Details

sample91.0ms

Algorithm

intervals

Results

50.0ms	93×	body	1280	valid
12.0ms	26×	body	640	valid
12.0ms	125×	body	80	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	90
5	90
4	71
3	55
2	39
1	21
0	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

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:

14.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0ms	(hypot 1 x)
12.0ms	(/ 1/2 (hypot 1 x))
42.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
3.0ms	(hypot 1 x)
10.0ms	(/ 1/2 (hypot 1 x))
74.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	2028
4	2028
3	1859
2	563
1	225
0	113

prune331.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.7b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `insert-posit16` `distribute-lft-out`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `sqrt-prod` `div-inv` `difference-of-squares`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out--`

Counts

4 → 87

Calls

4 calls:

28.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
7.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))
12.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
6.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))
60.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	2006
3	2006
2	714
1	232
0	106

prune460.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
0.2b	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
0.4b	(* (+ (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))) (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))))
1.3b	(- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
110×	`sqrt-prod`
88×	`times-frac`
68×	`*-un-lft-identity`
62×	`add-cube-cbrt`
20×	`difference-of-squares`
14×	`associate-r`
12×	`associate-/r` `associate-/l`
10×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
4×	`frac-times` `flip3--` `associate-l` `insert-posit16` `flip--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `cbrt-undiv` `sqrt-undiv` `clear-num` `frac-2neg` `distribute-lft-in` `div-exp` `associate-l/` `associate-r/` `div-inv` `distribute-lft-out--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 191

Calls

4 calls:

5.0ms	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
5.0ms	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
70.0ms	(* (+ (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))) (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))))
11.0ms	(- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
84.0ms	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
316.0ms	(* (+ (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))) (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))))
132.0ms	(- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))

simplify1.2s

Counts

203 → 203

Iterations

Iter	Nodes
done	2001
3	2001
2	1183
1	377
0	165

prune934.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
0.4b	(* (+ (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))) (log (exp (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))))))
1.3b	(log (exp (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))))
1.3b	(- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
81×	`sqrt-prod`
60×	`times-frac`
47×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`log-pow` `difference-of-squares`
28×	`exp-prod`
18×	`associate-r`
15×	`log-prod`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `exp-sum` `associate-/l` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sub-neg` `associate-l` `insert-posit16`
3×	`distribute-lft-out--`
2×	`associate-*l/`
1×	`cbrt-undiv` `log-div` `sqrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

9.0ms	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
203.0ms	(* (+ (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))) (log (exp (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))))))
56.0ms	(log (exp (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))))
17.0ms	(- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))

series663.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sqrt 1/2) (sqrt (hypot 1 x)))
310.0ms	(* (+ (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))) (log (exp (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x)))))))
140.0ms	(log (exp (- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))))
134.0ms	(- (sqrt 1/2) (/ (sqrt 1/2) (sqrt (hypot 1 x))))

simplify1.2s

Counts

175 → 175

Iterations

Iter	Nodes
done	2007
3	2007
2	1012
1	417
0	195

prune815.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 15.4b

regimes120.0ms

Accuracy

0% (0.8b remaining)

Error of 15.2b against oracle of 14.4b and baseline of 15.2b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.2s	2787×	body	1280	valid
963.0ms	4079×	body	80	valid
362.0ms	651×	body	640	valid
113.0ms	324×	body	320	valid
40.0ms	159×	body	160	valid