Details

sample46.0ms

Algorithm

intervals

Results

31.0ms

256×

body

valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
3	20
2	19
1	13
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize43.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite723.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
40×	`distribute-lft-out`
26×	`associate-l`
14×	`sqrt-prod`
7×	`add-log-exp`
6×	`swap-sqr`
4×	`add-sqr-sqrt`
3×	`pow1` `sum-log` `add-cube-cbrt`
2×	`+-commutative` `associate-+l+` `flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `insert-posit16`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

2 → 53

Calls

2 calls:

283.0ms	(+ (+ (* x x) (* y y)) (* z z))
437.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series204.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (+ (* x x) (* y y)) (* z z))
155.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify9.0s

Counts

59 → 59

Iterations

Iter	Nodes
done	5033
3	3200
2	530
1	159
0	63

prune225.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

145×	`*-un-lft-identity`
80×	`distribute-lft-out`
56×	`sqrt-prod`
52×	`associate-l`
17×	`cbrt-prod`
12×	`add-sqr-sqrt` `swap-sqr`
9×	`add-cube-cbrt`
8×	`sqrt-div`
7×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 109

Calls

4 calls:

160.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
407.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
366.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
329.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
161.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
137.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
134.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.8s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
3	2007
2	495
1	171
0	82

prune461.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 14.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* (+ (+ (* x x) (* y y)) (* z z)) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
34.1b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
41.9b	(cbrt (* (+ (+ (* x x) (* y y)) (* z z)) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

216×	`*-un-lft-identity`
120×	`distribute-lft-out`
106×	`associate-l`
44×	`sqrt-prod`
38×	`cbrt-prod`
34×	`associate-r`
23×	`add-sqr-sqrt`
18×	`swap-sqr`
14×	`flip3-+` `sqrt-div` `flip-+`
12×	`add-cube-cbrt`
10×	`pow1`
9×	`add-log-exp`
8×	`frac-times` `cbrt-div`
6×	`add-cbrt-cube` `add-exp-log`
4×	`associate-l/` `associate-r/` `insert-posit16` `unswap-sqr`
3×	`sum-log`
2×	`+-commutative` `associate-+l+` `sqrt-pow1` `pow1/2` `pow3` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `pow1/3` `pow-prod-down` `prod-exp` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 165

Calls

4 calls:

255.0ms	(+ (+ (* x x) (* y y)) (* z z))
1.6s	(* (+ (+ (* x x) (* y y)) (* z z)) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
319.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
1.4s	(cbrt (* (+ (+ (* x x) (* y y)) (* z z)) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (+ (* x x) (* y y)) (* z z))
320.0ms	(* (+ (+ (* x x) (* y y)) (* z z)) (sqrt (+ (+ (* x x) (* y y)) (* z z))))
159.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
145.0ms	(cbrt (* (+ (+ (* x x) (* y y)) (* z z)) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))

simplify1.7s

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
2	1140
1	311
0	150

prune716.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 14.5b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 14.5b

regimes854.0ms

Accuracy

53.8% (8.2b remaining)

Error of 25.4b against oracle of 17.3b and baseline of 34.9b

bsearch170.0ms

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

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

883.0ms

8000×

body

valid