Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	288×	body	80	nan
9.0ms	55×	body	1280	valid
5.0ms	142×	body	80	valid
4.0ms	31×	body	640	valid
2.0ms	22×	body	320	valid
0.0ms	6×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite100.0ms

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:

11.0ms	(sqrt (+ x 1.0))
88.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series137.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(sqrt (+ x 1.0))
99.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts

41 → 41

Iterations

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

prune136.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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)))

rewrite134.0ms

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:

11.0ms	(sqrt (+ x 1.0))
48.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
70.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series393.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(sqrt (+ x 1.0))
101.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
241.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify757.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1548
1	371
0	156

prune318.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
0.2b	(cbrt (+ 1.0 x))
0.2b	(cbrt (+ 1.0 x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-/r` `associate-l` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

36.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
20.0ms	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
6.0ms	(cbrt (+ 1.0 x))
6.0ms	(cbrt (+ 1.0 x))

series677.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
156.0ms	(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
149.0ms	(cbrt (+ 1.0 x))
119.0ms	(cbrt (+ 1.0 x))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	4262
1	880
0	328

prune853.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
0.1b	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity`
700×	`sqrt-prod`
594×	`times-frac`
280×	`distribute-lft-out`
254×	`add-sqr-sqrt`
252×	`add-cube-cbrt`
36×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
14×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 445

Calls

4 calls:

58.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
28.0ms	(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
39.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
123.0ms	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.7s

Counts

4 → 12

Calls

4 calls:

210.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
263.0ms	(sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))
543.0ms	(/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))
671.0ms	(/ (/ 1.0 (sqrt (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify1.9s

Counts

457 → 457

Iterations

Iter	Nodes
done	5000
2	4280
1	1140
0	478

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes99.0ms

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

sample2.1s

Algorithm

intervals

Results

792.0ms	7906×	body	80	nan
384.0ms	1654×	body	1280	valid
229.0ms	4072×	body	80	valid
175.0ms	1305×	body	640	valid
71.0ms	670×	body	320	valid
21.0ms	299×	body	160	valid