Details

sample86.0ms

Algorithm

intervals

Results

17.0ms	54×	body	1280	valid
17.0ms	267×	body	80	nan
10.0ms	41×	body	640	valid
9.0ms	134×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify18.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize23.0ms

Local error

Found 1 expressions with local error:

3.3b	(- (sqrt (+ x 1)) (sqrt x))

rewrite56.0ms

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

54.0ms

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

series83.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

83.0ms

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

simplify2.2s

Counts: 74 → 74

prune674.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite83.0ms

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

49.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
34.0ms	(+ (sqrt (+ x 1)) (sqrt x))

series194.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

104.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
89.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts: 78 → 78

prune737.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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

rewrite89.0ms

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

60.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
27.0ms	(+ (sqrt (+ x 1)) (sqrt x))
0.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
0.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(expm1 (log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
162.0ms	(log1p (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
110.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
62.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts: 108 → 108

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt`
9×	`pow1` `times-frac`
8×	`sqrt-pow1` `sqrt-div` `add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `div-exp` `flip-+` `distribute-lft-out`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 95

Calls

4 calls:

Slowest

11.0ms	(sqrt (sqrt (+ x 1)))
11.0ms	(sqrt (sqrt (+ x 1)))
8.0ms	(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
0.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))

series443.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(/ 1 (fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x)))
140.0ms	(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (sqrt x))
48.0ms	(sqrt (sqrt (+ x 1)))
40.0ms	(sqrt (sqrt (+ x 1)))

simplify1.9s

Counts: 107 → 107

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

744.0ms	1222×	body	640	valid
626.0ms	7971×	body	80	nan
529.0ms	1717×	body	1280	valid
233.0ms	4134×	body	80	valid
136.0ms	627×	body	320	valid
32.0ms	300×	body	160	valid