Details

sample51.0ms

Algorithm

intervals

Results

11.0ms	54×	body	1280	valid
9.0ms	225×	body	80	nan
6.0ms	134×	body	80	valid
5.0ms	33×	body	640	valid
3.0ms	26×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite45.0ms

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` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 35

Calls

2 calls:

8.0ms	(sqrt (+ x 1.0))
35.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series128.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(sqrt (+ x 1.0))
87.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts

41 → 41

Iterations

Iter	Nodes
done	5006
3	1605
2	539
1	193
0	86

prune240.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.7b	(- (+ x 1.0) x)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt` `times-frac` `sqrt-prod`
19×	`add-cube-cbrt`
16×	`distribute-lft-out--`
11×	`add-log-exp`
8×	`difference-of-squares`
6×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
5×	`pow1`
3×	`flip3-+` `flip-+`
2×	`sum-log` `flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `associate--l+` `div-inv`

Counts

4 → 112

Calls

4 calls:

9.0ms	(sqrt (+ x 1.0))
42.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
131.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
30.0ms	(- (+ x 1.0) x)

series286.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ x 1.0))
86.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
155.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify1.7s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1696
1	489
0	188

prune559.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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)))

rewrite89.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 71

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
33.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
45.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series349.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(sqrt (+ x 1.0))
96.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
195.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5066
3	3825
2	1131
1	371
0	156

prune365.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ x 1.0)))
0.0b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 161

Calls

4 calls:

13.0ms	(sqrt (sqrt (+ x 1.0)))
13.0ms	(sqrt (sqrt (+ x 1.0)))
49.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
80.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (sqrt (+ x 1.0)))
158.0ms	(sqrt (sqrt (+ x 1.0)))
201.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
57.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify3.1s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
3	4926
2	1591
1	578
0	251

prune735.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample1.9s

Algorithm

intervals

Results

710.0ms	7962×	body	80	nan
372.0ms	1731×	body	1280	valid
241.0ms	1264×	body	640	valid
140.0ms	4053×	body	80	valid
98.0ms	633×	body	320	valid
21.0ms	319×	body	160	valid