Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	55×	body	1280	valid
15.0ms	218×	body	80	nan
10.0ms	35×	body	640	valid
9.0ms	133×	body	80	valid
5.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

simplify33.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize20.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite32.0ms

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

26.0ms	(- (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series114.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

75.0ms	(- (sqrt (+ x 1)) (sqrt x))
39.0ms	(sqrt (+ x 1))

simplify1.5s

Counts: 43 → 43

prune276.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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))

rewrite59.0ms

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

30.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms	(+ (sqrt (+ x 1)) (sqrt x))
9.0ms	(sqrt (+ x 1))

series224.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

91.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
88.0ms	(+ (sqrt (+ x 1)) (sqrt x))
44.0ms	(sqrt (+ x 1))

simplify1.0s

Counts: 87 → 87

prune741.0ms

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))))

rewrite287.0ms

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

135.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
51.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
49.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
38.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
119.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
115.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
80.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.0s

Counts: 294 → 294

prune3.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

204×	`*-un-lft-identity`
182×	`sqrt-prod`
137×	`times-frac`
129×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
68×	`distribute-lft-out`
33×	`associate-r`
27×	`associate-l`
21×	`add-exp-log`
20×	`unswap-sqr`
15×	`pow1` `associate-/r*`
13×	`add-cbrt-cube`
11×	`pow-flip`
10×	`sqrt-pow1` `associate-/r/`
7×	`sqrt-div`
6×	`div-exp` `associate-/l*`
5×	`flip3-+` `flip-+` `div-inv` `inv-pow`
4×	`pow1/2` `prod-exp` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`frac-times` `swap-sqr` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative`

Counts

4 → 251

Calls

4 calls:

Slowest

172.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
36.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
29.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series534.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

178.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
155.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
101.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
99.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.0s

Counts: 263 → 263

prune2.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes59.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

645.0ms	4208×	body	80	valid
464.0ms	1666×	body	1280	valid
447.0ms	7729×	body	80	nan
304.0ms	1214×	body	640	valid
88.0ms	618×	body	320	valid
55.0ms	294×	body	160	valid