403.0ms)

Iter	Nodes	Cost
0	383	6427
1	1227	5663
done	5000	5443

prune696.0ms

Filtered

180 candidates to 287 candidates (-59.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	287	2	289

Merged error: 0.2b

Counts

289 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 6)))
0.1b	(/ 2.0 (pow x 4))
0.2b	(/ 2.0 (pow x 6))
0.3b	(/ 2.0 (* x x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
40×	`*-un-lft-identity`
38×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down`
19×	`add-exp-log`
15×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp` `sqr-pow`
6×	`add-log-exp`
5×	`div-inv`
4×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num`
2×	`pow-to-exp` `pow-exp` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `frac-add` `prod-exp` `sum-log` `cbrt-unprod` `flip-+`

Counts

4 → 125

Calls

4 calls:

16.0ms	(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 6)))
5.0ms	(/ 2.0 (pow x 4))
5.0ms	(/ 2.0 (pow x 6))
5.0ms	(/ 2.0 (* x x))

series24.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 6)))
4.0ms	(/ 2.0 (pow x 4))
5.0ms	(/ 2.0 (pow x 6))
3.0ms	(/ 2.0 (* x x))

simplify397.0ms

Counts

137 → 137

Iterations

Useful iterations: done (393.0ms)

Iter	Nodes	Cost
0	209	1499
1	435	1373
2	1365	1262
done	5000	1260

prune262.0ms

Filtered

98 candidates to 137 candidates (-39.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Merged error: 0.0b

Counts

139 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x 4)
0.1b	(/ 2.0 (pow x 4))
0.2b	(/ (/ 2.0 x) x)
0.2b	(/ 2.0 (pow x 6))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
80×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`unpow-prod-down`
20×	`add-exp-log`
19×	`associate-/l*`
17×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`div-exp` `sqr-pow`
7×	`div-inv`
5×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-unpow` `frac-2neg` `pow-exp` `clear-num`
1×	`pow-pow` `associate-/l/`

Counts

4 → 177

Calls

4 calls:

2.0ms	(pow x 4)
5.0ms	(/ 2.0 (pow x 4))
7.0ms	(/ (/ 2.0 x) x)
5.0ms	(/ 2.0 (pow x 6))

series15.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow x 4)
4.0ms	(/ 2.0 (pow x 4))
3.0ms	(/ (/ 2.0 x) x)
5.0ms	(/ 2.0 (pow x 6))

simplify427.0ms

Counts

189 → 189

Iterations

Useful iterations: 2 (164.0ms)

Iter	Nodes	Cost
0	281	1983
1	583	1829
2	1761	1663
done	5000	1663

prune316.0ms

Filtered

127 candidates to 189 candidates (-48.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	188	6	194

Merged error: 0b

Counts

194 → 6

regimes57.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.7b

bsearch31.0ms

Steps

Iters	Range		Point
9	0.009971872296741319	901.3230478674768	207.2843131073097
9	-174458.2165831976	-0.46594774775336223	-285.5514038748799

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	71
1	52	71
2	63	71
3	67	71
4	68	71
done	68	71

end0.0ms

sample682.0ms

Algorithm

intervals

Results

226.0ms	1858×	body	640	valid
143.0ms	4281×	body	80	valid
117.0ms	1222×	body	320	valid
39.0ms	639×	body	160	valid

Details

sample24.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite46.0ms

series13.0ms

simplify621.0ms

prune191.0ms

localize16.0ms

rewrite88.0ms

series33.0ms

simplify418.0ms

prune696.0ms

localize12.0ms

rewrite35.0ms

series24.0ms

simplify397.0ms

prune262.0ms

localize15.0ms

rewrite27.0ms

series15.0ms

simplify427.0ms

prune316.0ms

regimes57.0ms

bsearch31.0ms

simplify11.0ms

end0.0ms

sample682.0ms

Profiling