Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	54×	body	1280	valid
10.0ms	253×	body	80	nan
6.0ms	143×	body	80	valid
6.0ms	34×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
2.5b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

6.0ms	(sqrt (+ 1.0 x))
78.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series145.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(sqrt (+ 1.0 x))
106.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify688.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1090
1	323
0	139

prune272.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

7.0ms	(sqrt (+ 1.0 x))
36.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
70.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ 1.0 x))
64.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
187.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify1.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2042
1	439
0	173

prune452.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (+ 1.0 0) (pow (+ (sqrt (+ 1.0 x)) (sqrt x)) 1))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
40×	`times-frac`
37×	`distribute-lft-out`
32×	`sqrt-prod`
30×	`add-sqr-sqrt` `unpow-prod-down`
27×	`add-cube-cbrt`
10×	`associate-/r*`
8×	`add-exp-log`
7×	`fma-def`
5×	`add-cbrt-cube` `add-log-exp` `sqr-pow`
4×	`pow1` `associate-/l*`
3×	`expm1-log1p-u` `flip3-+` `div-exp` `flip-+` `log1p-expm1-u`
2×	`sqrt-div` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `hypot-def` `div-inv`

Counts

3 → 114

Calls

3 calls:

6.0ms	(sqrt (+ 1.0 x))
29.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
98.0ms	(/ (+ 1.0 0) (pow (+ (sqrt (+ 1.0 x)) (sqrt x)) 1))

series261.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(sqrt (+ 1.0 x))
77.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
140.0ms	(/ (+ 1.0 0) (pow (+ (sqrt (+ 1.0 x)) (sqrt x)) 1))

simplify1.4s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	2703
1	529
0	207

prune433.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
708×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
270×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
8×	`hypot-def`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 461

Calls

4 calls:

36.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
35.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
63.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
120.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

series942.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
239.0ms	(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
377.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
146.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))

simplify2.2s

Counts

473 → 473

Iterations

Iter	Nodes
done	5000
2	4313
1	1103
0	448

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
2	16
1	15
0	11

end0.0ms

sample1.4s

Algorithm

intervals

Results

401.0ms	7946×	body	80	nan
291.0ms	1750×	body	1280	valid
192.0ms	1314×	body	640	valid
156.0ms	4066×	body	80	valid
47.0ms	560×	body	320	valid
22.0ms	310×	body	160	valid