Details

sample88.0ms

Algorithm

intervals

Results

28.0ms	259×	body	80	nan
19.0ms	53×	body	1280	valid
11.0ms	42×	body	640	valid
10.0ms	137×	body	80	valid
3.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize20.0ms

Local error

Found 1 expressions with local error:

2.6b	(- (sqrt (+ x 1)) (sqrt x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out`

Counts

1 → 20

Calls

1 calls:

52.0ms

(- (sqrt (+ x 1)) (sqrt x))

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

(- (sqrt (+ x 1)) (sqrt x))

simplify1.1s

Counts

23 → 23

Iterations

Iter	Nodes
done	2004
4	2004
3	697
2	280
1	111
0	50

prune222.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+` `insert-posit16`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 61

Calls

2 calls:

30.0ms	(+ (sqrt (+ x 1)) (sqrt x))
33.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series169.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(+ (sqrt (+ x 1)) (sqrt x))
85.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	2001
4	2001
3	1082
2	485
1	195
0	90

prune644.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 282

Calls

4 calls:

31.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
44.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
51.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
171.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
80.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
105.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
99.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify1.1s

Counts

294 → 294

Iterations

Iter	Nodes
done	2000
3	2000
2	940
1	452
0	229

prune3.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

rewrite229.0ms

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:

22.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
31.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
40.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
110.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
108.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
132.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
102.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.6s

Counts

475 → 475

Iterations

Iter	Nodes
done	2000
3	2000
2	1688
1	865
0	364

prune4.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes61.0ms

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

sample2.4s

Algorithm

intervals

Results

566.0ms	1731×	body	1280	valid
476.0ms	8060×	body	80	nan
469.0ms	309×	body	160	valid
286.0ms	1241×	body	640	valid
280.0ms	4070×	body	80	valid
101.0ms	649×	body	320	valid