Details

sample82.0ms

Algorithm

intervals

Results

21.0ms	203×	body	80	valid
9.0ms	18×	body	1280	valid
8.0ms	256×	pre	80	true
4.0ms	10×	body	640	valid
3.0ms	15×	body	160	valid
3.0ms	10×	body	320	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5008
4	2175
3	446
2	97
1	31
0	15

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize49.0ms

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))

3.5b

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

21.1b

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

rewrite2.0s

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:

542.0ms

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

1.2s

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

140.0ms

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

series3.2s

Counts

3 → 9

Calls

3 calls:

1.0s

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

1.4s

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

703.0ms

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

simplify5.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5002
2	3093
1	690
0	225

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.1b	(+ (* (/ (/ (+ alpha beta) 1) (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)

rewrite5.4s

Algorithm

rewrite-expression-head

Rules

1015×	`times-frac`
755×	`*-un-lft-identity`
655×	`add-sqr-sqrt`
413×	`add-cube-cbrt`
333×	`sqrt-prod`
153×	`associate-r`
121×	`distribute-lft-out`
118×	`associate-l`
64×	`add-exp-log`
50×	`add-cbrt-cube`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
37×	`associate-/l*`
35×	`div-exp` `unswap-sqr`
34×	`div-inv`
24×	`cbrt-undiv`
20×	`flip3-+` `flip-+`
14×	`associate-/r*`
12×	`prod-exp`
9×	`cbrt-unprod`
8×	`sqrt-div`
6×	`pow1` `add-log-exp`
4×	`1-exp`
2×	`frac-2neg` `div-sub` `clear-num` `associate-/l/`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 696

Calls

4 calls:

3.5s	(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
453.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
437.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
659.0ms	(+ (* (/ (/ (+ alpha beta) 1) (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)

series6.7s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
442.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
779.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.4s	(+ (* (/ (/ (+ alpha beta) 1) (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)

simplify11.3s

Counts

708 → 708

Iterations

Iter	Nodes
done	5000
1	2296
0	728

prune9.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize197.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.1b	(+ (* (/ (+ 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)
7.1b	(+ (* (/ (+ 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)
7.1b	(+ (* (/ (+ 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)

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

267×	`times-frac`
212×	`*-un-lft-identity`
168×	`add-sqr-sqrt`
120×	`add-cube-cbrt`
88×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-lft-out`
21×	`associate-/l*`
18×	`associate-/r/`
12×	`flip3-+` `flip-+`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`associate-/r*`
4×	`pow1`
3×	`cbrt-undiv` `+-commutative` `div-exp` `sum-log`
2×	`sqrt-div` `div-sub`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 226

Calls

4 calls:

554.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
380.0ms	(+ (* (/ (+ 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)
506.0ms	(+ (* (/ (+ 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)
366.0ms	(+ (* (/ (+ 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)

series3.6s

Counts

4 → 12

Calls

4 calls:

466.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.1s	(+ (* (/ (+ 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)
1.1s	(+ (* (/ (+ 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)
959.0ms	(+ (* (/ (+ 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)

simplify4.3s

Counts

238 → 238

Iterations

Iter	Nodes
done	5008
2	2944
1	887
0	353

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize254.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- beta alpha))
7.1b	(+ (* (/ (+ 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)
7.1b	(+ (* (/ (+ 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)
7.1b	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))))) 1.0)

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`+-commutative` `flip3-+` `sum-log` `flip-+`
2×	`cbrt-div`
1×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 48

Calls

4 calls:

8.0ms	(cbrt (- beta alpha))
397.0ms	(+ (* (/ (+ 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)
356.0ms	(+ (* (/ (+ 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)
1.3s	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))))) 1.0)

series2.1s

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt (- beta alpha))
617.0ms	(+ (* (/ (+ 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)
552.0ms	(+ (* (/ (+ 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)
658.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))))) 1.0)

simplify4.7s

Counts

60 → 60

Iterations

Iter	Nodes
done	5005
2	1231
1	368
0	144

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

regimes1.1s

Accuracy

18% (5.2b remaining)

Error of 11.1b against oracle of 6.0b and baseline of 12.3b

bsearch137.0ms

Steps

Iters	Range		Point
7	3.1689190823829048e+218	6.106825492056067e+219	3.27712724994482e+219

simplify18.0ms

Iterations

Iter	Nodes
done	41
1	41
0	33

end0.0ms

sample3.1s

Algorithm

intervals

Results

980.0ms	494×	body	1280	valid
706.0ms	6366×	body	80	valid
412.0ms	8000×	pre	80	true
407.0ms	588×	body	640	valid
163.0ms	335×	body	320	valid
42.0ms	217×	body	160	valid