Details

sample85.0ms

Algorithm

intervals

Results

22.0ms	61×	body	1280	valid
21.0ms	270×	body	80	nan
9.0ms	34×	body	640	valid
9.0ms	125×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize22.0ms

Local error

Found 2 expressions with local error:

3.5b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite66.0ms

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

58.0ms	(- (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series118.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

79.0ms	(- (sqrt (+ x 1)) (sqrt x))
40.0ms	(sqrt (+ x 1))

simplify1.5s

Counts: 98 → 98

prune826.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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))

rewrite75.0ms

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

40.0ms	(+ (sqrt (+ x 1)) (sqrt x))
29.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
5.0ms	(sqrt (+ x 1))

series225.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

94.0ms	(+ (sqrt (+ x 1)) (sqrt x))
89.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
42.0ms	(sqrt (+ x 1))

simplify1.5s

Counts: 102 → 102

prune800.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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))))

rewrite279.0ms

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×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `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 → 290

Calls

4 calls:

Slowest

170.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
44.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
31.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
28.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
108.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
92.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
82.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.2s

Counts: 302 → 302

prune3.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
708×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
270×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
17×	`add-exp-log`
15×	`pow1`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube`
8×	`div-exp` `hypot-def` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 479

Calls

4 calls:

Slowest

73.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
46.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
41.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
30.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
111.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
108.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
107.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.4s

Counts: 491 → 491

prune5.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

728.0ms	1769×	body	1280	valid
505.0ms	8156×	body	80	nan
312.0ms	1177×	body	640	valid
282.0ms	4039×	body	80	valid
139.0ms	656×	body	320	valid
83.0ms	359×	body	160	valid