Details

sample68.0ms

Algorithm

intervals

Results

16.0ms	61×	body	1280	valid
14.0ms	272×	body	80	nan
8.0ms	39×	body	640	valid
7.0ms	124×	body	80	valid
3.0ms	16×	body	320	valid
2.0ms	16×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize76.0ms

Local error

Found 2 expressions with local error:

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

rewrite145.0ms

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:

29.0ms	(sqrt (+ x 1.0))
112.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series180.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(sqrt (+ x 1.0))
122.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify3.7s

Counts

43 → 43

Iterations

Iter	Nodes
done	5001
3	1606
2	534
1	195
0	88

prune491.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 30.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(sqrt (+ x 1.0))
0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
4.4b	(- (+ x 1.0) x)

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt` `times-frac` `sqrt-prod`
19×	`add-cube-cbrt`
16×	`distribute-lft-out--`
11×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
4×	`insert-posit16`
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+` `div-inv`

Counts

4 → 116

Calls

4 calls:

79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
21.0ms	(sqrt (+ x 1.0))
282.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(- (+ x 1.0) x)

series400.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
40.0ms	(sqrt (+ x 1.0))
251.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.0ms	(- (+ x 1.0) x)

simplify3.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	1594
1	492
0	192

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

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)))

rewrite198.0ms

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:

60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(sqrt (+ x 1.0))
104.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series386.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
50.0ms	(sqrt (+ x 1.0))
231.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify6.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
3	3721
2	1104
1	374
0	159

prune634.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize125.0ms

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))))

rewrite778.0ms

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:

110.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
87.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
111.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
336.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

238.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
288.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
514.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
225.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify5.9s

Counts

461 → 461

Iterations

Iter	Nodes
done	5005
2	2614
1	1049
0	445

prune2.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

683.0ms	8083×	body	80	nan
479.0ms	1761×	body	1280	valid
348.0ms	1275×	body	640	valid
251.0ms	4044×	body	80	valid
104.0ms	595×	body	320	valid
31.0ms	325×	body	160	valid