Details

sample78.0ms

Algorithm

intervals

Results

22.0ms	61×	body	1280	valid
17.0ms	272×	body	80	nan
11.0ms	39×	body	640	valid
9.0ms	124×	body	80	valid
3.0ms	16×	body	320	valid
2.0ms	16×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
26.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series455.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sqrt (+ x 1.0))
421.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.6s

Counts

43 → 43

Iterations

Iter	Nodes
done	5001
3	2820
2	671
1	195
0	88

prune129.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `insert-posit16` `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 → 74

Calls

3 calls:

19.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
4.0ms	(sqrt (+ x 1.0))
28.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
47.0ms	(sqrt (+ x 1.0))
193.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.1s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1551
1	374
0	159

prune288.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`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`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 449

Calls

4 calls:

30.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
37.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
46.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
105.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
229.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
395.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
171.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify2.3s

Counts

461 → 461

Iterations

Iter	Nodes
done	5001
2	4129
1	1075
0	445

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

248×	`*-un-lft-identity`
234×	`times-frac`
180×	`sqrt-prod`
124×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
72×	`distribute-lft-out`
36×	`associate-/l*`
14×	`sqrt-div`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`pow1` `div-inv`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 243

Calls

4 calls:

36.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
59.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
206.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
421.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
336.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify3.0s

Counts

255 → 255

Iterations

Iter	Nodes
done	5001
2	4453
1	1011
0	397

prune985.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes43.0ms

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

sample2.2s

Algorithm

intervals

Results

623.0ms	1275×	body	640	valid
492.0ms	1761×	body	1280	valid
431.0ms	8083×	body	80	nan
246.0ms	4044×	body	80	valid
109.0ms	595×	body	320	valid
61.0ms	325×	body	160	valid