Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	137×	body	80	valid
8.0ms	280×	body	80	nan
8.0ms	58×	body	1280	valid
4.0ms	38×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	9×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.7b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite92.0ms

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-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

21.0ms	(sqrt (+ x 1.0))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series130.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(sqrt (+ x 1.0))
93.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify76.0ms

Counts: 41 → 41

prune89.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite129.0ms

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

Counts

3 → 71

Calls

3 calls:

12.0ms	(sqrt (+ x 1.0))
47.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
65.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series351.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ x 1.0))
98.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
214.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify109.0ms

Counts: 80 → 80

prune240.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

16.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(sqrt (sqrt (+ x 1.0)))
71.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
63.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt (sqrt (+ x 1.0)))
155.0ms	(sqrt (sqrt (+ x 1.0)))
225.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
38.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify77.0ms

Counts: 173 → 173

prune623.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

61.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
5.0ms	(cbrt (+ x 1.0))

series479.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
126.0ms	(cbrt (+ x 1.0))
111.0ms	(cbrt (+ x 1.0))
119.0ms	(cbrt (+ x 1.0))

simplify86.0ms

Counts: 107 → 107

prune749.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

418.0ms	8218×	body	80	nan
332.0ms	1741×	body	1280	valid
250.0ms	1267×	body	640	valid
131.0ms	4051×	body	80	valid
59.0ms	609×	body	320	valid
23.0ms	332×	body	160	valid