Details

sample108.0ms

Algorithm

intervals

Results

63.0ms	98×	body	1280	valid
15.0ms	125×	body	80	valid
11.0ms	20×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	3×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	25
2	25
1	21
0	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
8×	`sqrt-prod` `add-log-exp`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `difference-of-squares`
3×	`distribute-lft-out` `distribute-lft-out--`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

0.0ms	(hypot 1 x)
17.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
24.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
53.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1 x)
27.0ms	(+ (/ 1/2 (hypot 1 x)) 1/2)
68.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
66.0ms	(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify4.9s

Counts

70 → 70

Iterations

Iter	Nodes
4	4361
3	1348
2	419
1	177
0	84

prune629.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 x)
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
1.1b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`sqrt-prod`
5×	`pow1` `add-cube-cbrt` `distribute-lft-out`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
2×	`flip3-+` `sqrt-div` `flip-+` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `times-frac` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

0.0ms	(hypot 1 x)
19.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
38.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
11.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot 1 x)
46.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
74.0ms	(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
52.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify6.4s

Counts

68 → 68

Iterations

Iter	Nodes
4	4338
3	1314
2	434
1	195
0	98

prune632.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1/2 (hypot 1 x)) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
0.1b	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
1.1b	(- 1/2 (/ 1/2 (hypot 1 x)))
1.1b	(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
57×	`add-cbrt-cube` `add-exp-log`
52×	`times-frac`
43×	`*-un-lft-identity`
39×	`add-cube-cbrt`
26×	`associate-l`
25×	`pow1`
22×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`associate-r`
13×	`swap-sqr`
8×	`add-log-exp`
6×	`frac-times` `associate-*r/` `pow-prod-up` `unswap-sqr`
5×	`div-inv`
4×	`pow-prod-down` `associate-*l/` `insert-posit16` `difference-of-squares`
2×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `pow-sqr` `*-commutative` `flip--` `distribute-lft-out--`
1×	`cube-unmult`

Counts

4 → 159

Calls

4 calls:

52.0ms	(* (/ 1/2 (hypot 1 x)) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
25.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
21.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
6.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ 1/2 (hypot 1 x)) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
21.0ms	(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
37.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))
59.0ms	(- 1/2 (/ 1/2 (hypot 1 x)))

simplify3.0s

Counts

171 → 171

Iterations

Iter	Nodes
3	5038
2	1527
1	579
0	192

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b	(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
1.1b	(- 1 (* (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `distribute-lft-out`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 62

Calls

4 calls:

20.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
19.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
44.0ms	(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
5.0ms	(- 1 (* (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
51.0ms	(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
51.0ms	(+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)
136.0ms	(- 1 (* (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

simplify4.7s

Counts

74 → 74

Iterations

Iter	Nodes
4	5737
3	1576
2	493
1	212
0	87

prune734.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.8b

regimes103.0ms

Accuracy

0% (0.0b remaining)

Error of 14.3b against oracle of 14.2b and baseline of 14.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	24
1	24
0	18

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.2s	2822×	body	1280	valid
491.0ms	4119×	body	80	valid
324.0ms	620×	body	640	valid
112.0ms	298×	body	320	valid
28.0ms	141×	body	160	valid