Details

sample92.0ms

Algorithm

intervals

Results

39.0ms	84×	body	1280	valid
12.0ms	133×	body	80	valid
8.0ms	23×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	25
3	25
2	23
1	19
0	9

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

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	(+ 1/2 (/ 1/2 (hypot 1 x)))
2.2b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite103.0ms

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:

18.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
8.0ms	(/ 1/2 (hypot 1 x))
19.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
56.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
106.0ms	(/ 1/2 (hypot 1 x))
87.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
186.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.6s

Counts

127 → 127

Iterations

Iter	Nodes
3	2798
2	1136
1	488
0	213

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
1.6b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
56×	`add-cube-cbrt`
46×	`times-frac`
39×	`prod-diff`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `fma-neg`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `difference-of-squares`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 138

Calls

4 calls:

8.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
82.0ms	(/ 1/2 (hypot 1 x))
89.0ms	(/ 1/2 (hypot 1 x))
93.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.7s

Counts

150 → 150

Iterations

Iter	Nodes
3	3717
2	1403
1	537
0	217

prune1.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(cbrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.5b	(* (cbrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (cbrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.6b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
49×	`add-cube-cbrt`
39×	`prod-diff`
32×	`cbrt-prod`
28×	`times-frac`
16×	`cbrt-div`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `div-inv`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

4 → 150

Calls

4 calls:

9.0ms	(cbrt (+ 1/2 (/ 1/2 (hypot 1 x))))
8.0ms	(cbrt (+ 1/2 (/ 1/2 (hypot 1 x))))
50.0ms	(* (cbrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (cbrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
8.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series574.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (+ 1/2 (/ 1/2 (hypot 1 x))))
169.0ms	(cbrt (+ 1/2 (/ 1/2 (hypot 1 x))))
156.0ms	(* (cbrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (cbrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
90.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.9s

Counts

162 → 162

Iterations

Iter	Nodes
3	5388
2	1776
1	656
0	270

prune2.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* -3/16 (* (* x x) (* x x)))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
19.0b	(fma (* (* (* x x) (* x x)) (* x x)) 5/32 (* -3/16 (* (* x x) (* x x))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

244×	`pow1`
72×	`pow-prod-up`
59×	`pow-prod-down`
46×	`add-cbrt-cube` `add-exp-log`
44×	`pow-sqr`
36×	`pow-plus`
29×	`prod-exp` `cbrt-unprod`
26×	`pow2`
6×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `*-commutative` `unswap-sqr`
2×	`swap-sqr`
1×	`fma-udef`

Counts

4 → 174

Calls

4 calls:

101.0ms	(* -3/16 (* (* x x) (* x x)))
27.0ms	(* (* x x) (* x x))
34.0ms	(* (* x x) (* x x))
0.0ms	(fma (* (* (* x x) (* x x)) (* x x)) 5/32 (* -3/16 (* (* x x) (* x x))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* -3/16 (* (* x x) (* x x)))
40.0ms	(* (* x x) (* x x))
36.0ms	(* (* x x) (* x x))
232.0ms	(fma (* (* (* x x) (* x x)) (* x x)) 5/32 (* -3/16 (* (* x x) (* x x))))

simplify949.0ms

Counts

186 → 186

Iterations

Iter	Nodes
3	2034
2	604
1	203
0	97

prune2.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes65.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.5b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	28

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	2878×	body	1280	valid
396.0ms	4009×	body	80	valid
303.0ms	646×	body	640	valid
95.0ms	319×	body	320	valid
28.0ms	148×	body	160	valid