Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	198×	body	80	valid
11.0ms	12×	body	320	valid
7.0ms	20×	body	1280	valid
5.0ms	20×	body	640	valid
5.0ms	256×	pre	80	true
1.0ms	6×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2483
3	453
2	102
1	31
0	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize48.0ms

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))

1.8b

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

22.3b

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

rewrite949.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

200.0ms

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

703.0ms

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

42.0ms

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

series866.0ms

Counts

3 → 9

Calls

3 calls:

359.0ms

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

377.0ms

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

129.0ms

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

simplify2.4s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	4479
1	697
0	225

prune859.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.0b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite908.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

64.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
216.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
479.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
134.0ms	(+ (* (+ 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:

111.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
276.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
347.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
404.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.5s

Counts

307 → 307

Iterations

Iter	Nodes
done	5001
1	1142
0	385

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize99.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.0b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.0b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.0b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite761.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
131×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
90×	`associate-r`
63×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
6×	`pow1`
5×	`div-inv`
4×	`associate-l`
3×	`cbrt-undiv` `+-commutative` `sum-log` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-*l/`
1×	`pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 150

Calls

4 calls:

399.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
120.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
110.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
119.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.6s

Counts

4 → 12

Calls

4 calls:

334.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
402.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
444.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
382.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.4s

Counts

162 → 162

Iterations

Iter	Nodes
done	5000
1	882
0	274

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (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)))
2.1b	(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
8.1b	(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

6211×	`times-frac`
4294×	`*-un-lft-identity`
3048×	`add-sqr-sqrt`
2585×	`sqrt-prod`
2326×	`add-cube-cbrt`
1077×	`associate-r`
645×	`distribute-lft-out`
339×	`distribute-lft-out--` `difference-of-squares`
262×	`associate-/r/`
174×	`associate-/l*`
134×	`flip3-+` `flip-+`
131×	`div-inv`
36×	`sqrt-div`
32×	`add-cbrt-cube` `add-exp-log`
15×	`cbrt-undiv` `div-exp`
14×	`associate-/r*`
11×	`unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`div-sub`
4×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`+-commutative` `sum-log` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 2569

Calls

4 calls:

608.0ms	(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
214.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.1s	(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
314.0ms	(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

259.0ms	(/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
322.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
358.0ms	(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
474.0ms	(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify4.3s

Counts

2581 → 2581

Iterations

Iter	Nodes
done	5000
0	1739

prune13.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes462.0ms

Accuracy

16.5% (5.7b remaining)

Error of 11.5b against oracle of 5.8b and baseline of 12.6b

bsearch100.0ms

Steps

Iters	Range		Point
8	2.3502842158912643e+199	3.966593715172402e+202	1.8574715806610076e+202

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	6317×	body	80	valid
360.0ms	8000×	pre	80	true
215.0ms	528×	body	1280	valid
188.0ms	589×	body	640	valid
82.0ms	359×	body	320	valid
63.0ms	207×	body	160	valid