Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	62×	body	1280	valid
12.0ms	213×	body	80	nan
8.0ms	134×	body	80	valid
7.0ms	30×	body	640	valid
5.0ms	26×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite34.0ms

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))
29.0ms	(- (sqrt (+ x 1)) (sqrt x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(sqrt (+ x 1))
66.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify526.0ms

Counts

43 → 43

Iterations

Iter	Nodes
done	2000
3	848
2	350
1	165
0	81

prune196.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))
0.0b	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
1.7b	(+ x (- 1 x))

rewrite116.0ms

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:

18.0ms	(+ (sqrt (+ x 1)) (sqrt x))
4.0ms	(sqrt (+ x 1))
80.0ms	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
12.0ms	(+ x (- 1 x))

series242.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (sqrt (+ x 1)) (sqrt x))
37.0ms	(sqrt (+ x 1))
118.0ms	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	(+ x (- 1 x))

simplify572.0ms

Counts

121 → 121

Iterations

Iter	Nodes
done	2001
2	938
1	339
0	146

prune392.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite82.0ms

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`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 78

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
23.0ms	(+ (sqrt (+ x 1)) (sqrt x))
52.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series198.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ x 1))
78.0ms	(+ (sqrt (+ x 1)) (sqrt x))
88.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify981.0ms

Counts

87 → 87

Iterations

Iter	Nodes
done	2001
3	1453
2	647
1	245
0	120

prune345.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(sqrt (sqrt (+ x 1)))
0.2b	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.2b	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x 1)))
10.0ms	(sqrt (sqrt (+ x 1)))
47.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
45.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (sqrt (+ x 1)))
62.0ms	(sqrt (sqrt (+ x 1)))
101.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
49.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify863.0ms

Counts

181 → 181

Iterations

Iter	Nodes
done	2001
2	990
1	442
0	211

prune550.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

761.0ms	4127×	body	80	valid
543.0ms	7964×	body	80	nan
537.0ms	1749×	body	1280	valid
427.0ms	1191×	body	640	valid
107.0ms	624×	body	320	valid
35.0ms	309×	body	160	valid