Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	60×	body	1280	valid
7.0ms	243×	body	80	nan
4.0ms	132×	body	80	valid
4.0ms	33×	body	640	valid
2.0ms	23×	body	320	valid
0.0ms	8×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite104.0ms

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:

7.0ms	(sqrt (+ x 1.0))
96.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series149.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
113.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.5s

Counts

41 → 41

Iterations

Useful iterations: done (2.5s)

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

prune138.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite101.0ms

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))
35.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
56.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series317.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(sqrt (+ x 1.0))
81.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
195.0ms	(/ 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

prune244.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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))))

rewrite146.0ms

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:

15.0ms	(sqrt (sqrt (+ x 1.0)))
14.0ms	(sqrt (sqrt (+ x 1.0)))
52.0ms	(/ 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))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (sqrt (+ x 1.0)))
150.0ms	(sqrt (sqrt (+ x 1.0)))
211.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
50.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify3.4s

Counts

173 → 173

Iterations

Useful iterations: done (3.4s)

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

prune601.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
57×	`sqrt-prod`
36×	`times-frac`
33×	`distribute-lft-out`
26×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+`
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 → 92

Calls

3 calls:

8.0ms	(sqrt (+ x 1.0))
48.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
77.0ms	(/ (sqrt 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series406.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(sqrt (+ x 1.0))
125.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
231.0ms	(/ (sqrt 1.0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.3s

Counts

101 → 101

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	174	1596
1	379	1426
2	946	1354
3	2652	1327
done	5000	1320

prune328.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes115.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
done	12	13

end0.0ms

sample2.1s

Algorithm

intervals

Results

665.0ms	1261×	body	640	valid
406.0ms	1686×	body	1280	valid
328.0ms	7865×	body	80	nan
195.0ms	4165×	body	80	valid
133.0ms	605×	body	320	valid
19.0ms	283×	body	160	valid