Details

sample76.0ms

Algorithm

intervals

Results

19.0ms	57×	body	1280	valid
18.0ms	298×	body	80	nan
9.0ms	135×	body	80	valid
8.0ms	31×	body	640	valid
5.0ms	26×	body	320	valid
1.0ms	7×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

5.0ms	(sqrt (+ x 1))
27.0ms	(- (sqrt (+ x 1)) (sqrt x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(sqrt (+ x 1))
87.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify2.6s

Counts

43 → 43

Iterations

Iter	Nodes
5	4263
4	1592
3	732
2	350
1	159
0	81

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

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`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
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 → 78

Calls

3 calls:

5.0ms	(sqrt (+ x 1))
27.0ms	(+ (sqrt (+ x 1)) (sqrt x))
31.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(sqrt (+ x 1))
64.0ms	(+ (sqrt (+ x 1)) (sqrt x))
90.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.7s

Counts

87 → 87

Iterations

Iter	Nodes
4	2183
3	1035
2	523
1	237
0	120

prune514.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x 1)))
10.0ms	(sqrt (sqrt (+ x 1)))
39.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
46.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series199.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (sqrt (+ x 1)))
39.0ms	(sqrt (sqrt (+ x 1)))
94.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
26.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.9s

Counts

181 → 181

Iterations

Iter	Nodes
3	2049
2	964
1	432
0	211

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity`
290×	`sqrt-prod`
168×	`times-frac`
136×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
43×	`swap-sqr`
31×	`pow1`
27×	`sqrt-pow1` `associate-r` `associate-l`
16×	`unswap-sqr`
14×	`add-exp-log` `associate-/r/`
12×	`associate-/r*`
11×	`pow-flip` `inv-pow`
10×	`add-cbrt-cube`
9×	`pow1/2` `pow-prod-up` `div-inv`
7×	`flip3-+` `flip-+`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-down` `pow-sqr`
4×	`div-exp` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 282

Calls

4 calls:

51.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
43.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
38.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
167.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
123.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
98.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
113.0ms	(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

simplify1.2s

Counts

294 → 294

Iterations

Iter	Nodes
3	2040
2	881
1	442
0	229

prune2.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

783.0ms	1228×	body	640	valid
550.0ms	8131×	body	80	nan
525.0ms	1712×	body	1280	valid
302.0ms	4144×	body	80	valid
99.0ms	608×	body	320	valid
32.0ms	308×	body	160	valid