Details

sample54.0ms

Algorithm

intervals

Results

38.0ms

256×

body

valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize36.0ms

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)
34.1b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`*-un-lft-identity` `add-cube-cbrt`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `sum-log` `insert-posit16` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp`

Counts

3 → 70

Calls

3 calls:

25.0ms	(+ (+ (* x x) (* y y)) (* z z))
120.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
51.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series406.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (+ (* x x) (* y y)) (* z z))
86.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
268.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.8s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
3	4834
2	833
1	278
0	126

prune423.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.7b

localize48.0ms

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 (/ 1 3.0)))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite139.0ms

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` `add-log-exp` `unswap-sqr`
6×	`associate-l`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`sum-log` `sqrt-pow1` `pow1/2` `pow-prod-down` `insert-posit16`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-unprod` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 80

Calls

3 calls:

30.0ms	(+ (+ (* x x) (* y y)) (* z z))
86.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
21.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series432.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ (+ (* x x) (* y y)) (* z z))
234.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
144.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5005
3	3886
2	789
1	305
0	138

prune483.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* z z) (* x x)) (* y y))
0.0b	(+ (* z z) (* x x))
0.4b	(/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
34.1b	(sqrt (+ (+ (* z z) (* x x)) (* y y)))

rewrite126.0ms

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-+` `insert-posit16`
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 → 106

Calls

4 calls:

43.0ms	(+ (+ (* z z) (* x x)) (* y y))
13.0ms	(+ (* z z) (* x x))
38.0ms	(/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
30.0ms	(sqrt (+ (+ (* z z) (* x x)) (* y y)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (+ (* z z) (* x x)) (* y y))
49.0ms	(+ (* z z) (* x x))
294.0ms	(/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0))
150.0ms	(sqrt (+ (+ (* z z) (* x x)) (* y y)))

simplify2.5s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
3	4545
2	974
1	339
0	155

prune571.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

localize11.0ms

Local error

Found 1 expressions with local error:

0.2b	(* z (sqrt 0.3333333333333333))

rewrite10.0ms

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` `insert-posit16` `add-log-exp`

Counts

1 → 23

Calls

1 calls:

9.0ms

(* z (sqrt 0.3333333333333333))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(* z (sqrt 0.3333333333333333))

simplify3.5s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
4	1927
3	530
2	209
1	73
0	38

prune75.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.6b

regimes882.0ms

Accuracy

32.7% (19.4b remaining)

Error of 25.6b against oracle of 6.2b and baseline of 35.1b

bsearch233.0ms

Steps

Iters	Range		Point
8	2.3947030903309598e+106	9.970465804684252e+109	9.794009169674087e+109
9	-1.060032766889974e-201	-4.267635367026549e-210	-8.598460374864875e-202
8	-4.047764226026223e-95	-1.8795600190319444e-98	-1.9111814054112648e-98
7	-6.313709833010039e+137	-4.230695651283264e+135	-6.208442960829875e+137

simplify10.0ms

Iterations

Iter	Nodes
done	44
2	44
1	41
0	32

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8000×

body

valid