Details

sample72.0ms

Algorithm

intervals

Results

18.0ms	204×	body	80	valid
9.0ms	22×	body	640	valid
9.0ms	256×	pre	80	true
6.0ms	13×	body	1280	valid
3.0ms	9×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	102	29
3	452	29
4	2090	29
done	5001	29

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

2.3b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

19.5b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `flip--`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 111

Calls

3 calls:

227.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

826.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

100.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series935.0ms

Counts

3 → 9

Calls

3 calls:

346.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

455.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

134.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.7s

Counts

120 → 120

Iterations

Useful iterations: 2 (579.0ms)

Iter	Nodes	Cost
0	225	4035
1	675	3821
2	2949	3577
done	5000	3577

prune525.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.3b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`+-commutative` `flip3--` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip--`

Counts

4 → 129

Calls

4 calls:

66.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
232.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
196.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
749.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
398.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
106.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
461.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify2.1s

Counts

141 → 141

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	227	3335
1	645	3154
2	2957	2864
done	5000	2862

prune555.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.2b	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
484×	`*-un-lft-identity`
408×	`add-sqr-sqrt`
260×	`add-cube-cbrt`
219×	`sqrt-prod`
153×	`associate-r`
67×	`distribute-lft-out`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
34×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/l*`
21×	`flip3-+` `flip-+`
19×	`div-inv`
15×	`unswap-sqr`
14×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 485

Calls

4 calls:

951.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
302.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
190.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
284.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

420.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
394.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
227.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
414.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify1.3s

Counts

497 → 497

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	568	20612
1	1675	19182
done	5001	18531

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.2b	(+ (cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
10.1b	(cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

295×	`times-frac`
259×	`*-un-lft-identity`
187×	`add-sqr-sqrt`
139×	`add-cube-cbrt`
108×	`sqrt-prod`
36×	`distribute-lft-out`
25×	`associate-/l*`
24×	`distribute-lft-out--` `difference-of-squares`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
8×	`cbrt-prod`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `sqrt-div` `div-exp`
3×	`cube-div` `cbrt-div` `associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `cube-mult` `frac-times` `unpow-prod-down` `pow1/3` `unpow3` `cube-prod` `associate-r/` `associate-l/` `sum-log` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 280

Calls

4 calls:

257.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
213.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
16.0ms	(+ (cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
3.0ms	(cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
194.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
440.0ms	(+ (cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
405.0ms	(cbrt (pow (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

simplify2.1s

Counts

292 → 292

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	459	11881
1	1112	10879
2	3656	10278
done	5000	10277

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

regimes328.0ms

Accuracy

2.4% (6.2b remaining)

Error of 12.4b against oracle of 6.2b and baseline of 12.5b

bsearch126.0ms

Steps

Iters	Range		Point
8	1.176656138705441e+97	2.9487777469176966e+100	1.0932916019061694e+100

simplify30.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	65
1	40	65
done	40	65

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	6338×	body	80	valid
275.0ms	528×	body	1280	valid
267.0ms	8000×	pre	80	true
194.0ms	574×	body	640	valid
167.0ms	353×	body	320	valid
84.0ms	207×	body	160	valid