Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize34.0ms

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))

rewrite144.0ms

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:

28.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(+ (* x x) (* y y))
73.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series497.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (+ (* x x) (* y y)) (* z z))
52.0ms	(+ (* x x) (* y y))
99.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
294.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.3s

Counts

90 → 90

Iterations

Iter	Nodes
done	5002
2	1039
1	333
0	139

prune532.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
0.3b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
33.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite154.0ms

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:

46.0ms	(+ (+ (* x x) (* y y)) (* z z))
13.0ms	(+ (* x x) (* y y))
62.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
28.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (+ (* x x) (* y y)) (* z z))
30.0ms	(+ (* x x) (* y y))
329.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
144.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.7s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	4557
2	968
1	336
0	152

prune712.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.6b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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-+l+` `sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 88

Calls

4 calls:

24.0ms	(+ (+ (* x x) (* y y)) (* z z))
9.0ms	(+ (* x x) (* y y))
100.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
25.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (+ (* x x) (* y y)) (* z z))
39.0ms	(+ (* x x) (* y y))
245.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
153.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
3	4921
2	1000
1	360
0	151

prune418.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.6b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (- x) (sqrt 3.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
44×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
21×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-/l*`
7×	`neg-mul-1`
6×	`associate-/r*`
3×	`add-cbrt-cube` `add-exp-log`
1×	`neg-sub0` `pow1` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `distribute-frac-neg` `div-inv` `add-log-exp`

Counts

1 → 90

Calls

1 calls:

11.0ms

(/ (- x) (sqrt 3.0))

series73.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

(/ (- x) (sqrt 3.0))

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1590
2	606
1	258
0	131

prune249.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 18.6b

regimes1.4s

Accuracy

63.4% (7.1b remaining)

Error of 25.3b against oracle of 18.2b and baseline of 37.5b

bsearch96.0ms

Steps

Iters	Range		Point
9	2.0211714536012746e+139	5.300661243002492e+148	1.1291324194830627e+141
9	-7.865186934299256e+122	-7.770626555509823e+115	-6.360018800503746e+121

simplify13.0ms

Iterations

Iter	Nodes
done	31
2	31
1	29
0	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

740.0ms

8000×

body

valid