Details

sample106.0ms

Algorithm

intervals

Results

64.0ms	91×	body	1280	valid
13.0ms	125×	body	80	valid
11.0ms	26×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify92.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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:

4.0ms	(/ 1/2 (hypot 1 x))
17.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
17.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
54.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1/2 (hypot 1 x))
60.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
86.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
111.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.0s

Counts

127 → 127

Iterations

Iter	Nodes
done	2018
2	1396
1	507
0	213

prune442.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) 1))
1.0b	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`distribute-lft-out`
20×	`times-frac`
19×	`add-cube-cbrt`
8×	`sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `hypot-def` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `fma-neg` `prod-diff` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate--r+` `associate-/l/`
1×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 112

Calls

4 calls:

17.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
17.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
313.0ms	(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) 1))
6.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
89.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
1.3s	(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))) 1))
226.0ms	(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	2002
1	874
0	299

prune720.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* (* x (* x x)) (* x (* x x)))
18.0b	(- (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)) (* (* (* x x) (* x x)) 11/128))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

389×	`pow1`
157×	`pow-prod-up`
99×	`pow-prod-down`
57×	`add-cbrt-cube` `add-exp-log`
53×	`pow-sqr`
40×	`pow-plus`
38×	`prod-exp` `cbrt-unprod`
29×	`pow2`
15×	`cube-unmult`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `*-commutative`
2×	`swap-sqr` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `fma-udef` `flip--`

Counts

4 → 217

Calls

4 calls:

31.0ms	(* x (* x x))
31.0ms	(* (* x x) (* x x))
136.0ms	(* (* x (* x x)) (* x (* x x)))
12.0ms	(- (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)) (* (* (* x x) (* x x)) 11/128))

series325.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* x (* x x))
56.0ms	(* (* x x) (* x x))
85.0ms	(* (* x (* x x)) (* x (* x x)))
121.0ms	(- (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)) (* (* (* x x) (* x x)) 11/128))

simplify1.2s

Counts

229 → 229

Iterations

Iter	Nodes
done	2001
2	1275
1	466
0	170

prune428.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
18.8b	(fma (sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8))) (sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8))) (* (* (* x x) (* x x)) -11/128))
21.0b	(sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)))
21.0b	(sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
6×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

38.0ms	(* (* x x) (* x x))
0.0ms	(fma (sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8))) (sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8))) (* (* (* x x) (* x x)) -11/128))
1.0ms	(sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)))
2.0ms	(sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (* x x) (* x x))
300.0ms	(fma (sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8))) (sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8))) (* (* (* x x) (* x x)) -11/128))
231.0ms	(sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)))
315.0ms	(sqrt (fma (* (* x (* x x)) (* x (* x x))) 69/1024 (* (* x x) 1/8)))

simplify567.0ms

Counts

121 → 121

Iterations

Iter	Nodes
done	2004
2	824
1	306
0	127

prune426.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch1.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.3s	2848×	body	1280	valid
386.0ms	4058×	body	80	valid
366.0ms	626×	body	640	valid
94.0ms	316×	body	320	valid
30.0ms	152×	body	160	valid