Details

sample44.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	22	14
3	24	14
done	24	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.4b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

18.0ms	(+ (* x x) (* y y))
55.0ms	(+ (+ (* x x) (* y y)) (* z z))
105.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series456.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* x x) (* y y))
52.0ms	(+ (+ (* x x) (* y y)) (* z z))
65.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
295.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.4s

Counts

90 → 90

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	139	1707
1	319	1620
2	948	1477
3	3245	1461
done	5000	1461

prune428.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
30.4b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3-+` `associate-*r/` `sum-log` `flip-+`
3×	`associate-r` `associate-l`
2×	`+-commutative` `sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

9.0ms	(+ (* x x) (* y y))
36.0ms	(+ (+ (* x x) (* y y)) (* z z))
105.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
49.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* x x) (* y y))
69.0ms	(+ (+ (* x x) (* y y)) (* z z))
88.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
241.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	106	1158
1	297	1092
2	1056	972
done	5001	956

prune258.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
30.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

18.0ms	(+ (* x x) (* y y))
62.0ms	(+ (+ (* x x) (* y y)) (* z z))
85.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* x x) (* y y))
73.0ms	(+ (+ (* x x) (* y y)) (* z z))
372.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
157.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts

114 → 114

Iterations

Useful iterations: 3 (830.0ms)

Iter	Nodes	Cost
0	152	2524
1	323	2299
2	882	2199
3	2863	2173
done	5001	2173

prune471.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
30.3b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite309.0ms

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-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`sum-log`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`+-commutative` `frac-times` `associate-*l/`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 88

Calls

4 calls:

15.0ms	(+ (* x x) (* y y))
53.0ms	(+ (+ (* x x) (* y y)) (* z z))
165.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
70.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* x x) (* y y))
53.0ms	(+ (+ (* x x) (* y y)) (* z z))
231.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
129.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.4s

Counts

100 → 100

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	151	1959
1	346	1800
2	952	1681
3	3417	1657
done	5000	1657

prune357.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.0b

regimes539.0ms

Accuracy

55.2% (11.3b remaining)

Error of 23.8b against oracle of 12.5b and baseline of 37.8b

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	44
1	26	44
done	26	44

end0.0ms

sample1.1s

Algorithm

intervals

Results

656.0ms

8000×

body

valid