Details

sample78.0ms

Algorithm

intervals

Results

19.0ms	198×	body	80	valid
10.0ms	20×	body	1280	valid
8.0ms	256×	pre	80	true
8.0ms	20×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
4	2146
3	448
2	97
1	31
0	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize24.0ms

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)))

rewrite976.0ms

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:

213.0ms

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

702.0ms

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

57.0ms

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

series850.0ms

Counts

3 → 9

Calls

3 calls:

366.0ms

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

362.0ms

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

121.0ms

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

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5016
2	3101
1	690
0	225

prune795.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize23.0ms

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)

rewrite817.0ms

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:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
183.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
433.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
133.0ms	(+ (* (+ 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:

127.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
235.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
375.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
374.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify3.1s

Counts

307 → 307

Iterations

Iter	Nodes
done	5001
2	4222
1	1123
0	385

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize76.0ms

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)

rewrite809.0ms

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:

496.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
109.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
108.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
88.0ms	(+ (* (+ 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:

348.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
442.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
402.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
377.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify2.4s

Counts

162 → 162

Iterations

Iter	Nodes
done	5008
2	3402
1	866
0	274

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- beta alpha))
0.7b	(cbrt (- beta alpha))
2.1b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
4.4b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

207×	`add-exp-log`
94×	`prod-exp`
87×	`div-exp`
84×	`add-cbrt-cube`
58×	`cbrt-unprod`
51×	`cbrt-undiv`
13×	`*-un-lft-identity`
12×	`1-exp`
11×	`add-sqr-sqrt`
10×	`cbrt-prod`
9×	`frac-times` `pow1`
7×	`add-cube-cbrt`
6×	`associate-*r/` `add-log-exp`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`cbrt-div` `associate-l`
3×	`pow-prod-down`
2×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `associate-r` `*-commutative` `distribute-lft-out`

Counts

4 → 123

Calls

4 calls:

3.0ms	(cbrt (- beta alpha))
4.0ms	(cbrt (- beta alpha))
2.3s	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
2.2s	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (- beta alpha))
194.0ms	(cbrt (- beta alpha))
374.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
454.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify3.8s

Counts

135 → 135

Iterations

Iter	Nodes
done	5003
2	3807
1	1021
0	337

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

regimes592.0ms

Accuracy

16.3% (5.7b remaining)

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

bsearch154.0ms

Steps

Iters	Range		Point
9	4.309904012345806e+203	4.9405188995777975e+210	2.6817473048651766e+206

simplify13.0ms

Iterations

Iter	Nodes
done	42
1	42
0	32

end0.0ms

sample1.8s

Algorithm

intervals

Results

628.0ms	6317×	body	80	valid
281.0ms	8000×	pre	80	true
264.0ms	528×	body	1280	valid
212.0ms	589×	body	640	valid
126.0ms	359×	body	320	valid
30.0ms	207×	body	160	valid