Details

sample63.0ms

Algorithm

intervals

Results

14.0ms	312×	body	80	nan
10.0ms	49×	body	1280	valid
8.0ms	48×	body	640	valid
6.0ms	123×	body	80	valid
4.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify7.0ms

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: 31.6b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite74.0ms

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:

13.0ms	(sqrt (+ x 1.0))
59.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ x 1.0))
76.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.0s

Counts

41 → 41

Iterations

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

prune186.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
20×	`sqrt-prod`
18×	`times-frac`
17×	`distribute-lft-out`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

2 → 57

Calls

2 calls:

6.0ms	(sqrt (+ x 1.0))
44.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series243.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
207.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify1.1s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
2	1385
1	333
0	142

prune282.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite65.0ms

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:

22.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
29.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
7.0ms	(cbrt (+ x 1.0))

series589.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
126.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
114.0ms	(cbrt (+ x 1.0))
129.0ms	(cbrt (+ x 1.0))

simplify3.8s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	4828
1	879
0	327

prune767.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `cbrt-div` `add-cube-cbrt`
4×	`pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series503.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (+ x 1.0))
140.0ms	(cbrt (+ x 1.0))
97.0ms	(cbrt (+ x 1.0))
137.0ms	(cbrt (+ x 1.0))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	2011
2	526
1	176
0	77

prune613.0ms

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

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

807.0ms	1648×	body	1280	valid
358.0ms	7998×	body	80	nan
243.0ms	4138×	body	80	valid
191.0ms	1266×	body	640	valid
105.0ms	668×	body	320	valid
20.0ms	280×	body	160	valid