Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	255×	body	80	valid
2.0ms	70×	body	80	nan
0.0ms	1×	body	1280	valid

simplify2.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `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` `div-inv`

Counts

3 → 61

Calls

3 calls:

13.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
6.0ms	(sqrt (+ 1.0 x))
57.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

series351.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
55.0ms	(sqrt (+ 1.0 x))
223.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

simplify727.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1500
1	317
0	137

prune325.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ 1.0 x))))
0.3b	(/ x (sqrt (+ 1.0 (sqrt (+ 1.0 x)))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ 1.0 x))))) (/ x (sqrt (+ 1.0 (sqrt (+ 1.0 x))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ 1.0 x)))))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
106×	`times-frac`
101×	`*-un-lft-identity`
71×	`sqrt-prod`
65×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`distribute-lft-out` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`frac-times` `rem-sqrt-square` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow`

Counts

4 → 205

Calls

4 calls:

22.0ms	(sqrt (+ 1.0 (sqrt (+ 1.0 x))))
38.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ 1.0 x)))))
216.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ 1.0 x))))) (/ x (sqrt (+ 1.0 (sqrt (+ 1.0 x))))))
39.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ 1.0 x)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (+ 1.0 (sqrt (+ 1.0 x))))
578.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ 1.0 x)))))
199.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ 1.0 x))))) (/ x (sqrt (+ 1.0 (sqrt (+ 1.0 x))))))
290.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ 1.0 x)))))

simplify810.0ms

Counts

217 → 217

Iterations

Iter	Nodes
done	5000
1	846
0	302

prune719.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 132

Calls

4 calls:

12.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
6.0ms	(sqrt (+ 1.0 x))
40.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ 1.0 x))))
119.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ 1.0 x)))))

series650.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
34.0ms	(sqrt (+ 1.0 x))
404.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ 1.0 x))))
143.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ 1.0 x)))))

simplify3.1s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	3946
1	548
0	213

prune579.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.2b	(/ x (+ 1.0 (sqrt (+ 1.0 x))))
0.2b	(pow (/ x (+ 1.0 (sqrt (+ 1.0 x)))) 3)
32.2b	(cbrt (pow (/ x (+ 1.0 (sqrt (+ 1.0 x)))) 3))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
60×	`times-frac`
49×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `flip-+`
5×	`div-inv`
4×	`associate-/r*` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `associate-/l*`
2×	`cube-div` `cube-mult` `cbrt-undiv` `sqrt-div` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `cbrt-div` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `rem-cbrt-cube`

Counts

4 → 157

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 x))
37.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))
57.0ms	(pow (/ x (+ 1.0 (sqrt (+ 1.0 x)))) 3)
46.0ms	(cbrt (pow (/ x (+ 1.0 (sqrt (+ 1.0 x)))) 3))

series865.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ 1.0 x))
204.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))
370.0ms	(pow (/ x (+ 1.0 (sqrt (+ 1.0 x)))) 3)
254.0ms	(cbrt (pow (/ x (+ 1.0 (sqrt (+ 1.0 x)))) 3))

simplify1.9s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	4641
1	799
0	254

prune553.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	8
1	8
0	6

end0.0ms

sample814.0ms

Algorithm

intervals

Results

409.0ms	7998×	body	80	valid
149.0ms	2683×	body	80	nan
0.0ms	2×	body	1280	valid