Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	55×	body	1280	valid
7.0ms	211×	body	80	nan
6.0ms	46×	body	640	valid
5.0ms	132×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	7×	body	160	valid

simplify7.0ms

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: 29.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite82.0ms

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:

7.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series133.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(sqrt (+ x 1.0))
90.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.4s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
3	1569
2	532
1	195
0	88

prune166.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 29.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b	(+ x (- 1.0 x))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
45×	`distribute-lft-out`
32×	`sqrt-prod`
30×	`times-frac`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
11×	`add-log-exp`
8×	`distribute-lft-out--`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `flip3-+` `flip-+` `associate-/l*`
4×	`insert-posit16`
3×	`sum-log`
2×	`+-commutative` `associate-+r+` `associate-+r-` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 109

Calls

4 calls:

10.0ms	(sqrt (+ x 1.0))
37.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
81.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
17.0ms	(+ x (- 1.0 x))

series312.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ x 1.0))
97.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
165.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.0ms	(+ x (- 1.0 x))

simplify1.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	1480
1	446
0	183

prune446.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite114.0ms

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:

7.0ms	(sqrt (+ x 1.0))
53.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
52.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series299.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(sqrt (+ x 1.0))
79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
184.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	5012
3	3786
2	1149
1	374
0	159

prune333.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`insert-posit16` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 254

Calls

4 calls:

64.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
72.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
278.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

565.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
218.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
230.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
275.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.3s

Counts

266 → 266

Iterations

Iter	Nodes
done	5000
2	1897
1	695
0	313

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes89.0ms

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

sample1.9s

Algorithm

intervals

Results

586.0ms	1264×	body	640	valid
447.0ms	7974×	body	80	nan
335.0ms	1720×	body	1280	valid
191.0ms	4071×	body	80	valid
66.0ms	613×	body	320	valid
58.0ms	332×	body	160	valid