Details

sample73.0ms

Algorithm

intervals

Results

20.0ms	61×	body	1280	valid
16.0ms	270×	body	80	nan
9.0ms	34×	body	640	valid
8.0ms	125×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize19.0ms

Local error

Found 2 expressions with local error:

3.5b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite74.0ms

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:

Slowest

65.0ms	(- (sqrt (+ x 1)) (sqrt x))
8.0ms	(sqrt (+ x 1))

series134.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

97.0ms	(- (sqrt (+ x 1)) (sqrt x))
37.0ms	(sqrt (+ x 1))

simplify1.6s

Counts: 43 → 43

prune342.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite68.0ms

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:

Slowest

34.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms	(+ (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))

series215.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

99.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
77.0ms	(+ (sqrt (+ x 1)) (sqrt x))
39.0ms	(sqrt (+ x 1))

simplify1.0s

Counts: 87 → 87

prune802.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite267.0ms

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:

Slowest

152.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
43.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
36.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

164.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
102.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
92.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
89.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.1s

Counts: 294 → 294

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite250.0ms

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:

Slowest

104.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
43.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
40.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
36.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
161.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
149.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
128.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.2s

Counts: 475 → 475

prune4.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm

intervals

Results

632.0ms	1769×	body	1280	valid
449.0ms	8156×	body	80	nan
379.0ms	1177×	body	640	valid
234.0ms	4039×	body	80	valid
142.0ms	656×	body	320	valid
40.0ms	359×	body	160	valid