Details

sample109.0ms

Algorithm

intervals

Results

53.0ms	90×	body	1280	valid
23.0ms	18×	body	640	valid
14.0ms	129×	body	80	valid
5.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	23
2	23
1	19
0	9

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
1.7b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`sqrt-prod`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1`
4×	`insert-posit16` `difference-of-squares`
3×	`associate-/r` `associate-/l` `distribute-lft-out--`
2×	`sqrt-div` `distribute-lft-out`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

4 → 73

Calls

4 calls:

7.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
11.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
36.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
10.0ms	(/ 1/2 (hypot 1 x))
2.0ms	(hypot 1 x)
63.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify7.1s

Counts

85 → 85

Iterations

Iter	Nodes
4	4136
3	1270
2	431
1	208
0	113

prune803.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `insert-posit16`
3×	`associate-/r` `associate-/l`
2×	`difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1/2 (hypot 1 x))
1.0ms	(hypot 1 x)
1.0ms	(hypot 1 x)
47.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify6.7s

Counts

72 → 72

Iterations

Iter	Nodes
4	4143
3	1149
2	352
1	148
0	80

prune672.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `insert-posit16`
3×	`associate-/r` `associate-/l`
2×	`difference-of-squares`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1/2 (hypot 1 x))
1.0ms	(hypot 1 x)
1.0ms	(hypot 1 x)
46.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify6.0s

Counts

72 → 72

Iterations

Iter	Nodes
4	4143
3	1149
2	352
1	148
0	80

prune762.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(hypot 1 x)
1.2b	(- 1/2 (/ 1/2 (hypot 1 x)))
1.3b	(log (exp (- 1/2 (/ 1/2 (hypot 1 x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
7×	`log-pow`
6×	`exp-prod` `add-cube-cbrt` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `difference-of-squares`
2×	`sub-neg` `times-frac` `exp-sum` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 54

Calls

4 calls:

0.0ms	(hypot 1 x)
0.0ms	(hypot 1 x)
10.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
22.0ms	(log (exp (- 1/2 (/ 1/2 (hypot 1 x)))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot 1 x)
3.0ms	(hypot 1 x)
50.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
43.0ms	(log (exp (- 1/2 (/ 1/2 (hypot 1 x)))))

simplify5.9s

Counts

66 → 66

Iterations

Iter	Nodes
5	5759
4	1756
3	683
2	295
1	148
0	77

prune764.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.8b

regimes107.0ms

Accuracy

0% (0.0b remaining)

Error of 14.9b against oracle of 14.8b and baseline of 14.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	19

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.4s	2863×	body	1280	valid
414.0ms	4051×	body	80	valid
322.0ms	635×	body	640	valid
101.0ms	310×	body	320	valid
29.0ms	141×	body	160	valid