Details

sample105.0ms

Algorithm

intervals

Results

33.0ms	58×	body	640	valid
23.0ms	267×	body	80	nan
17.0ms	37×	body	1280	valid
12.0ms	133×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify25.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize35.0ms

Local error

Found 3 expressions with local error:

3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b	(/ 1 (sqrt x))
0.2b	(/ 1 (sqrt (+ x 1)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
97×	`times-frac`
93×	`*-un-lft-identity`
60×	`sqrt-prod`
40×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`insert-posit16`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `inv-pow`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--`

Counts

3 → 150

Calls

3 calls:

Slowest

38.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
8.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))

series134.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

69.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
34.0ms	(/ 1 (sqrt (+ x 1)))
31.0ms	(/ 1 (sqrt x))

simplify736.0ms

Counts: 159 → 159

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.8b

localize60.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b	(* (cbrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (cbrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

888×	`add-sqr-sqrt`
638×	`times-frac`
551×	`*-un-lft-identity`
352×	`sqrt-prod`
332×	`cbrt-prod`
287×	`difference-of-squares`
135×	`distribute-lft-out--`
126×	`swap-sqr`
62×	`add-cube-cbrt`
60×	`div-inv`
44×	`associate-r` `associate-l`
27×	`distribute-lft-out`
24×	`cbrt-div`
11×	`pow1` `flip3--` `frac-sub` `flip--`
10×	`add-log-exp`
9×	`frac-times`
6×	`pow1/3` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `unswap-sqr`
3×	`sub-neg` `diff-log` `associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 408

Calls

4 calls:

Slowest

148.0ms	(* (cbrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (cbrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
43.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
36.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
28.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

220.0ms	(* (cbrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (cbrt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))
90.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
85.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
69.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify1.6s

Counts: 420 → 420

prune5.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.7b

localize94.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (sqrt (+ x 1)) (sqrt x))
3.3b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.3b	(- (/ 1 x) (/ 1 (+ x 1)))
0.6b	(cbrt (* (sqrt x) (sqrt (+ x 1))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
82×	`times-frac`
40×	`sqrt-prod`
38×	`difference-of-squares`
26×	`distribute-lft-out--`
14×	`add-cube-cbrt`
10×	`add-log-exp`
8×	`div-inv`
7×	`distribute-lft-out`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`cbrt-div` `sqrt-div` `associate-*r/` `frac-sub`
1×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 117

Calls

4 calls:

Slowest

32.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
25.0ms	(- (sqrt (+ x 1)) (sqrt x))
17.0ms	(- (/ 1 x) (/ 1 (+ x 1)))
8.0ms	(cbrt (* (sqrt x) (sqrt (+ x 1))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

111.0ms	(cbrt (* (sqrt x) (sqrt (+ x 1))))
91.0ms	(- (sqrt (+ x 1)) (sqrt x))
86.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
37.0ms	(- (/ 1 x) (/ 1 (+ x 1)))

simplify1.7s

Counts: 129 → 129

prune2.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.7b

localize152.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (sqrt (+ x 1)) (sqrt x))
3.3b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
3.3b	(- (/ 1 x) (/ 1 (+ x 1)))
0.6b	(cbrt (* (sqrt x) (sqrt (+ x 1))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`times-frac`
17×	`frac-sub`
14×	`difference-of-squares`
13×	`distribute-lft-out--`
10×	`associate-*r/` `add-log-exp`
8×	`frac-times` `associate-*l/` `un-div-inv` `add-cube-cbrt` `sqrt-prod`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `div-inv` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`cbrt-div` `sqrt-div`
1×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 95

Calls

4 calls:

Slowest

36.0ms	(- (sqrt (+ x 1)) (sqrt x))
24.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
21.0ms	(- (/ 1 x) (/ 1 (+ x 1)))
8.0ms	(cbrt (* (sqrt x) (sqrt (+ x 1))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

107.0ms	(cbrt (* (sqrt x) (sqrt (+ x 1))))
68.0ms	(- (sqrt (+ x 1)) (sqrt x))
38.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
30.0ms	(- (/ 1 x) (/ 1 (+ x 1)))

simplify683.0ms

Counts: 107 → 107

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.7b

regimes110.0ms

Accuracy

0% (0.9b remaining)

Error of 19.8b against oracle of 18.8b and baseline of 19.8b

bsearch6.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

677.0ms	7971×	body	80	nan
646.0ms	1837×	body	640	valid
589.0ms	1103×	body	1280	valid
448.0ms	629×	body	320	valid
374.0ms	4129×	body	80	valid
47.0ms	302×	body	160	valid