Details

sample25.0ms

Algorithm

intervals

Results

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

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17
done	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize13.0ms

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

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

Counts

4 → 465

Calls

4 calls:

106.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
327.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
482.0ms	(/ (/ (/ (+ (+ (+ 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))
287.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (/ (/ (+ (+ (+ 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))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify127.0ms

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552
done	5002	12552

prune938.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
58×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
53×	`times-frac`
38×	`add-cube-cbrt` `add-cbrt-cube`
28×	`div-exp`
18×	`associate-l`
16×	`prod-exp`
15×	`cbrt-undiv` `associate-r`
10×	`associate-/r*` `associate-/r/`
9×	`distribute-lft-out`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
5×	`rec-exp` `1-exp` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-r/` `associate-l/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 171

Calls

4 calls:

35.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
433.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
286.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
280.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
138.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
151.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify110.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	758	2684
1	4240	2303
2	5001	2270
done	5001	2270

prune376.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite806.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `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`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

366.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
208.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
111.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
113.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series407.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify64.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394
done	5003	2394

prune432.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
6.1b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

316×	`times-frac`
214×	`*-un-lft-identity`
184×	`sqrt-prod`
166×	`add-sqr-sqrt`
164×	`add-cube-cbrt`
42×	`associate-/r/`
38×	`flip3-+` `flip-+`
36×	`cbrt-div`
34×	`associate-/l*`
28×	`frac-times`
26×	`sqrt-div`
25×	`distribute-lft-out`
18×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-*l/`
9×	`div-inv`
8×	`associate-*r/`
7×	`associate-/r*`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`prod-exp` `cbrt-unprod` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 303

Calls

4 calls:

257.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
112.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
113.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
681.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
374.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify85.0ms

Counts

315 → 315

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1292	7763
1	5001	7317
done	5001	7317

prune983.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.3b

regimes78.0ms

Accuracy

59.4% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 4.0b

bsearch48.0ms

Steps

Iters	Range		Point
7	8.204955259617668e+197	5.2404437607380405e+199	8.345047959283739e+197

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23
done	30	23

end0.0ms

sample555.0ms

Algorithm

intervals

Results

279.0ms	8000×	body	80	valid
87.0ms	8000×	pre	80	true