Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	15	14
2	21	14
3	22	14
done	22	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
31.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
19.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series246.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x x) (* y y))
50.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
165.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: 3 (452.0ms)

Iter	Nodes	Cost
0	128	1436
1	293	1370
2	1143	1241
3	4497	1233
done	5000	1233

prune215.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
42.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
14.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series299.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* x x) (* y y))
172.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: 3 (720.0ms)

Iter	Nodes	Cost
0	140	1688
1	321	1556
2	1230	1455
3	4269	1429
done	5000	1429

prune212.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
25.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
16.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series349.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
221.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (384.0ms)

Iter	Nodes	Cost
0	141	2253
1	297	2047
2	981	1963
3	3487	1945
done	5001	1945

prune239.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 18.4b

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ x (sqrt 3.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
6×	`associate-/r*`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

3.0ms

(/ x (sqrt 3.0))

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(/ x (sqrt 3.0))

simplify2.9s

Counts

42 → 42

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	66	371
1	106	342
2	266	322
3	714	322
4	1456	322
5	2701	322
done	5000	322

prune68.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 18.4b

regimes526.0ms

Accuracy

63.3% (7.5b remaining)

Error of 25.4b against oracle of 17.9b and baseline of 38.3b

bsearch61.0ms

Steps

Iters	Range		Point
8	1.5491720421655856e+95	6.147715137559524e+97	5.859409778483319e+97
6	-3.1442305190809916e+143	-5.062787100137526e+142	-7.514594408204408e+142

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	36
1	32	36
done	32	36

end0.0ms

sample441.0ms

Algorithm

intervals

Results

266.0ms

8000×

body

valid