Details

sample89.0ms

Algorithm

intervals

Results

27.0ms	229×	body	80	nan
17.0ms	53×	body	640	valid
13.0ms	36×	body	1280	valid
11.0ms	143×	body	80	valid
3.0ms	13×	body	320	valid
2.0ms	11×	body	160	valid

simplify8.0ms

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: 18.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ 1 (sqrt (+ x 1)))
0.2b	(/ 1 (sqrt x))
2.7b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

1063×	`times-frac`
902×	`*-un-lft-identity`
788×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
580×	`sqrt-prod`
74×	`distribute-lft-out`
56×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
25×	`difference-of-squares`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube`
6×	`pow-flip` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `hypot-def` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 793

Calls

4 calls:

6.0ms	(sqrt (+ x 1))
10.0ms	(/ 1 (sqrt (+ x 1)))
11.0ms	(/ 1 (sqrt x))
33.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1))
33.0ms	(/ 1 (sqrt (+ x 1)))
50.0ms	(/ 1 (sqrt x))
119.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify2.4s

Counts

805 → 805

Iterations

Iter	Nodes
done	5000
2	2463
1	1435
0	651

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.3b

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

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
79×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
42×	`prod-diff`
39×	`add-cube-cbrt`
12×	`distribute-lft-out` `difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `hypot-def` `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 → 171

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
76.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
20.0ms	(* (sqrt x) (sqrt (+ x 1)))
42.0ms	(- (sqrt (+ x 1)) (sqrt x))

series339.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ x 1))
197.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
59.0ms	(* (sqrt x) (sqrt (+ x 1)))
56.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.5s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	1736
1	540
0	216

prune543.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 17.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(* (sqrt x) (sqrt (+ x 1)))
1.7b	(- (+ x 1) x)

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

299×	`*-un-lft-identity`
150×	`times-frac`
104×	`add-sqr-sqrt`
101×	`distribute-lft-out`
87×	`sqrt-prod`
56×	`add-cube-cbrt`
48×	`associate-/l*`
40×	`distribute-lft-out--`
20×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
12×	`prod-diff`
9×	`add-log-exp`
8×	`pow1` `associate-/r/`
7×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r*`
6×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `fma-neg` `sqrt-div` `associate-*r/` `insert-posit16` `log1p-expm1-u` `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 → 250

Calls

4 calls:

79.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
93.0ms	(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
18.0ms	(* (sqrt x) (sqrt (+ x 1)))
33.0ms	(- (+ x 1) x)

series326.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x)))
198.0ms	(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
55.0ms	(* (sqrt x) (sqrt (+ x 1)))
1.0ms	(- (+ x 1) x)

simplify1.5s

Counts

262 → 262

Iterations

Iter	Nodes
done	5001
2	2570
1	805
0	295

prune639.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

115×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
52×	`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×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `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` `hypot-def`
1×	`rem-sqrt-square` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 182

Calls

4 calls:

5.0ms	(sqrt (+ x 1))
30.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
56.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
19.0ms	(* (sqrt x) (sqrt (+ x 1)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (+ x 1))
71.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
195.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
59.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.4s

Counts

194 → 194

Iterations

Iter	Nodes
done	5004
2	1891
1	612
0	243

prune453.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.2s

Algorithm

intervals

Results

543.0ms	7961×	body	80	nan
503.0ms	1799×	body	640	valid
446.0ms	1102×	body	1280	valid
357.0ms	4171×	body	80	valid
155.0ms	604×	body	320	valid
43.0ms	324×	body	160	valid