Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	62×	body	1280	valid
5.0ms	231×	body	80	nan
3.0ms	46×	body	640	valid
2.0ms	116×	body	80	valid
1.0ms	23×	body	320	valid
0.0ms	9×	body	160	valid

simplify13.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

6.0ms	(sqrt (+ x 1.0))
46.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (+ x 1.0))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify729.0ms

Counts: 41 → 41

prune78.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
27.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt (+ x 1.0))
60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
129.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify412.0ms

Counts: 80 → 80

prune163.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

41.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
38.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
182.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
128.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
128.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
151.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify1.3s

Counts: 262 → 262

prune514.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
82×	`sqrt-prod`
46×	`times-frac`
40×	`distribute-lft-out`
34×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `sqrt-div` `associate-/r/`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `div-inv`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`sqrt-undiv` `sqrt-unprod` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

41.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
34.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
39.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
145.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
128.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
151.0ms	(/ (* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify845.0ms

Counts: 144 → 144

prune371.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

541.0ms	1755×	body	1280	valid
216.0ms	8124×	body	80	nan
93.0ms	1223×	body	640	valid
88.0ms	4064×	body	80	valid
62.0ms	626×	body	320	valid
13.0ms	332×	body	160	valid