Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	59×	body	640	valid
4.0ms	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))
8.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify663.0ms

Counts

111 → 111

Iterations

Useful iterations: done (660.0ms)

Iter	Nodes	Cost
0	174	1402
1	396	1329
2	1001	1263
3	2505	1257
done	5000	1256

prune190.0ms

Filtered

80 candidates to 111 candidates (-38.8%)

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))))

rewrite91.0ms

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))
16.0ms	(/ 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)))))
35.0ms	(* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (+ x 1.0))
6.0ms	(/ 1.0 (- (pow x 3) (pow 1.0 3)))
20.0ms	(- (/ 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))))

simplify569.0ms

Counts

287 → 287

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	383	6427
1	1227	5698
done	5001	5600

prune749.0ms

Filtered

188 candidates to 287 candidates (-52.7%)

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
24×	`unpow-prod-down`
19×	`add-exp-log`
15×	`associate-/r*`
14×	`add-log-exp`
13×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`div-exp` `sqr-pow`
6×	`div-inv`
5×	`distribute-lft-out--`
4×	`pow1` `cbrt-undiv` `diff-log`
3×	`distribute-rgt-neg-in` `frac-2neg` `clear-num` `frac-sub` `distribute-neg-frac` `distribute-lft-out`
2×	`pow-to-exp` `neg-log` `pow-exp` `sum-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `flip3-+` `frac-add` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `associate--r+` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

40.0ms	(- (neg (/ 2.0 (pow x 6))) (+ (/ 2.0 (pow x 4)) (/ 2.0 (* x x))))
5.0ms	(/ 2.0 (pow x 4))
5.0ms	(/ 2.0 (pow x 6))
5.0ms	(/ 2.0 (* x x))

series19.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (neg (/ 2.0 (pow x 6))) (+ (/ 2.0 (pow x 4)) (/ 2.0 (* x x))))
4.0ms	(/ 2.0 (pow x 4))
5.0ms	(/ 2.0 (pow x 6))
3.0ms	(/ 2.0 (* x x))

simplify548.0ms

Counts

149 → 149

Iterations

Useful iterations: done (544.0ms)

Iter	Nodes	Cost
0	252	2050
1	593	1917
2	2014	1799
done	5001	1747

prune297.0ms

Filtered

105 candidates to 149 candidates (-41.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	145	6	151

Merged error: 0.0b

Counts

151 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

50.0ms	(+ (/ 2.0 (pow x 4)) (/ (/ 2.0 x) x))
5.0ms	(/ 2.0 (pow x 4))
7.0ms	(/ (/ 2.0 x) x)
5.0ms	(/ 2.0 (pow x 6))

series22.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (/ 2.0 (pow x 4)) (/ (/ 2.0 x) x))
4.0ms	(/ 2.0 (pow x 4))
3.0ms	(/ (/ 2.0 x) x)
5.0ms	(/ 2.0 (pow x 6))

simplify495.0ms

Counts

186 → 186

Iterations

Useful iterations: done (489.0ms)

Iter	Nodes	Cost
0	299	2174
1	647	2021
2	1924	1866
done	5001	1832

prune352.0ms

Filtered

134 candidates to 186 candidates (-38.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	185	7	192

Merged error: 0b

Counts

192 → 7

regimes60.0ms

Accuracy

99.4% (0.2b remaining)

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

bsearch29.0ms

Steps

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

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	71
1	46	71
done	46	71

end0.0ms

sample652.0ms

Algorithm

intervals

Results

209.0ms	1858×	body	640	valid
142.0ms	4281×	body	80	valid
104.0ms	1222×	body	320	valid
40.0ms	639×	body	160	valid

Details

sample23.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite46.0ms

series13.0ms

simplify663.0ms

prune190.0ms

localize16.0ms

rewrite91.0ms

series34.0ms

simplify569.0ms

prune749.0ms

localize12.0ms

rewrite60.0ms

series19.0ms

simplify548.0ms

prune297.0ms

localize12.0ms

rewrite75.0ms

series22.0ms

simplify495.0ms

prune352.0ms

regimes60.0ms

bsearch29.0ms

simplify3.0ms

end0.0ms

sample652.0ms

Profiling