Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	45×	body	640	valid
12.0ms	49×	body	1280	valid
11.0ms	249×	body	80	nan
7.0ms	137×	body	80	valid
2.0ms	12×	body	320	valid
1.0ms	13×	body	160	valid

simplify11.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize11.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))

rewrite56.0ms

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

49.0ms	(- (sqrt (+ x 1)) (sqrt x))
5.0ms	(sqrt (+ x 1))

series114.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(- (sqrt (+ x 1)) (sqrt x))
45.0ms	(sqrt (+ x 1))

simplify2.0s

Counts: 98 → 98

prune768.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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))

rewrite53.0ms

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

28.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms	(+ (sqrt (+ x 1)) (sqrt x))
4.0ms	(sqrt (+ x 1))

series207.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

94.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
72.0ms	(+ (sqrt (+ x 1)) (sqrt x))
41.0ms	(sqrt (+ x 1))

simplify1.5s

Counts: 102 → 102

prune861.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.0b	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
17×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`add-exp-log`
7×	`fma-def`
6×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u` `pow1`
4×	`insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `log1p-udef` `expm1-log1p` `clear-num` `sum-log` `frac-2neg` `1-exp` `log1p-expm1` `div-inv` `pow-flip` `inv-pow` `expm1-udef`

Counts

4 → 96

Calls

4 calls:

Slowest

47.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms	(+ (sqrt (+ x 1)) (sqrt x))
0.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

229.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
152.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
89.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
63.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.5s

Counts: 108 → 108

prune999.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.3b	(cbrt (+ x 1))
0.2b	(* (cbrt (+ x 1)) (cbrt (+ x 1)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

Slowest

46.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))

series242.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

70.0ms	(cbrt (+ x 1))
67.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
64.0ms	(cbrt (+ x 1))
41.0ms	(cbrt (+ x 1))

simplify1.6s

Counts: 119 → 119

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

514.0ms	1693×	body	1280	valid
472.0ms	7752×	body	80	nan
350.0ms	1299×	body	640	valid
241.0ms	4078×	body	80	valid
124.0ms	620×	body	320	valid
30.0ms	310×	body	160	valid