Details

sample77.0ms

Algorithm

intervals

Results

21.0ms	248×	body	80	nan
17.0ms	64×	body	640	valid
11.0ms	33×	body	1280	valid
9.0ms	132×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
1.9b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite130.0ms

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:

15.0ms	(sqrt (+ x 1))
26.0ms	(/ 1 (sqrt (+ x 1)))
14.0ms	(/ 1 (sqrt x))
68.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1))
40.0ms	(/ 1 (sqrt (+ x 1)))
54.0ms	(/ 1 (sqrt x))
84.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify3.5s

Counts

179 → 179

Iterations

Iter	Nodes
done	5057
4	4762
3	2343
2	988
1	407
0	208

prune539.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
0.3b	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.5b	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
1.8b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite527.0ms

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:

125.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
250.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
78.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
46.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
179.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
39.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
66.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify3.3s

Counts

488 → 488

Iterations

Iter	Nodes
done	5007
2	4096
1	1604
0	513

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
0.3b	(/ (/ (- (+ x 1) x) (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
1.5b	(- (+ x 1) x)

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

583×	`*-un-lft-identity`
567×	`times-frac`
230×	`distribute-lft-out`
196×	`add-sqr-sqrt`
184×	`sqrt-prod`
160×	`add-cube-cbrt`
72×	`div-inv`
39×	`associate-/r/`
36×	`distribute-lft-out--`
34×	`associate-*l/`
29×	`associate-/r*`
21×	`add-exp-log`
19×	`flip3-+` `flip-+`
18×	`associate-/l*` `difference-of-squares`
17×	`add-cbrt-cube`
9×	`div-exp` `add-log-exp`
8×	`pow1`
7×	`cbrt-undiv`
6×	`pow-flip`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`rec-exp` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `1-exp` `div-sub` `inv-pow`
1×	`sum-log` `sub-neg` `flip3--` `frac-add` `prod-exp` `associate--l+` `cbrt-unprod` `flip--` `associate-/l/`

Counts

4 → 358

Calls

4 calls:

28.0ms	(/ 1 (sqrt (+ x 1)))
13.0ms	(/ 1 (sqrt x))
231.0ms	(/ (/ (- (+ x 1) x) (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
45.0ms	(- (+ x 1) x)

series250.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (sqrt (+ x 1)))
34.0ms	(/ 1 (sqrt x))
177.0ms	(/ (/ (- (+ x 1) x) (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
2.0ms	(- (+ x 1) x)

simplify2.6s

Counts

370 → 370

Iterations

Iter	Nodes
done	5001
2	3929
1	1138
0	425

prune729.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
0.5b	(/ 1 (* (+ x 1) x))
5.1b	(/ (/ 1 (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

rewrite544.0ms

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:

14.0ms	(/ 1 (sqrt (+ x 1)))
7.0ms	(/ 1 (sqrt x))
21.0ms	(/ 1 (* (+ x 1) x))
486.0ms	(/ (/ 1 (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (sqrt (+ x 1)))
37.0ms	(/ 1 (sqrt x))
32.0ms	(/ 1 (* (+ x 1) x))
211.0ms	(/ (/ 1 (* (+ x 1) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

simplify2.0s

Counts

335 → 335

Iterations

Iter	Nodes
done	5001
2	2375
1	981
0	380

prune663.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	12

end0.0ms

sample2.1s

Algorithm

intervals

Results

643.0ms	8127×	body	80	nan
391.0ms	1115×	body	1280	valid
390.0ms	1781×	body	640	valid
341.0ms	4167×	body	80	valid
125.0ms	629×	body	320	valid
29.0ms	308×	body	160	valid