Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	284
1	15	284
2	22	284
3	25	284
done	25	284

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize34.0ms

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)
32.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite177.0ms

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:

12.0ms	(+ (* x x) (* y y))
43.0ms	(+ (+ (* x x) (* y y)) (* z z))
63.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
55.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series411.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* x x) (* y y))
49.0ms	(+ (+ (* x x) (* y y)) (* z z))
90.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
226.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.5s

Counts

90 → 90

Iterations

Useful iterations: 2 (463.0ms)

Iter	Nodes	Cost
0	139	35848
1	358	30150
2	1773	29800
done	5000	29800

prune622.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

localize38.0ms

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)))
32.8b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
9×	`pow1`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log` `flip3-+` `associate-*r/` `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` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

13.0ms	(+ (* x x) (* y y))
45.0ms	(+ (+ (* x x) (* y y)) (* z z))
96.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
30.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x x) (* y y))
60.0ms	(+ (+ (* x x) (* y y)) (* z z))
68.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
251.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	106	24840
1	349	19023
2	2028	18953
done	5001	18873

prune386.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.4b

localize19.0ms

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))
32.7b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite101.0ms

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:

6.0ms	(+ (* x x) (* y y))
23.0ms	(+ (+ (* x x) (* y y)) (* z z))
45.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
24.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x x) (* y y))
58.0ms	(+ (+ (* x x) (* y y)) (* z z))
332.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
159.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.4s

Counts

114 → 114

Iterations

Useful iterations: 2 (481.0ms)

Iter	Nodes	Cost
0	152	53357
1	361	47725
2	1869	47655
done	5000	47655

prune558.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.3b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite9.0ms

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:

8.0ms

(* x (sqrt 0.3333333333333333))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(* x (sqrt 0.3333333333333333))

simplify3.4s

Counts

25 → 25

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	37	3652
1	73	3380
2	199	3380
3	702	3340
4	1953	3340
5	3431	3340
done	5000	3340

prune95.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 19.3b

regimes1.1s

Accuracy

62.6% (7.4b remaining)

Error of 25.9b against oracle of 18.5b and baseline of 38.3b

bsearch115.0ms

Steps

Iters	Range		Point
9	5.605877450284385e+142	5.3446694412844105e+147	3.408719160070714e+143
9	-1.9449249655492605e+111	-9.548992574131866e+103	-2.1993493867760175e+110

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	666
1	28	666
2	30	666
done	30	666

end0.0ms

sample1.2s

Algorithm

intervals

Results

990.0ms

8000×

body

valid