Details

sample132.0ms

Algorithm

intervals

Results

39.0ms	71×	body	640	valid
27.0ms	258×	body	80	nan
26.0ms	42×	body	1280	valid
14.0ms	117×	body	80	valid
5.0ms	13×	body	320	valid
3.0ms	13×	body	160	valid

simplify13.0ms

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: 21.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite74.0ms

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:

9.0ms	(sqrt (+ x 1))
15.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))
40.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1))
33.0ms	(/ 1 (sqrt (+ x 1)))
38.0ms	(/ 1 (sqrt x))
91.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.0s

Counts

179 → 179

Iterations

Iter	Nodes
done	2007
3	2007
2	988
1	407
0	208

prune592.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
3.2b	(- (sqrt (+ x 1)) (sqrt x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`sqrt-prod`
36×	`*-un-lft-identity`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
5×	`distribute-lft-out`
4×	`associate-*r/` `insert-posit16` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 112

Calls

4 calls:

4.0ms	(sqrt (+ x 1))
79.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
17.0ms	(* (sqrt x) (sqrt (+ x 1)))
33.0ms	(- (sqrt (+ x 1)) (sqrt x))

series387.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1))
214.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
72.0ms	(* (sqrt x) (sqrt (+ x 1)))
61.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	2005
3	2005
2	1176
1	416
0	164

prune494.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
2.2b	(- (+ 1 x) x)

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

283×	`*-un-lft-identity`
150×	`times-frac`
97×	`distribute-lft-out`
96×	`add-sqr-sqrt`
87×	`sqrt-prod`
48×	`add-cube-cbrt` `associate-/l*`
40×	`distribute-lft-out--`
20×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
9×	`add-log-exp`
8×	`pow1` `associate-/r/`
7×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r*`
6×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `associate-*r/` `insert-posit16` `div-inv` `unswap-sqr`
3×	`div-sub` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--`
1×	`sum-log` `sub-neg` `sqrt-unprod` `associate--l+` `*-commutative`

Counts

4 → 226

Calls

4 calls:

120.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
96.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
23.0ms	(* (sqrt x) (sqrt (+ x 1)))
22.0ms	(- (+ 1 x) x)

series483.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
287.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
98.0ms	(* (sqrt x) (sqrt (+ x 1)))
2.0ms	(- (+ 1 x) x)

simplify831.0ms

Counts

238 → 238

Iterations

Iter	Nodes
done	2011
2	2011
1	739
0	271

prune814.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1))))
0.2b	(* (/ 1 (sqrt x)) (/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1))))
0.2b	(/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

1113×	`*-un-lft-identity`
890×	`times-frac`
545×	`sqrt-prod`
422×	`add-sqr-sqrt`
418×	`distribute-lft-out`
332×	`add-cube-cbrt`
216×	`associate-r`
54×	`add-exp-log`
37×	`associate-/l*`
36×	`associate-/r/`
34×	`add-cbrt-cube`
25×	`unswap-sqr`
24×	`div-exp`
22×	`associate-l`
20×	`div-inv`
19×	`associate-/r*` `flip3-+` `flip-+`
14×	`cbrt-undiv`
12×	`prod-exp`
8×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `sqrt-div` `1-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-flip` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow`

Counts

4 → 656

Calls

4 calls:

63.0ms	(/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1))))
104.0ms	(* (/ 1 (sqrt x)) (/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1))))
49.0ms	(/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))

series1.0s

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1))))
302.0ms	(* (/ 1 (sqrt x)) (/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1))))
577.0ms	(/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1)))
40.0ms	(/ 1 (sqrt x))

simplify1.5s

Counts

668 → 668

Iterations

Iter	Nodes
done	2001
2	2001
1	1565
0	505

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample2.5s

Algorithm

intervals

Results

761.0ms	8102×	body	80	nan
616.0ms	1833×	body	640	valid
420.0ms	1110×	body	1280	valid
331.0ms	4151×	body	80	valid
162.0ms	609×	body	320	valid
37.0ms	297×	body	160	valid