Details

sample74.0ms

Algorithm

intervals

Results

16.0ms	270×	body	80	nan
12.0ms	49×	body	640	valid
11.0ms	36×	body	1280	valid
8.0ms	134×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	15×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
4.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

10.0ms	(sqrt (+ x 1.0))
18.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
82.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ x 1.0))
103.0ms	(/ 1.0 (sqrt (+ x 1.0)))
48.0ms	(/ 1.0 (sqrt x))
190.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.3s

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
3	3464
2	1158
1	462
0	216

prune726.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt x))
0.3b	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
3.9b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

260×	`times-frac`
240×	`*-un-lft-identity`
167×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
120×	`sqrt-prod`
70×	`distribute-lft-out`
28×	`swap-sqr`
22×	`associate-r` `associate-l`
20×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
18×	`frac-sub`
16×	`div-inv` `difference-of-squares`
13×	`frac-times` `associate-l/` `associate-r/`
11×	`pow1` `associate-/l/`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`pow2` `sub-neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `frac-add` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+`

Counts

4 → 267

Calls

4 calls:

5.0ms	(/ 1.0 (sqrt x))
166.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
35.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
31.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1.0 (sqrt x))
515.0ms	(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
43.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
85.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.8s

Counts

279 → 279

Iterations

Iter	Nodes
done	5000
1	1314
0	406

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
0.3b	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.2b	(- (+ x 1.0) x)

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

303×	`*-un-lft-identity`
296×	`times-frac`
124×	`sqrt-prod`
117×	`distribute-lft-out`
108×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
37×	`add-cbrt-cube` `add-exp-log`
35×	`associate-/r/`
34×	`div-inv`
30×	`associate-*l/`
27×	`associate-/r*`
17×	`flip3-+` `flip-+`
15×	`cbrt-undiv` `div-exp`
13×	`associate-/l*`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`sqrt-div` `diff-log` `distribute-lft-out--`
1×	`sum-log` `sub-neg` `flip3--` `frac-add` `associate--l+` `flip--` `difference-of-squares` `associate-/l/`

Counts

4 → 248

Calls

4 calls:

19.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
152.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
51.0ms	(- (+ x 1.0) x)

series797.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ 1.0 (sqrt (+ x 1.0)))
62.0ms	(/ 1.0 (sqrt x))
649.0ms	(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms	(- (+ x 1.0) x)

simplify1.5s

Counts

260 → 260

Iterations

Iter	Nodes
done	5001
1	1342
0	469

prune995.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
0.5b	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
4.2b	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

298×	`*-un-lft-identity`
297×	`times-frac`
124×	`sqrt-prod`
116×	`distribute-lft-out`
106×	`add-sqr-sqrt` `add-cube-cbrt`
58×	`add-cbrt-cube` `add-exp-log`
37×	`associate-/r/`
35×	`div-inv`
32×	`associate-*l/`
28×	`associate-/r*`
21×	`cbrt-undiv` `div-exp`
18×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
14×	`associate-/l*`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
2×	`sqrt-div`
1×	`frac-add` `associate-/l/`

Counts

4 → 258

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
24.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
127.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ 1.0 (sqrt (+ x 1.0)))
52.0ms	(/ 1.0 (sqrt x))
43.0ms	(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
627.0ms	(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.5s

Counts

270 → 270

Iterations

Iter	Nodes
done	5000
1	1276
0	453

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample2.0s

Algorithm

intervals

Results

673.0ms	7925×	body	80	nan
332.0ms	1171×	body	1280	valid
325.0ms	1805×	body	640	valid
168.0ms	4036×	body	80	valid
144.0ms	665×	body	320	valid
57.0ms	323×	body	160	valid