Details

sample28.0ms

Algorithm

intervals

Results

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

simplify2.5s

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.0b	(+ (+ alpha beta) (* beta alpha))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

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-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
9×	`add-log-exp`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `sum-log` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 467

Calls

4 calls:

349.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
28.0ms	(+ (+ alpha beta) (* beta alpha))
502.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
290.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
16.0ms	(+ (+ alpha beta) (* beta alpha))
199.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.5s

Counts

479 → 479

Iterations

Iter	Nodes
done	5003
2	4654
1	1458
0	608

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize33.0ms

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)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.3b	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

484×	`times-frac`
370×	`*-un-lft-identity`
302×	`sqrt-prod`
284×	`add-sqr-sqrt`
224×	`add-cube-cbrt`
83×	`swap-sqr`
64×	`distribute-lft-out`
63×	`associate-r` `associate-l`
38×	`associate-/r/`
21×	`flip3-+` `flip-+`
19×	`pow1` `div-inv`
16×	`unswap-sqr`
15×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r*`
9×	`associate-/l*`
8×	`sqrt-pow1` `pow1/2` `sqrt-div`
7×	`associate-/l/`
5×	`pow-prod-up`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr`
2×	`frac-times` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `*-commutative`

Counts

4 → 355

Calls

4 calls:

510.0ms	(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
921.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
326.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
340.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series585.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
188.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
95.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
109.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.7s

Counts

367 → 367

Iterations

Iter	Nodes
done	5032
2	3936
1	1070
0	553

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.5b	(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

2560×	`times-frac`
1662×	`*-un-lft-identity`
1416×	`sqrt-prod`
1082×	`add-sqr-sqrt` `add-cube-cbrt`
290×	`distribute-lft-out`
144×	`associate-/l*`
120×	`associate-/r/`
68×	`div-inv`
62×	`flip3-+` `flip-+`
20×	`associate-/r*` `add-exp-log`
18×	`add-cbrt-cube`
10×	`div-exp`
8×	`cbrt-undiv`
6×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `sqrt-div` `insert-posit16` `add-log-exp`
1×	`1-exp`

Counts

4 → 1211

Calls

4 calls:

433.0ms	(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
572.0ms	(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
343.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
450.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
202.0ms	(/ (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
122.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
109.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.9s

Counts

1223 → 1223

Iterations

Iter	Nodes
done	5000
1	3178
0	1347

prune7.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (+ alpha beta))
0.0b	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
1.5b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
145×	`*-un-lft-identity`
87×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
29×	`distribute-lft-out`
26×	`associate-/l*`
19×	`difference-of-squares`
16×	`associate-/r/`
15×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+`
11×	`pow1`
10×	`associate-/r*`
8×	`div-inv`
6×	`swap-sqr`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`frac-times` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `associate-l/` `associate-r/` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 225

Calls

4 calls:

64.0ms	(* (+ alpha beta) (+ alpha beta))
437.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
569.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
417.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ alpha beta) (+ alpha beta))
58.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
250.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
117.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.9s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	3874
1	1081
0	380

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

regimes135.0ms

Accuracy

52% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch103.0ms

Steps

Iters	Range		Point
8	1.4934629267433437e+160	2.2468884298417645e+164	3.948042311878287e+161

simplify7.0ms

Iterations

Iter	Nodes
done	44
1	44
0	31

end0.0ms

sample1.1s

Algorithm

intervals

Results

629.0ms	8000×	body	80	valid
354.0ms	8000×	pre	80	true