Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify92.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize146.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

18.0ms	(+ (* x x) (* y y))
246.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
62.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series479.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ (* x x) (* y y))
96.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
317.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify8.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	4236
2	929
1	298
0	131

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.4b

localize104.0ms

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))
34.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

20.0ms	(+ (* x x) (* y y))
159.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
81.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series671.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+ (* x x) (* y y))
413.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
201.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify5.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
3	2784
2	773
1	300
0	144

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 18.3b

localize173.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* z z)) (* y y))
0.3b	(/ (/ (sqrt (+ (+ (* x x) (* z z)) (* y y))) (fabs (cbrt 3.0))) (sqrt (cbrt 3.0)))
0.4b	(/ (sqrt (+ (+ (* x x) (* z z)) (* y y))) (fabs (cbrt 3.0)))
34.5b	(sqrt (+ (+ (* x x) (* z z)) (* y y)))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

396×	`times-frac`
243×	`sqrt-prod`
220×	`add-sqr-sqrt`
219×	`*-un-lft-identity` `add-cube-cbrt`
69×	`cbrt-prod`
28×	`associate-/l*`
12×	`associate-/r*` `div-inv`
11×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `insert-posit16`
3×	`sum-log` `flip3-+` `flip-+` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

4 → 317

Calls

4 calls:

101.0ms	(+ (+ (* x x) (* z z)) (* y y))
143.0ms	(/ (/ (sqrt (+ (+ (* x x) (* z z)) (* y y))) (fabs (cbrt 3.0))) (sqrt (cbrt 3.0)))
149.0ms	(/ (sqrt (+ (+ (* x x) (* z z)) (* y y))) (fabs (cbrt 3.0)))
91.0ms	(sqrt (+ (+ (* x x) (* z z)) (* y y)))

series1.7s

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ (+ (* x x) (* z z)) (* y y))
922.0ms	(/ (/ (sqrt (+ (+ (* x x) (* z z)) (* y y))) (fabs (cbrt 3.0))) (sqrt (cbrt 3.0)))
477.0ms	(/ (sqrt (+ (+ (* x x) (* z z)) (* y y))) (fabs (cbrt 3.0)))
218.0ms	(sqrt (+ (+ (* x x) (* z z)) (* y y)))

simplify4.8s

Counts

329 → 329

Iterations

Iter	Nodes
done	5000
2	1991
1	873
0	401

prune3.8s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 11.1b

localize80.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (/ y (fabs (cbrt 3.0))) (sqrt (cbrt 3.0)))
0.4b	(/ y (fabs (cbrt 3.0)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
122×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
84×	`sqrt-prod`
42×	`cbrt-prod`
16×	`associate-/l*`
12×	`associate-/r*` `div-inv`
9×	`add-cbrt-cube` `add-exp-log`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 183

Calls

2 calls:

28.0ms	(/ (/ y (fabs (cbrt 3.0))) (sqrt (cbrt 3.0)))
11.0ms	(/ y (fabs (cbrt 3.0)))

series389.0ms

Counts

2 → 6

Calls

2 calls:

295.0ms	(/ (/ y (fabs (cbrt 3.0))) (sqrt (cbrt 3.0)))
93.0ms	(/ y (fabs (cbrt 3.0)))

simplify7.5s

Counts

189 → 189

Iterations

Iter	Nodes
done	5004
3	4463
2	1233
1	541
0	267

prune2.0s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 11.1b

regimes5.3s

Accuracy

48% (13.5b remaining)

Error of 25.8b against oracle of 12.2b and baseline of 38.2b

bsearch130.0ms

Steps

Iters	Range		Point
7	2.99988769581893e+36	1.242935524573972e+38	1.2252148173535669e+38
8	-1.0203615019194824e+155	-6.1961078044177e+151	-6.305761339015559e+151

simplify46.0ms

Iterations

Iter	Nodes
done	33
3	33
2	32
1	28
0	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

764.0ms

8000×

body

valid