Details

sample58.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
12.0ms	245×	body	80	nan
7.0ms	138×	body	80	valid
4.0ms	21×	body	640	valid
3.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite38.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 91

Calls

2 calls:

5.0ms	(sqrt (+ x 1.0))
32.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series129.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(sqrt (+ x 1.0))
87.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2301
2	786
1	324
0	141

prune337.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.4b	(- (+ x 1.0) x)

rewrite212.0ms

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` `insert-posit16` `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 → 148

Calls

4 calls:

5.0ms	(sqrt (+ x 1.0))
42.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
100.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
62.0ms	(- (+ x 1.0) x)

series317.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (+ x 1.0))
79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
194.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify1.7s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
2	1734
1	562
0	221

prune597.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite91.0ms

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-+` `insert-posit16` `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 → 88

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
32.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
51.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series376.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(sqrt (+ x 1.0))
107.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
217.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	4108
2	1217
1	396
0	165

prune354.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

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))))

rewrite263.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 465

Calls

4 calls:

38.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
30.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
109.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

242.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
252.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
492.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
198.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify3.1s

Counts

477 → 477

Iterations

Iter	Nodes
done	5043
2	2610
1	1078
0	451

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.4s

Algorithm

intervals

Results

386.0ms	7851×	body	80	nan
283.0ms	1731×	body	1280	valid
220.0ms	1233×	body	640	valid
167.0ms	4077×	body	80	valid
87.0ms	636×	body	320	valid
55.0ms	323×	body	160	valid