Details

sample30.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5193
4	4059
3	641
2	119
1	36
0	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

3.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`

Counts

3 → 453

Calls

3 calls:

335.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

406.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

319.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series593.0ms

Counts

3 → 9

Calls

3 calls:

201.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

250.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

142.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.0s

Counts

462 → 462

Iterations

Iter	Nodes
done	5000
2	4299
1	1387
0	582

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

819×	`times-frac`
601×	`*-un-lft-identity`
360×	`sqrt-prod`
355×	`add-sqr-sqrt`
349×	`add-cube-cbrt`
126×	`distribute-lft-out`
71×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
10×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l/`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
2×	`sqrt-div`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 481

Calls

4 calls:

197.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
339.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
205.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
285.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
132.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
85.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.2s

Counts

493 → 493

Iterations

Iter	Nodes
done	5004
2	3005
1	1215
0	691

prune3.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
0.3b	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

1494×	`times-frac`
1264×	`sqrt-prod`
987×	`*-un-lft-identity`
975×	`add-sqr-sqrt`
617×	`add-cube-cbrt`
238×	`swap-sqr`
161×	`distribute-lft-out`
132×	`associate-r` `associate-l`
84×	`associate-/r/`
49×	`unswap-sqr`
44×	`flip3-+` `flip-+`
42×	`div-inv`
29×	`associate-/l*`
22×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`pow1` `sqrt-div`
7×	`cbrt-undiv` `div-exp`
5×	`sqrt-undiv` `associate-/l/`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 820

Calls

4 calls:

221.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
599.0ms	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))))
254.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
244.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series635.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
173.0ms	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))))
95.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
128.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.9s

Counts

832 → 832

Iterations

Iter	Nodes
done	5001
1	2372
0	670

prune4.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
0.2b	(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))) (sqrt (+ (+ alpha beta) (* 2 1))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
198×	`sqrt-prod`
191×	`*-un-lft-identity`
133×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`associate-/l*`
29×	`distribute-lft-out`
22×	`associate-/r/`
19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r*`
13×	`flip3-+` `flip-+`
11×	`div-inv`
8×	`associate-/l/`
7×	`cbrt-undiv` `sqrt-div` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
3×	`sqrt-undiv`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `sqrt-unprod` `associate-l/` `associate-r/`

Counts

4 → 278

Calls

4 calls:

273.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
202.0ms	(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))) (sqrt (+ (+ alpha beta) (* 2 1))))
266.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
283.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
217.0ms	(/ (* (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))) (sqrt (+ (+ alpha beta) (* 2 1))))
144.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.2s

Counts

290 → 290

Iterations

Iter	Nodes
done	5001
2	2141
1	782
0	380

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

regimes156.0ms

Accuracy

0% (2.5b remaining)

Error of 3.5b against oracle of 1.0b and baseline of 3.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

760.0ms	8000×	body	80	valid
647.0ms	8000×	pre	80	true