Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	60×	body	1280	valid
9.0ms	243×	body	80	nan
5.0ms	132×	body	80	valid
5.0ms	33×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite92.0ms

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:

15.0ms	(sqrt (+ x 1.0))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series127.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(sqrt (+ x 1.0))
88.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.4s

Counts

41 → 41

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	84	488
1	183	440
2	432	410
3	1028	402
4	2702	390
done	5000	382

prune112.0ms

Pruning

3 alts after pruning (2 fresh and 1 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))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite113.0ms

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:

7.0ms	(sqrt (+ x 1.0))
45.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
58.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series348.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(sqrt (+ x 1.0))
86.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
210.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.8s

Counts

80 → 80

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	152	1125
1	343	1018
2	891	935
3	2607	919
done	5000	915

prune284.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

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-exp-log` `add-cbrt-cube` `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-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

19.0ms	(sqrt (sqrt (+ x 1.0)))
11.0ms	(sqrt (sqrt (+ x 1.0)))
50.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
82.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series522.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt (sqrt (+ x 1.0)))
132.0ms	(sqrt (sqrt (+ x 1.0)))
223.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
43.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify3.3s

Counts

173 → 173

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	249	2955
1	523	1830
2	1399	1719
3	4228	1650
done	5001	1631

prune531.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (cbrt 1.0)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

135×	`*-un-lft-identity`
112×	`times-frac`
56×	`sqrt-prod`
53×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
40×	`associate-/r*`
36×	`cbrt-prod`
15×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`cbrt-undiv` `div-exp`
5×	`add-log-exp`
4×	`pow1`
3×	`div-inv`
2×	`flip3-+` `sqrt-div` `prod-exp` `cbrt-unprod` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `associate-/r/` `associate-/l*`

Counts

3 → 130

Calls

3 calls:

9.0ms	(sqrt (+ x 1.0))
41.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
93.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (cbrt 1.0)))

series416.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(sqrt (+ x 1.0))
105.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
271.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ (sqrt (+ x 1.0)) (sqrt x)) (cbrt 1.0)))

simplify1.5s

Counts

139 → 139

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	253	2695
1	611	2447
2	1908	2272
done	5000	2209

prune370.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	12	16
done	12	16

end0.0ms

sample1.9s

Algorithm

intervals

Results

717.0ms	1686×	body	1280	valid
306.0ms	7865×	body	80	nan
206.0ms	1261×	body	640	valid
185.0ms	4165×	body	80	valid
93.0ms	605×	body	320	valid
17.0ms	283×	body	160	valid