Details

sample96.0ms

Algorithm

intervals

Results

20.0ms	58×	body	640	valid
19.0ms	278×	body	80	nan
19.0ms	134×	body	80	valid
16.0ms	36×	body	1280	valid
5.0ms	18×	body	320	valid
2.0ms	10×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	13
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

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))
2.8b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite83.0ms

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:

4.0ms	(sqrt (+ x 1))
8.0ms	(/ 1 (sqrt (+ x 1)))
9.0ms	(/ 1 (sqrt x))
59.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series202.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1))
31.0ms	(/ 1 (sqrt (+ x 1)))
49.0ms	(/ 1 (sqrt x))
85.0ms	(- (/ 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

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.9b

localize16.0ms

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))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
2.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite143.0ms

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))
89.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
24.0ms	(* (sqrt x) (sqrt (+ x 1)))
24.0ms	(- (sqrt (+ x 1)) (sqrt x))

series423.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ x 1))
203.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
91.0ms	(* (sqrt x) (sqrt (+ x 1)))
92.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

124 → 124

Iterations

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

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
2.2b	(- (+ 1 x) x)

rewrite273.0ms

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:

93.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
117.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))
38.0ms	(- (+ 1 x) x)

series410.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
244.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
81.0ms	(* (sqrt x) (sqrt (+ x 1)))
2.0ms	(- (+ 1 x) x)

simplify1.0s

Counts

238 → 238

Iterations

Iter	Nodes
done	2011
2	2011
1	739
0	271

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
0.5b	(* (sqrt x) (sqrt x))
2.5b	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
9.5b	(* (/ (+ 1 0) (+ (* x (sqrt x)) (* (+ x 1) (sqrt (+ x 1))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
60×	`sqrt-div`
52×	`*-un-lft-identity`
44×	`sqrt-prod`
38×	`frac-times`
36×	`pow1`
35×	`associate-l`
33×	`flip3-+` `flip-+`
32×	`frac-add`
30×	`add-cube-cbrt`
28×	`associate-*r/`
19×	`swap-sqr`
17×	`times-frac` `flip3--` `flip--`
16×	`sqrt-pow1` `pow1/2` `associate-r`
13×	`add-cbrt-cube` `add-exp-log`
11×	`associate-*l/`
10×	`pow-prod-up` `distribute-lft-out` `unswap-sqr`
8×	`pow3`
7×	`pow-prod-down`
6×	`pow-sqr` `add-log-exp`
4×	`prod-exp` `sum-cubes` `cbrt-unprod` `insert-posit16`
3×	`*-commutative`
2×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-/r/`
1×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `distribute-rgt-out--` `diff-log` `div-exp` `div-inv`

Counts

4 → 207

Calls

4 calls:

26.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
9.0ms	(* (sqrt x) (sqrt x))
10.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
162.0ms	(* (/ (+ 1 0) (+ (* x (sqrt x)) (* (+ x 1) (sqrt (+ x 1))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
21.0ms	(* (sqrt x) (sqrt x))
80.0ms	(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))
174.0ms	(* (/ (+ 1 0) (+ (* x (sqrt x)) (* (+ x 1) (sqrt (+ x 1))))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

simplify1.1s

Counts

219 → 219

Iterations

Iter	Nodes
done	2011
2	2011
1	1456
0	362

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes52.0ms

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
done	16
1	16
0	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

748.0ms	8086×	body	80	nan
537.0ms	1853×	body	640	valid
422.0ms	1118×	body	1280	valid
267.0ms	4080×	body	80	valid
133.0ms	649×	body	320	valid
58.0ms	300×	body	160	valid