Details

sample89.0ms

Algorithm

intervals

Results

23.0ms	61×	body	640	valid
18.0ms	218×	body	80	nan
15.0ms	30×	body	1280	valid
12.0ms	133×	body	80	valid
6.0ms	24×	body	320	valid
2.0ms	8×	body	160	valid

simplify29.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize43.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b	(/ 1 (sqrt x))
0.1b	(/ 1 (sqrt (+ x 1)))
0.0b	(sqrt (+ x 1))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `times-frac`
64×	`sqrt-prod`
42×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*` `add-log-exp`
4×	`sqrt-div` `div-exp` `insert-posit16`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `associate-/r/` `flip-+` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 167

Calls

4 calls:

Slowest

31.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
16.0ms	(/ 1 (sqrt (+ x 1)))
8.0ms	(sqrt (+ x 1))
7.0ms	(/ 1 (sqrt x))

series188.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
42.0ms	(/ 1 (sqrt x))
33.0ms	(/ 1 (sqrt (+ x 1)))
32.0ms	(sqrt (+ x 1))

simplify849.0ms

Counts: 179 → 179

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.7b

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b	(- (sqrt (+ x 1)) (sqrt x))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b	(sqrt (+ x 1))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`sqrt-prod`
36×	`*-un-lft-identity`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
5×	`distribute-lft-out`
4×	`associate-*r/` `insert-posit16` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 112

Calls

4 calls:

Slowest

65.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
31.0ms	(- (sqrt (+ x 1)) (sqrt x))
17.0ms	(* (sqrt x) (sqrt (+ x 1)))
5.0ms	(sqrt (+ x 1))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

184.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
67.0ms	(- (sqrt (+ x 1)) (sqrt x))
57.0ms	(* (sqrt x) (sqrt (+ x 1)))
29.0ms	(sqrt (+ x 1))

simplify1.5s

Counts: 124 → 124

prune805.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt x) (sqrt (+ x 1)))
0.2b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
47×	`add-sqr-sqrt`
45×	`distribute-lft-out`
39×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `associate-r*`
6×	`flip3-+` `associate-l` `flip-+` `add-log-exp`
5×	`prod-exp`
4×	`sqrt-div` `associate-*r/` `insert-posit16` `div-inv` `unswap-sqr`
3×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

Slowest

319.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
29.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms	(+ (sqrt (+ x 1)) (sqrt x))
18.0ms	(* (sqrt x) (sqrt (+ x 1)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

197.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
72.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
60.0ms	(* (sqrt x) (sqrt (+ x 1)))
52.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify505.0ms

Counts: 182 → 182

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

1994×	`*-un-lft-identity`
1977×	`times-frac`
1891×	`sqrt-prod`
753×	`distribute-lft-out`
684×	`add-sqr-sqrt`
676×	`add-cube-cbrt`
339×	`associate-/l*`
68×	`sqrt-div`
66×	`associate-/r/`
54×	`add-exp-log`
34×	`flip3-+` `add-cbrt-cube` `flip-+`
33×	`div-inv`
30×	`div-exp`
19×	`associate-/r*`
17×	`pow1`
16×	`cbrt-undiv`
8×	`pow-flip`
7×	`sqrt-pow1` `pow1/2` `associate-r`
6×	`associate-l` `prod-exp` `pow-div`
4×	`rec-exp` `1-exp` `associate-*r/` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `pow-prod-down`
2×	`inv-pow` `associate-/l/`
1×	`sqrt-unprod` `*-commutative`

Counts

4 → 1096

Calls

4 calls:

Slowest

103.0ms	(/ (/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1))))
78.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
32.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
17.0ms	(* (sqrt x) (sqrt (+ x 1)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

201.0ms	(/ (/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1))))
127.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
76.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
70.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.2s

Counts: 1108 → 1108

prune10.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

764.0ms	1804×	body	640	valid
422.0ms	7729×	body	80	nan
371.0ms	1083×	body	1280	valid
301.0ms	4196×	body	80	valid
141.0ms	612×	body	320	valid
35.0ms	305×	body	160	valid