Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	54×	body	1280	valid
10.0ms	267×	body	80	nan
6.0ms	41×	body	640	valid
5.0ms	134×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify10.0ms

Counts: 1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize14.0ms

Local error

Found 1 expressions with local error:

3.3b	(- (sqrt (+ x 1)) (sqrt x))

rewrite28.0ms

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:

Slowest

28.0ms

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

series75.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

75.0ms

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

simplify1.7s

Counts: 23 → 23

prune195.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite50.0ms

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:

Slowest

31.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms	(+ (sqrt (+ x 1)) (sqrt x))

series204.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

123.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
81.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify998.0ms

Counts: 67 → 67

prune627.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
0.2b	(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
74×	`*-un-lft-identity`
37×	`pow1`
32×	`distribute-lft-out`
30×	`add-sqr-sqrt`
28×	`sqrt-div`
18×	`sqrt-pow1` `pow1/2`
17×	`add-exp-log`
16×	`add-cube-cbrt`
15×	`swap-sqr`
14×	`flip3-+` `flip-+` `pow-flip`
11×	`add-cbrt-cube`
10×	`pow-prod-up`
9×	`associate-r` `associate-l`
8×	`frac-times` `associate-/r/`
6×	`pow-prod-down` `pow-sqr`
4×	`div-exp` `associate-l/` `prod-exp` `associate-r/` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`times-frac` `associate-/l*`
2×	`pow2` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `pow-plus` `1-exp` `cbrt-unprod`
1×	`clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `-commutative` `div-inv` `inv-pow`

Counts

4 → 158

Calls

4 calls:

Slowest

142.0ms	(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
76.0ms	(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
22.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

141.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
140.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
125.0ms	(/ 1 (* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
57.0ms	(* (sqrt (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.0s

Counts: 170 → 170

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (- 1/2))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
32×	`sqrt-prod` `distribute-lft-out`
19×	`pow1`
13×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
10×	`pow-unpow` `swap-sqr`
9×	`add-exp-log`
8×	`flip3-+` `flip-+` `add-log-exp`
6×	`pow-pow` `add-cbrt-cube` `associate-r` `associate-l`
4×	`frac-times` `insert-posit16`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`neg-sub0` `distribute-rgt-in` `pow-to-exp` `pow-neg` `neg-mul-1` `unpow-prod-down` `distribute-lft-in` `*-commutative` `cbrt-unprod` `pow-sub` `unswap-sqr` `sqr-pow`

Counts

4 → 110

Calls

4 calls:

Slowest

168.0ms	(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
37.0ms	(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (- 1/2))
28.0ms	(+ (sqrt (+ x 1)) (sqrt x))
18.0ms	(+ (sqrt (+ x 1)) (sqrt x))

series450.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

224.0ms	(pow (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (- 1/2))
83.0ms	(+ (sqrt (+ x 1)) (sqrt x))
77.0ms	(* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.7s

Counts: 122 → 122

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

731.0ms	1222×	body	640	valid
561.0ms	7971×	body	80	nan
559.0ms	1717×	body	1280	valid
341.0ms	4134×	body	80	valid
141.0ms	627×	body	320	valid
34.0ms	300×	body	160	valid