Details

sample59.0ms

Algorithm

intervals

Results

31.0ms	91×	body	1280	valid
8.0ms	131×	body	80	valid
6.0ms	21×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify106.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

0.0ms	(hypot 1 x)
10.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
5.0ms	(/ 1/2 (hypot 1 x))
88.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(hypot 1 x)
74.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
94.0ms	(/ 1/2 (hypot 1 x))
140.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify3.6s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4680
2	1393
1	511
0	212

prune471.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
11×	`flip3-+` `flip-+` `add-log-exp`
10×	`pow1` `sqrt-div`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-l` `sqrt-prod` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `fma-def` `associate-r` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `sum-log` `distribute-rgt-out` `fma-neg` `prod-diff` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `associate-l/` `associate-r/` `pow-prod-up` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `sub-neg` `frac-2neg` `distribute-lft1-in` `flip3--` `diff-log` `cube-unmult` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--`

Counts

4 → 125

Calls

4 calls:

5.0ms	(/ 1/2 (hypot 1 x))
110.0ms	(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
129.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
9.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1/2 (hypot 1 x))
193.0ms	(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
150.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
188.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify2.4s

Counts

137 → 137

Iterations

Iter	Nodes
done	5008
2	2741
1	768
0	272

prune865.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.5b	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
1.2b	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

rewrite594.0ms

Algorithm

rewrite-expression-head

Rules

264×	`sqrt-div`
144×	`frac-times`
134×	`sqrt-pow1`
129×	`pow1`
120×	`flip3-+` `flip-+`
63×	`pow-prod-up`
48×	`associate-l/` `associate-r/`
46×	`pow1/2`
37×	`pow-plus`
35×	`add-sqr-sqrt`
31×	`pow-prod-down`
25×	`*-un-lft-identity`
18×	`associate-l`
16×	`add-cube-cbrt`
15×	`pow-sqr`
14×	`sqrt-prod`
12×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
8×	`cube-unmult`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `swap-sqr` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-neg` `prod-diff` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`distribute-rgt-in` `distribute-lft-in` `difference-of-squares`
1×	`pow2` `sub-neg` `rem-square-sqrt` `flip3--` `sqrt-unprod` `diff-log` `flip--`

Counts

4 → 274

Calls

4 calls:

123.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
132.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
303.0ms	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
6.0ms	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

series559.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
121.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
128.0ms	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))))
174.0ms	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))))

simplify2.4s

Counts

286 → 286

Iterations

Iter	Nodes
done	5004
2	2144
1	749
0	352

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2)
0.5b	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2)))
1.2b	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2))))

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
20×	`sqrt-div`
17×	`pow1` `sqrt-prod`
15×	`associate-r` `add-cube-cbrt`
12×	`sqrt-pow1` `flip3-+` `associate-*l/` `flip-+`
11×	`associate-l`
9×	`unpow-prod-down` `add-exp-log`
8×	`frac-times` `add-cbrt-cube` `pow-prod-up`
6×	`pow1/2` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `pow-plus` `associate-*r/` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`pow-unpow` `fma-neg` `prod-diff` `pow-prod-down` `sqr-pow`
2×	`prod-exp` `*-commutative` `cbrt-unprod`
1×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3--` `sqrt-unprod` `diff-log` `cube-unmult` `pow-exp` `flip--`

Counts

4 → 131

Calls

4 calls:

127.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
37.0ms	(pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2)
300.0ms	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2)))
10.0ms	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
133.0ms	(pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2)
153.0ms	(* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2)))
209.0ms	(- 1 (* (sqrt (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (pow (+ (/ 1/2 (hypot 1 x)) 1/2) 3/2))))

simplify2.3s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	2108
1	681
0	245

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes169.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch175.0ms

Steps

Iters	Range		Point
9	1.7877411926250683e-07	0.113095154289168	0.01238224451402385
8	-0.018988436667384805	-1.4244285555183042e-05	-0.013043377732168978

simplify15.0ms

Iterations

Iter	Nodes
done	44
1	44
0	32

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2892×	body	1280	valid
486.0ms	153×	body	160	valid
396.0ms	3996×	body	80	valid
184.0ms	639×	body	640	valid
84.0ms	320×	body	320	valid