Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	54×	body	1280	valid
5.0ms	225×	body	80	nan
3.0ms	134×	body	80	valid
3.0ms	33×	body	640	valid
2.0ms	26×	body	320	valid
0.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

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 (+ x 1.0))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series133.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt (+ x 1.0))
101.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5003
3	2271
2	785
1	322
0	139

prune331.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
2.7b	(- (+ 1.0 x) x)

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
46×	`distribute-lft-out`
40×	`sqrt-prod`
36×	`times-frac`
29×	`add-cube-cbrt`
16×	`distribute-lft-out--`
12×	`prod-diff`
11×	`add-log-exp`
8×	`difference-of-squares`
7×	`fma-def`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `hypot-def` `div-inv`

Counts

4 → 144

Calls

4 calls:

12.0ms	(sqrt (+ 1.0 x))
52.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
169.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
67.0ms	(- (+ 1.0 x) x)

series359.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ 1.0 x))
102.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
202.0ms	(/ (- (+ 1.0 x) x) (+ (sqrt (+ 1.0 x)) (sqrt x)))
2.0ms	(- (+ 1.0 x) x)

simplify2.0s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
2	1716
1	558
0	217

prune638.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`distribute-lft-out`
20×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
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 → 85

Calls

3 calls:

13.0ms	(sqrt (+ 1.0 x))
56.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
73.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

series332.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ 1.0 x))
79.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
214.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify2.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	4094
2	1182
1	394
0	162

prune441.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ 1.0 x)))
0.0b	(sqrt (sqrt (+ 1.0 x)))
0.2b	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 169

Calls

4 calls:

13.0ms	(sqrt (sqrt (+ 1.0 x)))
15.0ms	(sqrt (sqrt (+ 1.0 x)))
49.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
57.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (sqrt (+ 1.0 x)))
91.0ms	(sqrt (sqrt (+ 1.0 x)))
210.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
34.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify1.7s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	1669
1	597
0	257

prune743.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes66.0ms

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	9
1	9
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

422.0ms	633×	body	320	valid
404.0ms	1731×	body	1280	valid
318.0ms	7962×	body	80	nan
197.0ms	1264×	body	640	valid
177.0ms	4053×	body	80	valid
20.0ms	319×	body	160	valid