Details

sample66.0ms

Algorithm

intervals

Results

32.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.3s

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize33.0ms

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))
2.2b	(/ (+ (+ (+ 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:

105.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
405.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
543.0ms	(/ (/ (/ (+ (+ (+ 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))
344.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
222.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
224.0ms	(/ (/ (/ (+ (+ (+ 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))
100.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Counts

477 → 477

Iterations

Iter	Nodes
done	5001
1	1609
0	602

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (+ (+ alpha beta) (* 2.0 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))) (+ 1.0 (+ (+ alpha beta) (* 2.0 1.0))))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

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-+r+`

Counts

4 → 465

Calls

4 calls:

69.0ms	(+ 1.0 (+ (+ alpha beta) (* 2.0 1.0)))
442.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
485.0ms	(/ (/ (/ (+ (+ (+ 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))))
314.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series581.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ 1.0 (+ (+ alpha beta) (* 2.0 1.0)))
202.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
253.0ms	(/ (/ (/ (+ (+ (+ 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))))
108.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.6s

Counts

477 → 477

Iterations

Iter	Nodes
done	5000
1	1614
0	602

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.7b

localize125.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite361.0ms

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×	`associate-/r*` `times-frac` `sqrt-prod`
4×	`frac-times` `pow1` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

159.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
78.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
73.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series660.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
119.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
95.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
101.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.6s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	2042
1	539
0	200

prune937.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.7b

localize68.0ms

Local error

Found 4 expressions with local error:

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))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
0.7b	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

354×	`times-frac`
240×	`*-un-lft-identity`
170×	`add-sqr-sqrt`
158×	`add-cube-cbrt`
82×	`associate-/l*`
40×	`distribute-lft-out`
36×	`associate-/r/`
34×	`add-cbrt-cube` `add-exp-log`
27×	`flip3-+` `flip-+`
26×	`sqrt-prod`
24×	`sqrt-div`
19×	`pow1`
16×	`cbrt-undiv` `div-exp`
15×	`div-inv`
11×	`swap-sqr`
8×	`frac-times` `sqrt-pow1` `pow1/2`
7×	`associate-/r` `associate-r` `associate-l*`
5×	`pow-prod-up`
4×	`associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `add-log-exp` `unswap-sqr` `associate-/l/`
3×	`clear-num` `frac-2neg` `pow-prod-down` `pow-sqr`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `*-commutative`

Counts

4 → 341

Calls

4 calls:

376.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
610.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
538.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
316.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
194.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
23.0ms	(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
97.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Counts

353 → 353

Iterations

Iter	Nodes
done	5000
1	1352
0	464

prune2.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.7b

regimes204.0ms

Accuracy

57.1% (1.0b remaining)

Error of 2.1b against oracle of 1.1b and baseline of 3.5b

bsearch74.0ms

Steps

Iters	Range		Point
9	2.930046285566794e+191	1.98860419215105e+200	6.365999385200842e+194

simplify8.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
206.0ms	8000×	pre	80	true