Details

sample89.0ms

Algorithm

intervals

Results

56.0ms	90×	body	1280	valid
11.0ms	134×	body	80	valid
6.0ms	16×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	7×	body	160	valid

simplify79.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
6	114
5	111
4	89
3	69
2	43
1	21
0	9

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
2.4b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
21×	`prod-diff`
20×	`sqrt-prod`
10×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `fma-def` `fma-neg` `associate-/l` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+` `hypot-def`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `div-inv` `flip--`

Counts

4 → 115

Calls

4 calls:

22.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
12.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms	(/ 1/2 (hypot 1 x))
51.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
69.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
92.0ms	(/ 1/2 (hypot 1 x))
147.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	2001
3	2001
2	1398
1	507
0	213

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
1.9b	(- (- 1 (/ 1/2 (hypot 1 x))) 1/2)

rewrite509.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
126×	`*-un-lft-identity`
102×	`prod-diff`
101×	`add-cube-cbrt`
82×	`times-frac`
41×	`associate--l+`
21×	`difference-of-squares`
11×	`fma-neg` `add-log-exp`
8×	`add-cbrt-cube` `add-exp-log` `div-inv` `distribute-lft-out--`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `flip--`
1×	`associate--l-`

Counts

4 → 215

Calls

4 calls:

16.0ms	(- 1 (/ 1/2 (hypot 1 x)))
7.0ms	(/ 1/2 (hypot 1 x))
9.0ms	(/ 1/2 (hypot 1 x))
470.0ms	(- (- 1 (/ 1/2 (hypot 1 x))) 1/2)

series359.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- 1 (/ 1/2 (hypot 1 x)))
84.0ms	(/ 1/2 (hypot 1 x))
81.0ms	(/ 1/2 (hypot 1 x))
116.0ms	(- (- 1 (/ 1/2 (hypot 1 x))) 1/2)

simplify1.5s

Counts

227 → 227

Iterations

Iter	Nodes
done	2001
3	2001
2	1833
1	725
0	286

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.5b	(- 1 (sqrt (/ 1/2 (hypot 1 x))))
29.4b	(fma (+ 1 (sqrt (/ 1/2 (hypot 1 x)))) (- 1 (sqrt (/ 1/2 (hypot 1 x)))) -1/2)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`sqrt-prod`
65×	`*-un-lft-identity`
59×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
6×	`pow1` `add-log-exp` `difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `rem-sqrt-square` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `flip--`

Counts

4 → 141

Calls

4 calls:

2.0ms	(sqrt (/ 1/2 (hypot 1 x)))
2.0ms	(sqrt (/ 1/2 (hypot 1 x)))
9.0ms	(- 1 (sqrt (/ 1/2 (hypot 1 x))))
0.0ms	(fma (+ 1 (sqrt (/ 1/2 (hypot 1 x)))) (- 1 (sqrt (/ 1/2 (hypot 1 x)))) -1/2)

series844.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(sqrt (/ 1/2 (hypot 1 x)))
164.0ms	(sqrt (/ 1/2 (hypot 1 x)))
148.0ms	(- 1 (sqrt (/ 1/2 (hypot 1 x))))
365.0ms	(fma (+ 1 (sqrt (/ 1/2 (hypot 1 x)))) (- 1 (sqrt (/ 1/2 (hypot 1 x)))) -1/2)

simplify1.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	2005
3	2005
2	1177
1	544
0	256

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.1b	(sqrt (/ 1/2 (hypot 1 x)))
0.7b	(* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))
1.9b	(- (- 1 (* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))) 1/2)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
92×	`sqrt-prod`
66×	`*-un-lft-identity`
62×	`times-frac`
60×	`add-cube-cbrt`
21×	`pow1`
18×	`swap-sqr` `prod-diff`
16×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
9×	`add-log-exp` `difference-of-squares` `unswap-sqr`
6×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `div-inv`
5×	`fma-neg` `associate--l+` `pow-prod-up`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u`
3×	`diff-log` `pow-prod-down` `pow-sqr`
2×	`sub-neg`
1×	`associate--l-` `pow2` `frac-times` `rem-square-sqrt` `pow-plus` `flip3--` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

5.0ms	(sqrt (/ 1/2 (hypot 1 x)))
4.0ms	(sqrt (/ 1/2 (hypot 1 x)))
30.0ms	(* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))
49.0ms	(- (- 1 (* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))) 1/2)

series698.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (/ 1/2 (hypot 1 x)))
146.0ms	(sqrt (/ 1/2 (hypot 1 x)))
220.0ms	(* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))
190.0ms	(- (- 1 (* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))) 1/2)

simplify1.3s

Counts

202 → 202

Iterations

Iter	Nodes
done	2006
3	2006
2	1384
1	542
0	257

prune2.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 30.3b

bsearch1.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.2s	2799×	body	1280	valid
537.0ms	4097×	body	80	valid
285.0ms	624×	body	640	valid
171.0ms	321×	body	320	valid
31.0ms	159×	body	160	valid