Details

sample28.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	25
3	25
2	22
1	15
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

40.0ms	(+ (+ (* x x) (* y y)) (* z z))
7.0ms	(+ (* x x) (* y y))
85.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
38.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series455.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (+ (* x x) (* y y)) (* z z))
57.0ms	(+ (* x x) (* y y))
75.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
268.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify875.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1770
1	358
0	139

prune579.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z z) (+ (pow y 2) (* x x)))
0.0b	(+ (pow y 2) (* x x))
0.4b	(* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (sqrt (/ 1 3.0)))
33.6b	(sqrt (+ (* z z) (+ (pow y 2) (* x x))))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

39.0ms	(+ (* z z) (+ (pow y 2) (* x x)))
10.0ms	(+ (pow y 2) (* x x))
106.0ms	(* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (sqrt (/ 1 3.0)))
70.0ms	(sqrt (+ (* z z) (+ (pow y 2) (* x x))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (* z z) (+ (pow y 2) (* x x)))
32.0ms	(+ (pow y 2) (* x x))
243.0ms	(* (sqrt (+ (* z z) (+ (pow y 2) (* x x)))) (sqrt (/ 1 3.0)))
172.0ms	(sqrt (+ (* z z) (+ (pow y 2) (* x x))))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2163
1	384
0	150

prune577.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* z z) (* y y)) (* x x))
0.0b	(+ (* z z) (* y y))
0.4b	(/ (sqrt (+ (+ (* z z) (* y y)) (* x x))) (sqrt 3.0))
33.6b	(sqrt (+ (+ (* z z) (* y y)) (* x x)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

44.0ms	(+ (+ (* z z) (* y y)) (* x x))
12.0ms	(+ (* z z) (* y y))
58.0ms	(/ (sqrt (+ (+ (* z z) (* y y)) (* x x))) (sqrt 3.0))
31.0ms	(sqrt (+ (+ (* z z) (* y y)) (* x x)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (+ (* z z) (* y y)) (* x x))
35.0ms	(+ (* z z) (* y y))
300.0ms	(/ (sqrt (+ (+ (* z z) (* y y)) (* x x))) (sqrt 3.0))
133.0ms	(sqrt (+ (+ (* z z) (* y y)) (* x x)))

simplify995.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1864
1	361
0	152

prune571.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.3b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(* (sqrt 0.3333333333333333) (- x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `associate-r`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `add-cbrt-cube` `add-exp-log`
2×	`unswap-sqr`
1×	`neg-mul-1` `pow-prod-down` `prod-exp` `*-commutative` `distribute-rgt-neg-out` `cbrt-unprod` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

12.0ms

(* (sqrt 0.3333333333333333) (- x))

series75.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

(* (sqrt 0.3333333333333333) (- x))

simplify4.1s

Counts

33 → 33

Iterations

Iter	Nodes
done	5001
3	4801
2	540
1	123
0	51

prune137.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 12.2b

regimes1.0s

Accuracy

45.5% (13.7b remaining)

Error of 26.0b against oracle of 12.3b and baseline of 37.5b

bsearch101.0ms

Steps

Iters	Range		Point
9	1.003350963699018e+79	6.556138372450062e+84	3.863641896649309e+84
7	-1.1660783759419484e+60	-2.076665684306524e+58	-1.1478837412905316e+60

simplify9.0ms

Iterations

Iter	Nodes
done	48
3	48
2	47
1	42
0	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

702.0ms

8000×

body

valid