Details

sample72.0ms

Algorithm

intervals

Results

37.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify654.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	557	35
done	5001	35

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* beta alpha)) 1.0)
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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 465

Calls

4 calls:

200.0ms	(+ (+ (+ alpha beta) (* beta alpha)) 1.0)
496.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
736.0ms	(/ (/ (/ (+ (+ (+ 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))
428.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (+ (+ alpha beta) (* beta alpha)) 1.0)
212.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
240.0ms	(/ (/ (/ (+ (+ (+ 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))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.0s

Counts

477 → 477

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	601	25958
1	1607	25186
done	5001	24283

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize31.0ms

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))))
0.3b	(/ (/ 1 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)))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

14603×	`times-frac`
8256×	`*-un-lft-identity`
5324×	`add-sqr-sqrt` `add-cube-cbrt`
1466×	`distribute-lft-out`
516×	`associate-/r/`
512×	`div-inv`
311×	`associate-/r*`
252×	`flip3-+` `flip-+`
114×	`add-exp-log`
96×	`div-exp`
52×	`add-cbrt-cube`
39×	`associate-/l*`
34×	`cbrt-undiv`
20×	`1-exp`
8×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 3941

Calls

4 calls:

496.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
757.0ms	(/ (+ (+ (+ 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))))
706.0ms	(/ (/ 1 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)))))
443.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series959.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
360.0ms	(/ (+ (+ (+ 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))))
205.0ms	(/ (/ 1 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)))))
129.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify4.8s

Counts

3953 → 3953

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	4155	306477
done	5000	285179

prune13.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.2b	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite5.1s

Algorithm

rewrite-expression-head

Rules

49626×	`times-frac`
26844×	`*-un-lft-identity`
17776×	`add-sqr-sqrt` `add-cube-cbrt`
9978×	`sqrt-prod`
4534×	`distribute-lft-out`
2472×	`associate-/r/`
1312×	`div-inv`
1161×	`flip3-+` `flip-+`
1110×	`sqrt-div`
181×	`associate-/l*`
92×	`associate-/r*`
79×	`add-exp-log`
57×	`div-exp`
49×	`add-cbrt-cube`
32×	`cbrt-undiv`
13×	`pow1`
8×	`pow-flip`
6×	`pow-div`
5×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
2×	`inv-pow`

Counts

4 → 12094

Calls

4 calls:

932.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
155.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
448.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
70.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
92.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
126.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify6.7s

Counts

12106 → 12106

Iterations

Useful iterations: 0 (2.0s)

Iter	Nodes	Cost
0	9087	1187995
done	9087	1187995

prune1.0m

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.3b

localize151.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (/ (/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))))) 1) (/ 1 (* (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))) (/ (/ (/ (cbrt 1) (sqrt (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.7m

Algorithm

rewrite-expression-head

Rules

155639×	`times-frac`
78190×	`*-un-lft-identity`
63819×	`add-sqr-sqrt`
52890×	`cbrt-prod`
52122×	`add-cube-cbrt`
37720×	`sqrt-prod`
32579×	`associate-r`
12090×	`distribute-lft-out`
4944×	`associate-/r/`
2550×	`div-inv`
2489×	`add-exp-log`
2273×	`flip3-+` `flip-+`
2002×	`cbrt-div`
1870×	`unswap-sqr`
1782×	`div-exp`
1486×	`sqrt-div`
595×	`prod-exp`
525×	`associate-l`
518×	`add-cbrt-cube`
443×	`cbrt-undiv`
245×	`1-exp`
173×	`frac-times`
140×	`cbrt-unprod`
113×	`associate-r/` `associate-l/`
98×	`rec-exp`
12×	`associate-/l*`
9×	`associate-/r*`
6×	`pow1` `associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 35532

Calls

4 calls:

3.6m	(* (/ (/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))))) 1) (/ 1 (* (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))) (/ (/ (/ (cbrt 1) (sqrt (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))))
467.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
446.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
371.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (/ (/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))))) 1) (/ 1 (* (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))) (/ (/ (/ (cbrt 1) (sqrt (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
86.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify17.7s

Counts

35544 → 35544

Iterations

Useful iterations: 0 (5.4s)

Iter	Nodes	Cost
0	35224	4501547
done	35224	4501547

prune3.4m

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 1.3b

regimes165.0ms

Accuracy

93.5% (0.2b remaining)

Error of 1.4b against oracle of 1.3b and baseline of 3.9b

bsearch2.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	104
1	31	104
done	31	104

end0.0ms

sample859.0ms

Algorithm

intervals

Results

491.0ms	8000×	body	80	valid
136.0ms	8000×	pre	80	true