Details

sample88.0ms

Algorithm

intervals

Results

32.0ms	53×	body	1280	valid
14.0ms	209×	body	80	nan
11.0ms	137×	body	80	valid
10.0ms	36×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	11×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize20.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (sqrt (+ x 1)) (sqrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`

Counts

1 → 71

Calls

1 calls:

Slowest

52.0ms

(- (sqrt (+ x 1)) (sqrt x))

series88.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

88.0ms

(- (sqrt (+ x 1)) (sqrt x))

simplify539.0ms

Counts: 122 → 74

prune588.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 72

Calls

2 calls:

Slowest

47.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
44.0ms	(+ (sqrt (+ x 1)) (sqrt x))

series173.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

92.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
81.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify955.0ms

Counts: 90 → 78

prune605.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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

36.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))
5.0ms	(cbrt (+ x 1))

series185.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

50.0ms	(cbrt (+ x 1))
47.0ms	(cbrt (+ x 1))
47.0ms	(cbrt (+ x 1))
40.0ms	(* (cbrt (+ x 1)) (cbrt (+ x 1)))

simplify712.0ms

Counts: 149 → 119

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

Slowest

37.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
4.0ms	(cbrt (+ x 1))
4.0ms	(cbrt (sqrt (+ x 1)))
3.0ms	(cbrt (sqrt (+ x 1)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

59.0ms	(cbrt (sqrt (+ x 1)))
50.0ms	(cbrt (+ x 1))
48.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))
42.0ms	(cbrt (sqrt (+ x 1)))

simplify433.0ms

Counts: 187 → 141

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

628.0ms	1648×	body	1280	valid
482.0ms	7809×	body	80	nan
273.0ms	1291×	body	640	valid
218.0ms	4129×	body	80	valid
97.0ms	622×	body	320	valid
33.0ms	310×	body	160	valid