Details

sample89.0ms

Algorithm

intervals

Results

24.0ms	64×	body	640	valid
20.0ms	246×	body	80	nan
14.0ms	31×	body	1280	valid
12.0ms	128×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	17
2	17
1	13
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
3.9b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite72.0ms

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))
9.0ms	(/ 1 (sqrt (+ x 1)))
7.0ms	(/ 1 (sqrt x))
46.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ x 1))
31.0ms	(/ 1 (sqrt (+ x 1)))
48.0ms	(/ 1 (sqrt x))
90.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.7s

Counts

179 → 179

Iterations

Iter	Nodes
4	3357
3	1666
2	902
1	394
0	208

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 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)))
3.9b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

rewrite223.0ms

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:

33.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
104.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
38.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
32.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
169.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
24.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
38.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

simplify2.2s

Counts

488 → 488

Iterations

Iter	Nodes
2	4391
1	1603
0	513

prune3.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
0.3b	(/ (/ (- (+ x 1) x) (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
3.4b	(- (+ x 1) x)

rewrite136.0ms

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-*r/`
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:

9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
80.0ms	(/ (/ (- (+ x 1) x) (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
31.0ms	(- (+ x 1) x)

series223.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (sqrt (+ x 1)))
28.0ms	(/ 1 (sqrt x))
158.0ms	(/ (/ (- (+ x 1) x) (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
1.0ms	(- (+ x 1) x)

simplify1.4s

Counts

370 → 370

Iterations

Iter	Nodes
2	3332
1	1094
0	425

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
0.4b	(/ 1 (* x (+ x 1)))
4.3b	(/ (/ 1 (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

rewrite86.0ms

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-*r/`
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))
14.0ms	(/ 1 (* x (+ x 1)))
51.0ms	(/ (/ 1 (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (sqrt (+ x 1)))
27.0ms	(/ 1 (sqrt x))
18.0ms	(/ 1 (* x (+ x 1)))
146.0ms	(/ (/ 1 (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

simplify953.0ms

Counts

335 → 335

Iterations

Iter	Nodes
2	2537
1	947
0	380

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	18
1	18
0	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

526.0ms	8213×	body	80	nan
445.0ms	616×	body	320	valid
430.0ms	1777×	body	640	valid
364.0ms	1108×	body	1280	valid
329.0ms	4162×	body	80	valid
40.0ms	337×	body	160	valid