Details

sample131.0ms

Algorithm

intervals

Results

44.0ms	49×	body	1280	valid
28.0ms	153×	body	80	valid
25.0ms	44×	body	640	valid
9.0ms	22×	body	320	valid
8.0ms	93×	body	80	nan
4.0ms	16×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
7	1916
6	531
5	212
4	89
3	41
2	22
1	15
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize28.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (log (/ x (+ x y))))
8.5b	(log (/ x (+ x y)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

54×	`log-prod`
46×	`*-un-lft-identity`
36×	`times-frac`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
9×	`distribute-lft-out`
7×	`add-exp-log`
6×	`pow1` `associate-/r/`
4×	`add-cbrt-cube` `associate-r`
3×	`flip3-+` `associate-l` `flip-+` `div-inv`
2×	`rem-log-exp` `log-pow` `insert-posit16` `add-log-exp`
1×	`log-div` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 86

Calls

2 calls:

27.0ms	(* x (log (/ x (+ x y))))
7.0ms	(log (/ x (+ x y)))

series162.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(* x (log (/ x (+ x y))))
71.0ms	(log (/ x (+ x y)))

simplify703.0ms

Counts

92 → 92

Iterations

Iter	Nodes
done	2001
3	1810
2	554
1	309
0	155

prune305.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 6.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))
4.6b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

61×	`log-prod`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
43×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `rem-log-exp` `flip-+`
6×	`pow1` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `add-cbrt-cube` `prod-exp` `insert-posit16` `add-log-exp`
2×	`log-div` `pow1/3` `associate-l/` `associate-r/` `log-pow` `div-inv`

Counts

4 → 112

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
14.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt x)
216.0ms	(cbrt x)
90.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
85.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify636.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	2002
2	915
1	467
0	232

prune668.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

144×	`log-prod`
138×	`cbrt-prod`
126×	`times-frac`
122×	`*-un-lft-identity`
86×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`distribute-lft-out`
13×	`add-exp-log`
7×	`pow1`
6×	`cbrt-div` `rem-log-exp` `associate-/r/`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 192

Calls

4 calls:

1.0ms	(cbrt x)
4.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
4.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
4.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt x)
114.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
109.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
89.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify835.0ms

Counts

204 → 204

Iterations

Iter	Nodes
done	2001
3	1468
2	549
1	320
0	175

prune874.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 4 expressions with local error:

2.9b	(log (/ (posit16->real (real->posit16 (cbrt x))) (cbrt (+ x y))))
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))
2.9b	(log (/ (cbrt x) (cbrt (+ x y))))
57.5b	(posit16->real (real->posit16 (cbrt x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

123×	`log-prod`
105×	`times-frac`
102×	`cbrt-prod` `*-un-lft-identity`
72×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`distribute-lft-out`
13×	`add-exp-log`
7×	`pow1`
6×	`cbrt-div` `rem-log-exp` `associate-/r/`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`remove-posit16`

Counts

4 → 168

Calls

4 calls:

9.0ms	(log (/ (posit16->real (real->posit16 (cbrt x))) (cbrt (+ x y))))
4.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
1.0ms	(posit16->real (real->posit16 (cbrt x)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(log (/ (posit16->real (real->posit16 (cbrt x))) (cbrt (+ x y))))
75.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
77.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
268.0ms	(posit16->real (real->posit16 (cbrt x)))

simplify812.0ms

Counts

180 → 180

Iterations

Iter	Nodes
done	2000
3	1587
2	660
1	436
0	244

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes93.0ms

Accuracy

39.1% (3.2b remaining)

Error of 3.8b against oracle of 0.6b and baseline of 5.8b

bsearch103.0ms

Steps

Iters	Range		Point
9	520296.8443274253	941504501108.8118	526918.3282767582

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	1487×	body	1280	valid
1.3s	1453×	body	640	valid
705.0ms	4851×	body	80	valid
351.0ms	838×	body	320	valid
328.0ms	3061×	body	80	nan
133.0ms	443×	body	160	valid