Details

sample63.0ms

Algorithm

intervals

Results

16.0ms	55×	body	1280	valid
15.0ms	278×	body	80	nan
9.0ms	39×	body	640	valid
8.0ms	134×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
2.8b	(- (sqrt (+ x 1)) (sqrt x))

rewrite43.0ms

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))
39.0ms	(- (sqrt (+ x 1)) (sqrt x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(sqrt (+ x 1))
66.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.0s

Counts

43 → 43

Iterations

Iter	Nodes
done	2000
4	2000
3	848
2	350
1	165
0	81

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.2b

localize34.0ms

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)))
2.2b	(+ x (- 1 x))

rewrite164.0ms

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:

39.0ms	(+ (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))
87.0ms	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
27.0ms	(+ x (- 1 x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (sqrt (+ x 1)) (sqrt x))
40.0ms	(sqrt (+ x 1))
84.0ms	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	(+ x (- 1 x))

simplify1.1s

Counts

121 → 121

Iterations

Iter	Nodes
done	2003
3	2003
2	938
1	339
0	146

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite75.0ms

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:

9.0ms	(sqrt (+ x 1))
30.0ms	(+ (sqrt (+ x 1)) (sqrt x))
35.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ x 1))
73.0ms	(+ (sqrt (+ x 1)) (sqrt x))
104.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	2001
4	2001
3	1453
2	647
1	245
0	120

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

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*`
17×	`add-exp-log`
15×	`pow1`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube`
8×	`div-exp` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 463

Calls

4 calls:

29.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
89.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
42.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
130.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
102.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
207.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.3s

Counts

475 → 475

Iterations

Iter	Nodes
done	2014
3	2014
2	1682
1	838
0	364

prune4.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes59.0ms

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	11
1	11
0	7

end0.0ms

sample2.6s

Algorithm

intervals

Results

757.0ms	4089×	body	80	valid
576.0ms	1698×	body	1280	valid
434.0ms	8086×	body	80	nan
365.0ms	1266×	body	640	valid
141.0ms	650×	body	320	valid
57.0ms	297×	body	160	valid