Details

sample92.0ms

Algorithm

intervals

Results

52.0ms	90×	body	1280	valid
14.0ms	134×	body	80	valid
8.0ms	16×	body	640	valid
3.0ms	9×	body	320	valid
1.0ms	7×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	23
2	23
1	19
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize29.0ms

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)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`times-frac`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`insert-posit16` `difference-of-squares`
3×	`associate-/r` `distribute-lft-out` `associate-/l` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+`
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 → 78

Calls

4 calls:

7.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
6.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms	(/ 1/2 (hypot 1 x))
21.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
27.0ms	(+ 1/2 (/ 1/2 (hypot 1 x)))
6.0ms	(/ 1/2 (hypot 1 x))
78.0ms	(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify10.4s

Counts

90 → 90

Iterations

Iter	Nodes
4	6157
3	1803
2	562
1	230
0	118

prune308.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

14.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
4.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
13.0ms	(/ 1/2 (hypot 1 x))
10.0ms	(/ 1/2 (hypot 1 x))
51.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify7.8s

Counts

99 → 99

Iterations

Iter	Nodes
4	4840
3	1407
2	510
1	213
0	106

prune456.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

localize29.0ms

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) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1) (+ (/ 1/2 (hypot 1 x)) 1/2)))
1.9b	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite668.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
42×	`distribute-lft-out`
24×	`add-sqr-sqrt`
21×	`times-frac`
19×	`add-cube-cbrt`
18×	`add-log-exp`
16×	`flip3-+` `flip-+`
10×	`pow1`
8×	`sum-log` `add-cbrt-cube` `frac-add` `add-exp-log`
7×	`associate-/r` `associate-l*`
6×	`sqrt-div` `associate-/r/`
5×	`sqrt-prod`
4×	`frac-times` `associate-r` `insert-posit16`
3×	`associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `associate-l/` `associate-r/` `pow-prod-up` `flip--` `associate--r+` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `associate-+r+` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `cube-unmult` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 133

Calls

4 calls:

86.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
247.0ms	(+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1) (+ (/ 1/2 (hypot 1 x)) 1/2))
327.0ms	(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1) (+ (/ 1/2 (hypot 1 x)) 1/2)))
4.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
82.0ms	(+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1) (+ (/ 1/2 (hypot 1 x)) 1/2))
246.0ms	(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1) (+ (/ 1/2 (hypot 1 x)) 1/2)))
110.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
2	2580
1	636
0	202

prune577.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))))
0.5b	(* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))
0.5b	(pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
1.9b	(- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

3215×	`flip3-+` `flip-+`
2636×	`frac-add`
2468×	`frac-times`
2396×	`sqrt-div`
1130×	`associate-/r/`
730×	`associate-*l/`
576×	`associate-*r/`
90×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
60×	`difference-of-squares`
54×	`times-frac`
41×	`sqr-pow`
29×	`add-cube-cbrt`
21×	`unpow-prod-down` `cube-prod`
20×	`pow1`
18×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
10×	`distribute-lft-out--`
8×	`cube-div`
7×	`pow-pow` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`cube-mult` `associate-l` `distribute-lft-out` `add-log-exp`
5×	`difference-cubes`
4×	`distribute-rgt-in` `distribute-lft-in` `insert-posit16`
3×	`pow-unpow` `associate-/r*`
2×	`sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `pow-exp` `pow-prod-up` `flip--` `rem-cube-cbrt` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `cube-unmult` `div-exp` `associate-r` `*-commutative` `div-inv`

Counts

4 → 1502

Calls

4 calls:

1.3s	(/ (- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))))
929.0ms	(* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))
24.0ms	(pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
15.0ms	(- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

series1.9s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))))
378.0ms	(* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))
131.0ms	(pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
179.0ms	(- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

simplify1.1m

Counts

1514 → 1514

Iterations

Iter	Nodes
1	17519
0	5298

prune28.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

regimes66.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	52
1	52
0	36

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.5s	2799×	body	1280	valid
317.0ms	4097×	body	80	valid
251.0ms	624×	body	640	valid
86.0ms	321×	body	320	valid
22.0ms	159×	body	160	valid