Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	53×	body	1280	valid
11.0ms	259×	body	80	nan
7.0ms	42×	body	640	valid
6.0ms	137×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize32.0ms

Local error

Found 1 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

1 → 71

Calls

1 calls:

47.0ms

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

series75.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

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

simplify3.0s

Counts

74 → 74

Iterations

Iter	Nodes
4	3405
3	1236
2	485
1	233
0	108

prune175.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
15×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `associate-/r/` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 72

Calls

2 calls:

43.0ms	(+ (sqrt (+ x 1)) (sqrt x))
55.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ (sqrt (+ x 1)) (sqrt x))
102.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.8s

Counts

78 → 78

Iterations

Iter	Nodes
4	2160
3	933
2	460
1	201
0	94

prune312.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize24.0ms

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)))))

rewrite254.0ms

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×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `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 → 290

Calls

4 calls:

29.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
35.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
37.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
147.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
82.0ms	(/ 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

302 → 302

Iterations

Iter	Nodes
3	2173
2	917
1	455
0	235

prune900.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize38.0ms

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))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
708×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
270×	`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` `hypot-def` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 479

Calls

4 calls:

46.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
49.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
78.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series575.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
148.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
146.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
112.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.0m

Counts

491 → 491

Iterations

Iter	Nodes
3	4201
2	1636
1	855
0	370

prune507.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	9
1	9
0	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

590.0ms	1731×	body	1280	valid
369.0ms	8060×	body	80	nan
166.0ms	4070×	body	80	valid
165.0ms	1241×	body	640	valid
85.0ms	649×	body	320	valid
21.0ms	309×	body	160	valid