Details

sample59.0ms

Algorithm

intervals

Results

29.0ms	81×	body	1280	valid
10.0ms	148×	body	80	valid
6.0ms	19×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

13.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
16.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
23.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
125.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(/ 1.0 (hypot 1.0 x))
123.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.7s

Counts

78 → 78

Iterations

Useful iterations: 4 (2.2s)

Iter	Nodes	Cost
0	112	1034
1	223	951
2	538	887
3	1394	885
4	4985	881
done	5000	881

prune276.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.7b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+`

Counts

4 → 81

Calls

4 calls:

11.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(/ 1.0 (hypot 1.0 x))
53.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.8s

Counts

93 → 93

Iterations

Useful iterations: 3 (700.0ms)

Iter	Nodes	Cost
0	112	1111
1	244	1028
2	720	960
3	2865	953
done	5002	953

prune422.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r/` `associate-/r` `associate-/l*` `add-log-exp`
4×	`associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `sqrt-div` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip-+`

Counts

4 → 85

Calls

4 calls:

19.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
16.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(/ 1.0 (hypot 1.0 x))
39.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify2.2s

Counts

97 → 97

Iterations

Useful iterations: 3 (854.0ms)

Iter	Nodes	Cost
0	135	1213
1	301	1136
2	839	1066
3	3029	1062
done	5001	1062

prune370.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
2.3b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
9×	`log-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `associate--r+` `add-log-exp`
5×	`pow1` `distribute-rgt-in` `distribute-lft-in`
4×	`associate--l+`
3×	`sub-neg` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 101

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
20.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
8.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
39.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
8.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: 3 (436.0ms)

Iter	Nodes	Cost
0	137	1333
1	252	1199
2	578	1087
3	1773	1083
done	5000	1083

prune542.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 12.5b

regimes112.0ms

Accuracy

0% (0.0b remaining)

Error of 14.7b against oracle of 14.6b and baseline of 14.7b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	28
1	21	28
done	21	28

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.7s	2825×	body	1280	valid
244.0ms	4098×	body	80	valid
164.0ms	619×	body	640	valid
57.0ms	311×	body	320	valid
18.0ms	147×	body	160	valid