Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	550	35
4	4087	35
done	5000	35

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

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:

118.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
478.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
617.0ms	(/ (/ (/ (+ (+ (+ 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))
438.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
150.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
170.0ms	(/ (/ (/ (+ (+ (+ 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))
105.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.4s

Counts

477 → 477

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	603	25954
1	1443	25182
2	4754	24241
done	5001	23501

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

3614×	`times-frac`
2164×	`*-un-lft-identity`
1424×	`add-sqr-sqrt` `add-cube-cbrt`
370×	`distribute-lft-out`
192×	`associate-/l*`
152×	`associate-/r/`
89×	`div-inv`
84×	`associate-/r*`
65×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`frac-2neg` `clear-num` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1332

Calls

4 calls:

263.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
291.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
577.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
436.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series740.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
200.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
215.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
113.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.9s

Counts

1344 → 1344

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	1589	83763
1	3830	78123
done	5001	75998

prune3.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

2394×	`times-frac`
1368×	`sqrt-prod`
1366×	`*-un-lft-identity`
1062×	`add-sqr-sqrt` `add-cube-cbrt`
268×	`associate-/r*`
152×	`distribute-lft-out`
110×	`associate-/r/`
60×	`div-inv`
52×	`flip3-+` `flip-+`
30×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`div-exp`
14×	`associate-/l*`
8×	`cbrt-undiv` `sqrt-div`
6×	`pow1`
4×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/` `add-log-exp`
2×	`pow-flip` `inv-pow`

Counts

4 → 1166

Calls

4 calls:

311.0ms	(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
325.0ms	(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
511.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
403.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
236.0ms	(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
95.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
127.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.9s

Counts

1178 → 1178

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	782	62138
1	1658	55246
2	3390	51636
done	5002	50628

prune2.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 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))

rewrite741.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod` `times-frac`
7×	`distribute-lft-out`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`pow1` `associate-/l*` `add-log-exp`
3×	`pow1/3` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 77

Calls

4 calls:

398.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
120.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
97.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
123.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series384.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
95.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
98.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
94.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify916.0ms

Counts

89 → 89

Iterations

Useful iterations: done (911.0ms)

Iter	Nodes	Cost
0	141	2116
1	367	2064
2	1241	1904
done	5001	1848

prune764.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes138.0ms

Accuracy

59.2% (1.6b remaining)

Error of 1.7b against oracle of 0.0b and baseline of 4.1b

bsearch100.0ms

Steps

Iters	Range		Point
7	9.711408253067022e+141	2.2840282335092652e+144	1.4606790468840281e+143

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	94
1	41	94
done	41	94

end0.0ms

sample1.2s

Algorithm

intervals

Results

713.0ms	8000×	body	80	valid
224.0ms	8000×	pre	80	true