Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

18.0ms	(+ (+ (* x x) (* y y)) (* z z))
28.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series260.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (+ (* x x) (* y y)) (* z z))
49.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
171.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.3s

Counts

76 → 76

Iterations

Useful iterations: 3 (409.0ms)

Iter	Nodes	Cost
0	123	1541
1	260	1473
2	790	1346
3	3018	1330
done	5001	1330

prune213.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
33.0b	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
33.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
9.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series248.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
48.0ms	(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
162.0ms	(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify1.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (413.0ms)

Iter	Nodes	Cost
0	90	992
1	244	945
2	857	841
3	3983	825
done	5000	825

prune140.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.2b	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
33.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

12.0ms	(+ (+ (* x x) (* y y)) (* z z))
36.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
165.0ms	(* (sqrt 0.3333333333333333) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.4s

Counts

69 → 69

Iterations

Useful iterations: 3 (428.0ms)

Iter	Nodes	Cost
0	92	1244
1	221	1146
2	752	1072
3	2976	1056
done	5000	1056

prune173.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
33.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 91

Calls

3 calls:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
23.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series361.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
224.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
101.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.1s

Counts

100 → 100

Iterations

Useful iterations: 3 (334.0ms)

Iter	Nodes	Cost
0	136	2358
1	265	2152
2	717	2068
3	2588	2042
done	5000	2042

prune244.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.5b

regimes433.0ms

Accuracy

48.4% (13.2b remaining)

Error of 25.4b against oracle of 12.2b and baseline of 37.7b

bsearch144.0ms

Steps

Iters	Range		Point
9	1.5308671146039946e+53	1.176638228465725e+60	1.1586965865467858e+60
8	1.6503559446657207e-225	8.39325558204359e-223	5.75865971739732e-225
7	-4.389466271088922e-269	-3.2613167836346877e-271	-2.24510505347645e-269
9	-6.5309962722429555e+122	-4.4188440889263735e+116	-1.1663424956880876e+121

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	59
1	38	59
done	38	59

end0.0ms

sample449.0ms

Algorithm

intervals

Results

274.0ms

8000×

body

valid