Details

sample71.0ms

Algorithm

intervals

Results

17.0ms	293×	body	80	nan
16.0ms	54×	body	1280	valid
11.0ms	41×	body	640	valid
7.0ms	115×	body	80	valid
6.0ms	33×	body	320	valid
2.0ms	13×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune24.0ms

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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
55×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
42×	`prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `hypot-def` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 92

Calls

2 calls:

Slowest

31.0ms	(- (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series111.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

72.0ms	(- (sqrt (+ x 1)) (sqrt x))
40.0ms	(sqrt (+ x 1))

simplify1.9s

Counts: 98 → 98

prune841.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

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))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
28×	`sqrt-prod`
22×	`distribute-lft-out`
21×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
7×	`fma-def` `add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/` `hypot-def`
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 → 93

Calls

3 calls:

Slowest

54.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms	(+ (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series241.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

122.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
86.0ms	(+ (sqrt (+ x 1)) (sqrt x))
33.0ms	(sqrt (+ x 1))

simplify1.3s

Counts: 102 → 102

prune844.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite142.0ms

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×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `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 → 177

Calls

4 calls:

Slowest

62.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
59.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))
9.0ms	(sqrt (sqrt (+ x 1)))
8.0ms	(sqrt (sqrt (+ x 1)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
38.0ms	(sqrt (sqrt (+ x 1)))
36.0ms	(sqrt (sqrt (+ x 1)))
29.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.1s

Counts: 189 → 189

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

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))))))

rewrite182.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `pow-sqr`
1×	`swap-sqr` `associate-r` `*-commutative`

Counts

4 → 177

Calls

4 calls:

Slowest

163.0ms	(* (sqrt (sqrt (+ x 1))) (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (cbrt (sqrt (+ x 1))))))
6.0ms	(cbrt (sqrt (+ x 1)))
3.0ms	(cbrt (sqrt (+ x 1)))
3.0ms	(cbrt (sqrt (+ x 1)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

46.0ms	(cbrt (sqrt (+ x 1)))
45.0ms	(cbrt (sqrt (+ x 1)))
44.0ms	(cbrt (sqrt (+ x 1)))
33.0ms	(* (sqrt (sqrt (+ x 1))) (* (sqrt (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (sqrt (cbrt (sqrt (+ x 1))))))

simplify922.0ms

Counts: 189 → 189

prune3.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

701.0ms	1791×	body	1280	valid
480.0ms	7822×	body	80	nan
358.0ms	4061×	body	80	valid
347.0ms	1239×	body	640	valid
108.0ms	590×	body	320	valid
37.0ms	319×	body	160	valid