Details

sample143.0ms

Algorithm

intervals

Results

30.0ms	59×	body	640	valid
30.0ms	277×	body	80	nan
25.0ms	38×	body	1280	valid
18.0ms	134×	body	80	valid
17.0ms	18×	body	320	valid
3.0ms	7×	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: 18.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
3.0b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite76.0ms

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))
9.0ms	(/ 1 (sqrt (+ x 1)))
6.0ms	(/ 1 (sqrt x))
55.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ x 1))
53.0ms	(/ 1 (sqrt (+ x 1)))
32.0ms	(/ 1 (sqrt x))
96.0ms	(- (/ 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

prune522.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.1b

localize33.0ms

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)))
3.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite179.0ms

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:

9.0ms	(sqrt (+ x 1))
114.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
20.0ms	(* (sqrt x) (sqrt (+ x 1)))
33.0ms	(- (sqrt (+ x 1)) (sqrt x))

series417.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1))
232.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
77.0ms	(* (sqrt x) (sqrt (+ x 1)))
74.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

124 → 124

Iterations

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

prune518.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.8b

localize47.0ms

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))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
2.7b	(- (+ 1 x) x)

rewrite258.0ms

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:

73.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
101.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
36.0ms	(* (sqrt x) (sqrt (+ x 1)))
44.0ms	(- (+ 1 x) x)

series444.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x)))
286.0ms	(/ (/ (- (+ 1 x) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
76.0ms	(* (sqrt x) (sqrt (+ x 1)))
2.0ms	(- (+ 1 x) x)

simplify815.0ms

Counts

238 → 238

Iterations

Iter	Nodes
done	2011
2	2011
1	739
0	271

prune732.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
49×	`add-sqr-sqrt`
42×	`distribute-lft-out`
40×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
10×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `associate-r*`
6×	`flip3-+` `sqrt-div` `associate-l` `flip-+`
5×	`prod-exp`
4×	`associate-*r/` `insert-posit16` `div-inv` `add-log-exp` `unswap-sqr`
3×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 172

Calls

4 calls:

4.0ms	(sqrt (+ x 1))
28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
65.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
16.0ms	(* (sqrt x) (sqrt (+ x 1)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (+ x 1))
91.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
252.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
61.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.1s

Counts

184 → 184

Iterations

Iter	Nodes
done	2001
3	2001
2	1820
1	583
0	235

prune521.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes77.0ms

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	14
1	14
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

777.0ms	1108×	body	1280	valid
708.0ms	1839×	body	640	valid
641.0ms	8141×	body	80	nan
317.0ms	4109×	body	80	valid
195.0ms	630×	body	320	valid
44.0ms	314×	body	160	valid