Details

sample61.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify550.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	554
2	111
1	33
0	14

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

localize24.0ms

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))
4.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.4s

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

Counts

4 → 465

Calls

4 calls:

101.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
390.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
544.0ms	(/ (/ (/ (+ (+ (+ 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))
330.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
173.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
166.0ms	(/ (/ (/ (+ (+ (+ 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))
101.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify825.0ms

Counts

477 → 477

Iterations

Iter	Nodes
done	5001
1	1609
0	602

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha))))
0.1b	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.8b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

4254×	`times-frac`
2985×	`*-un-lft-identity`
1628×	`add-sqr-sqrt` `add-cube-cbrt`
772×	`distribute-lft-out`
284×	`associate-/l*`
158×	`associate-/r/`
89×	`div-inv`
70×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
33×	`associate-/r*`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`clear-num` `frac-2neg` `add-log-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 1524

Calls

4 calls:

243.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))) (+ (+ alpha beta) (* 2.0 1.0)))
167.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha))))
462.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
187.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))

series614.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))) (+ (+ alpha beta) (* 2.0 1.0)))
96.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha))))
216.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
107.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ 1.0 (+ (+ (* alpha beta) beta) alpha)))

simplify3.0s

Counts

1536 → 1536

Iterations

Iter	Nodes
done	5000
1	4890
0	1601

prune4.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 1 (exp (log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.6b	(exp (log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))))
4.2b	(log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0)))
4.8b	(/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

3903×	`times-frac`
2687×	`*-un-lft-identity`
1486×	`add-sqr-sqrt` `add-cube-cbrt`
987×	`log-prod`
966×	`exp-sum`
673×	`distribute-lft-out`
240×	`associate-/l*`
123×	`associate-/r/`
69×	`div-inv`
55×	`flip3-+` `flip-+`
21×	`add-exp-log`
17×	`log-div`
16×	`exp-diff`
15×	`add-cbrt-cube`
13×	`div-exp`
9×	`associate-/r*`
7×	`cbrt-undiv`
6×	`pow1`
4×	`exp-prod` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `rem-log-exp` `log-pow`
1×	`rec-exp` `1-exp` `rem-exp-log`

Counts

4 → 1315

Calls

4 calls:

555.0ms	(/ (/ (/ 1 (exp (log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
55.0ms	(exp (log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))))
73.0ms	(log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0)))
138.0ms	(/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

248.0ms	(/ (/ (/ 1 (exp (log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
124.0ms	(exp (log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))))
122.0ms	(log (/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0)))
561.0ms	(/ (+ (* 2.0 1.0) (+ beta alpha)) (+ (+ alpha (+ beta (* alpha beta))) 1.0))

simplify2.9s

Counts

1327 → 1327

Iterations

Iter	Nodes
done	5000
1	4769
0	1827

prune4.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ 1 (* (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
1.8b	(* (/ (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ 1 (* (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
1.9b	(/ (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.9b	(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

1155×	`times-frac`
1139×	`*-un-lft-identity`
615×	`sqrt-prod`
559×	`add-sqr-sqrt`
472×	`add-cube-cbrt`
383×	`distribute-lft-out`
252×	`associate-l`
130×	`add-exp-log`
111×	`associate-r`
98×	`associate-/r/`
82×	`sqrt-div`
70×	`add-cbrt-cube`
66×	`flip3-+` `flip-+`
65×	`div-exp`
49×	`associate-/l*`
36×	`prod-exp`
33×	`frac-times` `cbrt-undiv`
25×	`div-inv`
21×	`unswap-sqr`
17×	`associate-l/` `associate-r/`
16×	`cbrt-unprod`
14×	`associate-/r*`
13×	`pow1`
8×	`rec-exp` `1-exp`
7×	`pow-flip`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-prod-up`
1×	`cube-unmult` `*-commutative` `inv-pow`

Counts

4 → 846

Calls

4 calls:

92.0ms	(/ 1 (* (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
1.6s	(* (/ (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ 1 (* (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
638.0ms	(/ (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
430.0ms	(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 1 (* (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
218.0ms	(* (/ (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ 1 (* (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
245.0ms	(/ (/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
143.0ms	(/ (+ 1.0 (+ (+ (* alpha beta) beta) alpha)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

simplify1.3s

Counts

858 → 858

Iterations

Iter	Nodes
done	5001
1	2522
0	748

prune4.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

67.6% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 3.9b

bsearch129.0ms

Steps

Iters	Range		Point
9	2.9934700075384335e+152	9.600750868010722e+158	6.628222884241032e+153

simplify13.0ms

Iterations

Iter	Nodes
done	45
2	45
1	44
0	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

790.0ms	8000×	body	80	valid
187.0ms	8000×	pre	80	true