Details

sample113.0ms

Algorithm

intervals

Results

53.0ms	79×	body	1280	valid
33.0ms	150×	body	80	valid
7.0ms	14×	body	640	valid
3.0ms	9×	body	160	valid
2.0ms	4×	body	320	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	25
2	25
1	21
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(+ (/ 1/2 (hypot 1 x)) 1/2)
0.0b	(/ 1/2 (hypot 1 x))
2.4b	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite78.0ms

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:

10.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
8.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
7.0ms	(/ 1/2 (hypot 1 x))
52.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
46.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
11.0ms	(/ 1/2 (hypot 1 x))
75.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify9.5s

Counts

90 → 90

Iterations

Iter	Nodes
4	5740
3	1683
2	543
1	231
0	118

prune870.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.9b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
6×	`add-log-exp`
4×	`pow1` `insert-posit16`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
2×	`associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 99

Calls

4 calls:

14.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(/ 1/2 (hypot 1 x))
3.0ms	(/ 1/2 (hypot 1 x))
4.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))
6.0ms	(/ 1/2 (hypot 1 x))
109.0ms	(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify842.0ms

Counts

111 → 111

Iterations

Iter	Nodes
3	2093
2	513
1	190
0	87

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1/2 (hypot 1 x))
0.0b	(/ 1/2 (hypot 1 x))
0.6b	(* (* (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)))
1.8b	(- (* 1 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))))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

136×	`frac-times`
108×	`flip3-+` `sqrt-div` `flip-+`
107×	`pow1`
53×	`pow-prod-up`
44×	`associate-l/` `associate-r/`
34×	`pow-plus`
32×	`sqrt-pow1` `pow1/2`
30×	`add-sqr-sqrt`
28×	`pow-prod-down`
22×	`*-un-lft-identity`
20×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
18×	`times-frac`
13×	`pow-sqr`
11×	`cube-unmult`
8×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`insert-posit16` `associate--r+`
2×	`difference-cubes` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `pow3` `*-commutative` `flip--` `difference-of-squares`

Counts

4 → 230

Calls

4 calls:

7.0ms	(/ 1/2 (hypot 1 x))
7.0ms	(/ 1/2 (hypot 1 x))
209.0ms	(* (* (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)))
154.0ms	(- (* 1 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))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1/2 (hypot 1 x))
11.0ms	(/ 1/2 (hypot 1 x))
76.0ms	(* (* (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)))
204.0ms	(- (* 1 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))))

simplify2.4s

Counts

242 → 242

Iterations

Iter	Nodes
2	4888
1	1045
0	323

prune3.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize117.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (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)))
0.6b	(* (* (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)))
0.6b	(* (* (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)))
1.7b	(- (* (* 1 1) (* 1 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))) (* (* (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)))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

408×	`frac-times`
324×	`flip3-+` `sqrt-div` `flip-+`
313×	`pow1`
159×	`pow-prod-up`
132×	`associate-l/` `associate-r/`
102×	`pow-plus`
96×	`sqrt-pow1` `pow1/2`
94×	`pow-prod-down`
40×	`add-cbrt-cube` `add-exp-log`
39×	`pow-sqr`
38×	`add-sqr-sqrt` `cube-unmult`
24×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
12×	`*-un-lft-identity`
8×	`associate--r+`
6×	`add-log-exp`
4×	`difference-cubes` `pow3` `add-cube-cbrt` `insert-posit16`
3×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 488

Calls

4 calls:

148.0ms	(* (* (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)))
190.0ms	(* (* (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)))
157.0ms	(* (* (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)))
854.0ms	(- (* (* 1 1) (* 1 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))) (* (* (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)))))

series732.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* (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)))
99.0ms	(* (* (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)))
76.0ms	(* (* (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)))
491.0ms	(- (* (* 1 1) (* 1 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))) (* (* (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)))))

simplify2.3s

Counts

500 → 500

Iterations

Iter	Nodes
2	5038
1	1115
0	319

prune8.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

regimes137.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.5b and baseline of 14.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	30
1	30
0	22

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.4s	2861×	body	1280	valid
430.0ms	4069×	body	80	valid
311.0ms	615×	body	640	valid
93.0ms	307×	body	320	valid
28.0ms	148×	body	160	valid