Details

sample55.0ms

Algorithm

intervals

Results

10.0ms	291×	body	80	nan
10.0ms	57×	body	1280	valid
6.0ms	43×	body	640	valid
5.0ms	128×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

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:

6.0ms	(sqrt (+ x 1.0))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series151.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(sqrt (+ x 1.0))
99.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.8s

Counts

41 → 41

Iterations

Iter	Nodes
done	5000
3	2862
2	671
1	193
0	86

prune202.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite111.0ms

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:

10.0ms	(sqrt (+ x 1.0))
26.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
69.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series352.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(sqrt (+ x 1.0))
114.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
200.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1548
1	371
0	156

prune423.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

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:

7.0ms	(sqrt (sqrt (+ x 1.0)))
7.0ms	(sqrt (sqrt (+ x 1.0)))
47.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
55.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(sqrt (sqrt (+ x 1.0)))
119.0ms	(sqrt (sqrt (+ x 1.0)))
192.0ms	(/ 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))))

simplify2.3s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	2744
1	586
0	251

prune819.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (sqrt (cbrt (+ x 1.0))))))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

360×	`sqrt-div`
178×	`cbrt-div`
140×	`frac-times`
116×	`flip3-+` `flip-+`
52×	`associate-*r/`
46×	`associate-*l/`
40×	`sqrt-pow1`
37×	`*-un-lft-identity`
32×	`cbrt-prod`
28×	`pow1`
25×	`add-sqr-sqrt`
20×	`pow1/3`
18×	`add-cube-cbrt`
17×	`associate-l`
16×	`pow-prod-down`
13×	`sqrt-prod`
12×	`pow-prod-up`
11×	`add-exp-log`
10×	`swap-sqr`
9×	`add-cbrt-cube` `distribute-lft-out`
8×	`pow1/2` `associate-r`
4×	`prod-exp` `pow-sqr` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`sqrt-unprod` `*-commutative`
1×	`pow2` `pow-plus`

Counts

4 → 197

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
7.0ms	(cbrt (+ x 1.0))
309.0ms	(* (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (sqrt (cbrt (+ x 1.0))))))
53.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (+ x 1.0))
138.0ms	(cbrt (+ x 1.0))
45.0ms	(* (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (sqrt (sqrt (cbrt (+ x 1.0))))))
142.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify1.9s

Counts

209 → 209

Iterations

Iter	Nodes
done	5001
2	2852
1	995
0	407

prune1.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes88.0ms

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

849.0ms	8152×	body	80	nan
328.0ms	1768×	body	1280	valid
153.0ms	1259×	body	640	valid
136.0ms	4038×	body	80	valid
62.0ms	632×	body	320	valid
19.0ms	303×	body	160	valid