Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	270×	body	80	nan
6.0ms	54×	body	1280	valid
3.0ms	135×	body	80	valid
3.0ms	31×	body	640	valid
1.0ms	21×	body	320	valid
1.0ms	15×	body	160	valid

simplify3.0ms

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: 29.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite70.0ms

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:

12.0ms	(sqrt (+ x 1.0))
56.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series145.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(sqrt (+ x 1.0))
94.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.6s

Counts

41 → 41

Iterations

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

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.0b	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
3.2b	(- (+ x 1.0) x)

rewrite244.0ms

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:

6.0ms	(sqrt (+ x 1.0))
36.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
164.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(- (+ x 1.0) x)

series379.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
110.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
235.0ms	(/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(- (+ x 1.0) x)

simplify1.4s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1696
1	489
0	188

prune527.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))

rewrite147.0ms

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:

12.0ms	(sqrt (+ x 1.0))
56.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
74.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series371.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(sqrt (+ x 1.0))
94.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
221.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify2.5s

Counts

80 → 80

Iterations

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

prune470.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 250

Calls

4 calls:

47.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
45.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
64.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
251.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

538.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
194.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
221.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
262.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify2.2s

Counts

262 → 262

Iterations

Iter	Nodes
done	5000
2	1879
1	689
0	310

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes96.0ms

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
done	9
1	9
0	7

end0.0ms

sample1.9s

Algorithm

intervals

Results

667.0ms	7925×	body	80	nan
396.0ms	1729×	body	1280	valid
254.0ms	4039×	body	80	valid
172.0ms	1249×	body	640	valid
108.0ms	659×	body	320	valid
21.0ms	324×	body	160	valid