Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify2.0s

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: 4.1b

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))
3.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

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:

27.0ms	(+ (+ alpha beta) (* beta alpha))
330.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
480.0ms	(/ (/ (/ (+ (+ (+ 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))
278.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ alpha beta) (* beta alpha))
145.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
164.0ms	(/ (/ (/ (+ (+ (+ 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))
85.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.8s

Counts

475 → 475

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	604	25900
1	1467	25129
2	4953	24192
done	5000	23452

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

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))))
3.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.0s

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:

645.0ms	(/ (/ (/ 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)))))
90.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
36.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
282.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (/ (/ 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)))))
42.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
66.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
83.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify4.8s

Counts

12106 → 12106

Iterations

Useful iterations: 0 (1.4s)

Iter	Nodes	Cost
0	9087	1187995
done	9087	1187995

prune32.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite731.0ms

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
522×	`sqrt-prod`
425×	`*-un-lft-identity`
325×	`add-sqr-sqrt`
323×	`add-cube-cbrt`
55×	`associate-/l*`
51×	`distribute-lft-out`
24×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-undiv` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 464

Calls

4 calls:

263.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
202.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
114.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
117.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series418.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
112.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
56.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.0s

Counts

476 → 476

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	455	23023
1	1032	20455
2	2184	19368
done	5000	18678

prune886.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.2b	(/ (+ (* 2.0 1.0) (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite606.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt` `sqrt-prod`
38×	`add-cube-cbrt`
10×	`associate-/r` `distribute-lft-out` `associate-/l`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

201.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
169.0ms	(/ (+ (* 2.0 1.0) (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
112.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
118.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series562.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
257.0ms	(/ (+ (* 2.0 1.0) (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
55.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify753.0ms

Counts

138 → 138

Iterations

Useful iterations: done (748.0ms)

Iter	Nodes	Cost
0	214	3616
1	513	3375
2	1605	3212
done	5000	3180

prune463.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

regimes88.0ms

Accuracy

35.1% (1.7b remaining)

Error of 2.8b against oracle of 1.1b and baseline of 3.7b

bsearch54.0ms

Steps

Iters	Range		Point
9	3.346468434766734e+140	7.57674529381864e+146	7.494253796401252e+146

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	52
1	30	52
done	30	52

end0.0ms

sample550.0ms

Algorithm

intervals

Results

282.0ms	8000×	body	80	valid
82.0ms	8000×	pre	80	true