Details

sample98.0ms

Algorithm

intervals

Results

32.0ms	49×	body	1280	valid
21.0ms	153×	body	80	valid
19.0ms	44×	body	640	valid
7.0ms	22×	body	320	valid
6.0ms	93×	body	80	nan
3.0ms	16×	body	160	valid

simplify695.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
6	545
5	216
4	91
3	41
2	22
1	15
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

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×	`expm1-log1p-u` `rem-log-exp` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`log-div` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 90

Calls

2 calls:

32.0ms	(* x (log (/ x (+ x y))))
9.0ms	(log (/ x (+ x y)))

series210.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(* x (log (/ x (+ x y))))
86.0ms	(log (/ x (+ x y)))

simplify800.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	2000
3	1782
2	538
1	279
0	159

prune386.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.9b

localize38.0ms

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)))))

rewrite25.0ms

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×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `pow1/3` `associate-l/` `associate-r/` `log-pow` `div-inv`

Counts

4 → 120

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
4.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
17.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series653.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt x)
247.0ms	(cbrt x)
73.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
85.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify914.0ms

Counts

132 → 132

Iterations

Iter	Nodes
done	2000
2	923
1	477
0	238

prune824.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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))))

rewrite26.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 200

Calls

4 calls:

1.0ms	(cbrt x)
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt x)
106.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
107.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
95.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify733.0ms

Counts

212 → 212

Iterations

Iter	Nodes
done	2001
3	1516
2	562
1	327
0	179

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize75.0ms

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)))

rewrite28.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`remove-posit16`

Counts

4 → 176

Calls

4 calls:

7.0ms	(log (/ (posit16->real (real->posit16 (cbrt x))) (cbrt (+ x y))))
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
0.0ms	(posit16->real (real->posit16 (cbrt x)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(log (/ (posit16->real (real->posit16 (cbrt x))) (cbrt (+ x y))))
94.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
98.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
264.0ms	(posit16->real (real->posit16 (cbrt x)))

simplify702.0ms

Counts

188 → 188

Iterations

Iter	Nodes
done	2000
3	1647
2	678
1	447
0	250

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes83.0ms

Accuracy

39.1% (3.2b remaining)

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

bsearch116.0ms

Steps

Iters	Range		Point
9	520296.8443274253	941504501108.8118	526918.3282767582

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1487×	body	1280	valid
811.0ms	1453×	body	640	valid
577.0ms	4851×	body	80	valid
319.0ms	838×	body	320	valid
283.0ms	3061×	body	80	nan
93.0ms	443×	body	160	valid