Details

sample27.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	110	35
3	480	35
4	2398	35
done	5000	35

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize13.0ms

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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite631.0ms

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-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

Calls

4 calls:

13.0ms	(+ (+ alpha beta) (* beta alpha))
175.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
263.0ms	(/ (/ (/ (+ (+ (+ 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))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
141.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms	(/ (/ (/ (+ (+ (+ 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))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify631.0ms

Counts

475 → 475

Iterations

Useful iterations: done (595.0ms)

Iter	Nodes	Cost
0	604	25900
1	1509	25129
done	5002	24972

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

87.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
32.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
31.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
32.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series415.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.5s

Counts

91 → 91

Iterations

Useful iterations: 3 (721.0ms)

Iter	Nodes	Cost
0	196	2722
1	502	2574
2	1425	2351
3	4954	2208
done	5000	2208

prune410.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.9b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite557.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
11×	`distribute-lft-out`
9×	`add-log-exp`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*` `div-inv`
3×	`associate-r` `prod-exp` `sum-log` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

13.0ms	(+ (+ alpha beta) (* beta alpha))
191.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
201.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
34.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
73.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.3s

Counts

153 → 153

Iterations

Useful iterations: 2 (511.0ms)

Iter	Nodes	Cost
0	252	5094
1	762	4949
2	3525	4494
done	5001	4494

prune395.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
1.9b	(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite765.0ms

Algorithm

rewrite-expression-head

Rules

120×	`*-un-lft-identity`
98×	`sqrt-prod`
91×	`times-frac`
90×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
29×	`swap-sqr`
26×	`distribute-lft-out`
22×	`add-exp-log` `add-cbrt-cube`
21×	`associate-r` `associate-l`
20×	`associate-/r/`
19×	`pow1`
14×	`flip3-+` `flip-+`
9×	`associate-/l*` `unswap-sqr`
8×	`sqrt-pow1` `pow1/2` `sqrt-div`
7×	`associate-/r*` `div-inv` `associate-/l/`
6×	`cbrt-undiv` `frac-times` `div-exp`
5×	`prod-exp` `pow-prod-up` `cbrt-unprod`
4×	`associate-r/` `associate-l/` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `pow-sqr`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `*-commutative`

Counts

4 → 210

Calls

4 calls:

337.0ms	(* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
129.0ms	(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
144.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
154.0ms	(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.1s

Counts

222 → 222

Iterations

Useful iterations: 2 (376.0ms)

Iter	Nodes	Cost
0	267	9624
1	682	6989
2	3342	6309
done	5001	6309

prune574.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

regimes96.0ms

Accuracy

93.3% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 3.5b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	100
1	37	100
done	37	100

end0.0ms

sample535.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
94.0ms	8000×	pre	80	true