Details

sample39.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	22
3	22
2	21
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`times-frac`
17×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `associate-/l`
2×	`rem-sqrt-square` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `flip-+`

Counts

2 → 54

Calls

2 calls:

115.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
39.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series304.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
204.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.0s

Counts

60 → 60

Iterations

Iter	Nodes
done	5010
3	2998
2	647
1	217
0	107

prune430.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
37.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`pow1`
2×	`flip3-+` `flip-+` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

2 → 78

Calls

2 calls:

55.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
29.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series499.0ms

Counts

2 → 6

Calls

2 calls:

339.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
160.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
4	4293
3	1362
2	485
1	217
0	119

prune428.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 14.9b

localize18.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
37.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`associate-r`
15×	`*-un-lft-identity`
13×	`times-frac` `add-cube-cbrt`
9×	`sqrt-div`
8×	`unswap-sqr`
7×	`pow1`
6×	`associate-l`
4×	`add-cbrt-cube` `add-exp-log`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`frac-times` `associate-*l/` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

2 → 64

Calls

2 calls:

82.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series376.0ms

Counts

2 → 6

Calls

2 calls:

220.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
156.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5009
3	1709
2	529
1	241
0	118

prune418.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 14.9b

localize9.0ms

Local error

Found 1 expressions with local error:

0.2b	(* z (sqrt 0.3333333333333333))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

13.0ms

(* z (sqrt 0.3333333333333333))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(* z (sqrt 0.3333333333333333))

simplify5.5s

Counts

25 → 25

Iterations

Iter	Nodes
done	5001
5	4710
4	1611
3	529
2	205
1	72
0	37

prune87.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 14.9b

regimes1.5s

Accuracy

62.5% (7.5b remaining)

Error of 25.1b against oracle of 17.6b and baseline of 37.7b

bsearch130.0ms

Steps

Iters	Range		Point
10	3.1068034585604e+112	4.9796964330528925e+125	4.471707363468376e+118
8	-3.4845569108032984e+105	-2.5523402779249368e+101	-8.656892189523162e+102

simplify14.0ms

Iterations

Iter	Nodes
done	33
3	33
2	32
1	28
0	23

end0.0ms

sample929.0ms

Algorithm

intervals

Results

651.0ms

8000×

body

valid