Details

sample94.0ms

Algorithm

intervals

Results

60.0ms	104×	body	1280	valid
9.0ms	124×	body	80	valid
7.0ms	20×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b	(/ 1/2 (hypot 1 x))
0.9b	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite62.0ms

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:

0.0ms	(hypot 1 x)
14.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
7.0ms	(/ 1/2 (hypot 1 x))
38.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot 1 x)
48.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
8.0ms	(/ 1/2 (hypot 1 x))
69.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5007
3	1535
2	561
1	225
0	113

prune322.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.0b	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.4b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite37.0ms

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:

5.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
14.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
12.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))
58.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
39.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.9s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	2637
2	715
1	232
0	106

prune401.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1/8 (/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x)))) (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4))
0.0b	(* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.1b	(/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x)))
0.4b	(- 1/8 (/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
77×	`times-frac`
50×	`*-un-lft-identity`
38×	`add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
20×	`associate-/l*`
15×	`difference-of-squares`
13×	`associate-l`
8×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`associate-/r` `associate-r*` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `flip3--` `associate-*r/` `associate-/r/` `flip--` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out`

Counts

4 → 153

Calls

4 calls:

100.0ms	(/ (- 1/8 (/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x)))) (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4))
57.0ms	(* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))
20.0ms	(/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x)))
20.0ms	(- 1/8 (/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ (- 1/8 (/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x)))) (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4))
78.0ms	(* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2))
56.0ms	(/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x)))
90.0ms	(- 1/8 (/ (/ 1/8 (hypot 1 x)) (* (hypot 1 x) (hypot 1 x))))

simplify2.3s

Counts

165 → 165

Iterations

Iter	Nodes
done	5007
2	3278
1	840
0	292

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.6b

localize135.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.1b	(* (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.1b	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.4b	(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

99×	`frac-times`
89×	`pow1`
88×	`add-cbrt-cube` `add-exp-log`
59×	`associate-*r/`
48×	`flip3-+` `flip-+`
46×	`prod-exp` `cbrt-unprod`
44×	`add-sqr-sqrt`
40×	`times-frac`
35×	`pow-prod-down` `associate-*l/`
32×	`*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-undiv` `div-exp`
15×	`swap-sqr` `associate-r` `associate-l`
9×	`pow-sqr` `pow-prod-up`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-log-exp`
5×	`pow-plus`
4×	`insert-posit16` `div-inv` `unswap-sqr`
3×	`pow2` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 249

Calls

4 calls:

149.0ms	(* (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
124.0ms	(* (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
25.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
8.0ms	(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
145.0ms	(* (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)))
38.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
109.0ms	(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))

simplify3.4s

Counts

261 → 261

Iterations

Iter	Nodes
done	5001
2	4912
1	944
0	261

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.6b

regimes133.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.4b and baseline of 14.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	2797×	body	1280	valid
460.0ms	167×	body	160	valid
322.0ms	4095×	body	80	valid
174.0ms	613×	body	640	valid
68.0ms	328×	body	320	valid