Details

sample53.0ms

Algorithm

intervals

Results

11.0ms	54×	body	1280	valid
9.0ms	223×	body	80	nan
7.0ms	42×	body	640	valid
6.0ms	130×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize11.0ms

Local error

Found 1 expressions with local error:

3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite91.0ms

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` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

90.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series73.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify860.0ms

Counts

22 → 22

Iterations

Useful iterations: done (859.0ms)

Iter	Nodes	Cost
0	59	310
1	134	285
2	443	263
3	1777	257
done	5001	250

prune75.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite101.0ms

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*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

34.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
64.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series327.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
235.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify608.0ms

Counts

61 → 61

Iterations

Useful iterations: done (606.0ms)

Iter	Nodes	Cost
0	128	947
1	308	865
2	1239	790
done	5001	782

prune142.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite505.0ms

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-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

70.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
49.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
301.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series978.0ms

Counts

4 → 12

Calls

4 calls:

454.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
150.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
162.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
213.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.5s

Counts

262 → 262

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	311	6170
1	703	4400
2	3220	4128
done	5002	4073

prune796.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
62×	`sqrt-prod`
37×	`times-frac`
36×	`add-sqr-sqrt` `distribute-lft-out`
29×	`add-cube-cbrt`
27×	`associate-l`
12×	`cbrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r*`
4×	`cbrt-div` `flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-r` `associate-/l*` `unswap-sqr`
2×	`pow1/3` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `-commutative` `cbrt-unprod`

Counts

4 → 118

Calls

4 calls:

64.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
161.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (cbrt 1.0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
42.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.3s

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
370.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (cbrt 1.0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
366.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
417.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	285	3149
1	714	2954
2	3106	2720
done	5001	2714

prune710.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes67.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

831.0ms	7921×	body	80	nan
366.0ms	1792×	body	1280	valid
170.0ms	1305×	body	640	valid
138.0ms	3991×	body	80	valid
99.0ms	601×	body	320	valid
61.0ms	311×	body	160	valid