Details

sample64.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify5.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5255
4	2870
3	497
2	106
1	33
0	14

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize141.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
9×	`add-log-exp`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `sum-log` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 467

Calls

4 calls:

68.0ms	(+ (+ alpha beta) (* beta alpha))
1.0s	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
1.5s	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
879.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (+ alpha beta) (* beta alpha))
250.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
255.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
150.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify9.4s

Counts

479 → 479

Iterations

Iter	Nodes
done	5003
2	4634
1	1452
0	608

prune5.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize161.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
58×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
53×	`times-frac`
38×	`add-cbrt-cube` `add-cube-cbrt`
28×	`div-exp`
18×	`associate-l`
16×	`prod-exp`
15×	`cbrt-undiv` `associate-r`
10×	`associate-/r*` `associate-/r/`
9×	`distribute-lft-out`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `unswap-sqr` `associate-/l/`
5×	`rec-exp` `1-exp` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 175

Calls

4 calls:

90.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
1.4s	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
814.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
871.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
281.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
284.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
125.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify7.1s

Counts

187 → 187

Iterations

Iter	Nodes
done	5005
2	3644
1	770
0	251

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize138.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.9b	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite4.8s

Algorithm

rewrite-expression-head

Rules

3939×	`times-frac`
2530×	`*-un-lft-identity`
1518×	`add-sqr-sqrt` `add-cube-cbrt`
506×	`distribute-lft-out`
311×	`associate-/r*`
186×	`associate-/r/`
96×	`div-inv`
92×	`flip3-+` `flip-+`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/l*`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1466

Calls

4 calls:

1.1s	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
1.3s	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
1.1s	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
873.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
406.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
252.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
141.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify11.8s

Counts

1478 → 1478

Iterations

Iter	Nodes
done	5000
1	4495
0	1532

prune15.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.1b

localize416.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (/ (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) 1)) (/ (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

1969×	`times-frac`
1038×	`*-un-lft-identity`
984×	`add-sqr-sqrt`
687×	`add-cube-cbrt`
660×	`cbrt-prod`
614×	`associate-r`
562×	`add-exp-log`
370×	`div-exp`
168×	`prod-exp`
153×	`distribute-lft-out`
142×	`add-cbrt-cube`
126×	`cbrt-undiv`
72×	`1-exp` `unswap-sqr`
60×	`cbrt-unprod`
58×	`associate-/r/`
34×	`div-inv`
31×	`flip3-+` `flip-+`
30×	`associate-l`
6×	`pow1` `cbrt-div`
4×	`insert-posit16` `add-log-exp`
3×	`pow1/3`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 902

Calls

4 calls:

5.3s	(* (/ (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) 1)) (/ (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
183.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
208.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
241.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series945.0ms

Counts

4 → 12

Calls

4 calls:

438.0ms	(* (/ (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) 1)) (/ (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
169.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
148.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
189.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify7.2s

Counts

914 → 914

Iterations

Iter	Nodes
done	5001
0	1543

prune13.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.1b

regimes463.0ms

Accuracy

0% (2.5b remaining)

Error of 3.8b against oracle of 1.4b and baseline of 3.8b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	26
1	26
0	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	8000×	body	80	valid
306.0ms	8000×	pre	80	true