Details

sample67.0ms

Algorithm

intervals

Results

22.0ms	54×	body	1280	valid
14.0ms	293×	body	80	nan
8.0ms	41×	body	640	valid
6.0ms	115×	body	80	valid
4.0ms	33×	body	320	valid
2.0ms	13×	body	160	valid

simplify10.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize11.0ms

Local error

Found 2 expressions with local error:

4.2b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite71.0ms

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

50.0ms	(- (sqrt (+ x 1)) (sqrt x))
20.0ms	(sqrt (+ x 1))

series92.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

63.0ms	(- (sqrt (+ x 1)) (sqrt x))
30.0ms	(sqrt (+ x 1))

simplify2.0s

Counts: 43 → 43

prune370.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite67.0ms

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

41.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms	(+ (sqrt (+ x 1)) (sqrt x))
6.0ms	(sqrt (+ x 1))

series176.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

82.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms	(+ (sqrt (+ x 1)) (sqrt x))
28.0ms	(sqrt (+ x 1))

simplify1.0s

Counts: 87 → 87

prune672.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

Slowest

45.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
37.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
5.0ms	(sqrt (sqrt (+ x 1)))
5.0ms	(sqrt (sqrt (+ x 1)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

102.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
66.0ms	(sqrt (sqrt (+ x 1)))
52.0ms	(sqrt (sqrt (+ x 1)))
30.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.2s

Counts: 181 → 181

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (+ x 1)))
0.4b	(cbrt (sqrt (+ x 1)))
0.4b	(cbrt (sqrt (+ x 1)))
0.3b	(* (sqrt (sqrt (+ x 1))) (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (cbrt (sqrt (+ x 1))))))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

402×	`sqrt-div`
168×	`cbrt-div`
136×	`frac-times`
111×	`flip3-+` `flip-+`
50×	`associate-*r/`
44×	`associate-*l/`
24×	`sqrt-prod`
21×	`cbrt-prod` `*-un-lft-identity`
18×	`pow1`
16×	`sqrt-pow1`
15×	`pow1/3`
14×	`add-cube-cbrt`
13×	`add-sqr-sqrt`
10×	`associate-l` `pow-prod-down` `pow-prod-up`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1/2`
4×	`insert-posit16` `distribute-lft-out` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `pow-sqr`
1×	`swap-sqr` `associate-r` `*-commutative`

Counts

4 → 169

Calls

4 calls:

Slowest

250.0ms	(* (sqrt (sqrt (+ x 1))) (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (cbrt (sqrt (+ x 1))))))
6.0ms	(cbrt (sqrt (+ x 1)))
5.0ms	(cbrt (sqrt (+ x 1)))
3.0ms	(cbrt (sqrt (+ x 1)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

62.0ms	(cbrt (sqrt (+ x 1)))
46.0ms	(cbrt (sqrt (+ x 1)))
37.0ms	(cbrt (sqrt (+ x 1)))
35.0ms	(* (sqrt (sqrt (+ x 1))) (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (cbrt (sqrt (+ x 1))))))

simplify994.0ms

Counts: 181 → 181

prune2.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	1791×	body	1280	valid
521.0ms	7822×	body	80	nan
311.0ms	1239×	body	640	valid
221.0ms	4061×	body	80	valid
90.0ms	590×	body	320	valid
33.0ms	319×	body	160	valid