Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	245×	body	80	nan
8.0ms	47×	body	1280	valid
6.0ms	44×	body	640	valid
5.0ms	130×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid

simplify12.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize19.0ms

Local error

Found 1 expressions with local error:

3.2b	(- (sqrt (+ x 1)) (sqrt x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out`

Counts

1 → 20

Calls

1 calls:

Slowest

50.0ms

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

series75.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

75.0ms

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

simplify1.4s

Counts: 23 → 23

prune223.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `div-exp` `associate-/r/` `flip-+` `insert-posit16`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

2 → 61

Calls

2 calls:

Slowest

32.0ms	(+ (sqrt (+ x 1)) (sqrt x))
27.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

109.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
79.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify872.0ms

Counts: 67 → 67

prune609.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`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` `pow-flip`
7×	`sqrt-pow1` `pow1/2`
6×	`pow-div`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `1-exp` `inv-pow`
1×	`associate-/l/`

Counts

4 → 463

Calls

4 calls:

Slowest

81.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
56.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
40.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
23.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
140.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
128.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
104.0ms	(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify1.3s

Counts: 475 → 475

prune4.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)
0.1b	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`sqrt-prod`
12×	`distribute-lft-out`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`add-log-exp`
4×	`add-exp-log`
3×	`pow-unpow` `pow-pow` `add-cbrt-cube` `insert-posit16`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 61

Calls

3 calls:

Slowest

45.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)
32.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms	(+ (sqrt (+ x 1)) (sqrt x))

series525.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

309.0ms	(pow (sqrt (+ (sqrt (+ x 1)) (sqrt x))) -2)
131.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
84.0ms	(+ (sqrt (+ x 1)) (sqrt x))

simplify1.2s

Counts: 70 → 70

prune681.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes47.0ms

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

617.0ms	4016×	body	80	valid
559.0ms	1783×	body	1280	valid
461.0ms	7827×	body	80	nan
326.0ms	1284×	body	640	valid
91.0ms	588×	body	320	valid
74.0ms	329×	body	160	valid