Details

sample122.0ms

Algorithm

intervals

Results

39.0ms	45×	body	1280	valid
21.0ms	47×	body	640	valid
20.0ms	213×	body	80	nan
15.0ms	134×	body	80	valid
9.0ms	26×	body	320	valid
1.0ms	4×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.0b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `times-frac`
64×	`sqrt-prod`
42×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*` `add-log-exp`
4×	`sqrt-div` `div-exp` `insert-posit16`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `associate-/r/` `flip-+` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 167

Calls

4 calls:

8.0ms	(sqrt (+ x 1))
16.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
55.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1))
46.0ms	(/ 1 (sqrt (+ x 1)))
37.0ms	(/ 1 (sqrt x))
95.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify644.0ms

Counts

179 → 179

Iterations

Iter	Nodes
done	2001
2	988
1	407
0	208

prune545.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.5b	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.5b	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
2.0b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

426×	`times-frac`
387×	`*-un-lft-identity`
340×	`add-sqr-sqrt`
208×	`sqrt-prod`
176×	`add-cube-cbrt`
98×	`distribute-lft-out`
86×	`add-exp-log`
71×	`swap-sqr`
50×	`pow1` `unswap-sqr`
49×	`associate-r` `associate-l`
48×	`pow-flip`
33×	`div-exp` `div-inv`
32×	`prod-exp` `frac-sub`
30×	`add-cbrt-cube`
18×	`frac-times` `associate-l/` `associate-r/` `un-div-inv` `pow-prod-up` `difference-of-squares` `associate-/l/`
16×	`rec-exp` `associate-/r*` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`
11×	`associate-/r/`
10×	`pow-prod-down` `pow-sqr`
9×	`cbrt-undiv`
8×	`sqrt-div` `cbrt-unprod`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `associate-/l*`
2×	`pow2` `pow-plus` `flip3--` `*-commutative` `flip--`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add`

Counts

4 → 476

Calls

4 calls:

41.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
30.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
127.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
29.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
32.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
164.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
61.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify1.3s

Counts

488 → 488

Iterations

Iter	Nodes
done	2009
1	1594
0	513

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
0.5b	(/ (/ (- (* (+ x 1) 1) x) (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
1.7b	(- (* (+ x 1) 1) x)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

414×	`times-frac`
397×	`*-un-lft-identity`
164×	`distribute-lft-out`
148×	`sqrt-prod`
139×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`div-inv`
39×	`associate-/r/`
34×	`associate-*l/`
29×	`associate-/r*`
21×	`add-exp-log`
19×	`flip3-+` `flip-+`
17×	`add-cbrt-cube`
15×	`associate-/l*`
9×	`div-exp`
8×	`pow1`
7×	`cbrt-undiv`
6×	`pow-flip` `add-log-exp`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `div-sub` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-add` `prod-exp` `cbrt-unprod` `flip--` `associate-/l/`

Counts

4 → 302

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
65.0ms	(/ (/ (- (* (+ x 1) 1) x) (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
15.0ms	(- (* (+ x 1) 1) x)

series284.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (sqrt (+ x 1)))
55.0ms	(/ 1 (sqrt x))
193.0ms	(/ (/ (- (* (+ x 1) 1) x) (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
1.0ms	(- (* (+ x 1) 1) x)

simplify823.0ms

Counts

314 → 314

Iterations

Iter	Nodes
done	2005
1	1082
0	405

prune922.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
0.6b	(/ 1 (* (+ x 1) x))
5.0b	(/ (/ 1 (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

417×	`times-frac`
399×	`*-un-lft-identity`
164×	`distribute-lft-out`
148×	`sqrt-prod`
141×	`add-sqr-sqrt` `add-cube-cbrt`
61×	`div-inv`
42×	`add-exp-log`
41×	`associate-/r/`
36×	`associate-*l/`
30×	`associate-/r*`
22×	`add-cbrt-cube`
20×	`flip3-+` `flip-+`
19×	`div-exp`
18×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv`
8×	`pow-flip`
6×	`rec-exp` `1-exp` `prod-exp`
4×	`clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
3×	`inv-pow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `cbrt-unprod`
1×	`pow-prod-down` `frac-add` `associate-/l/`

Counts

4 → 323

Calls

4 calls:

8.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
18.0ms	(/ 1 (* (+ x 1) x))
79.0ms	(/ (/ 1 (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (sqrt (+ x 1)))
30.0ms	(/ 1 (sqrt x))
31.0ms	(/ 1 (* (+ x 1) x))
242.0ms	(/ (/ 1 (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

simplify771.0ms

Counts

335 → 335

Iterations

Iter	Nodes
done	2002
1	981
0	380

prune684.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	11

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	1791×	body	640	valid
644.0ms	7964×	body	80	nan
559.0ms	1154×	body	1280	valid
444.0ms	4122×	body	80	valid
153.0ms	628×	body	320	valid
102.0ms	305×	body	160	valid