Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14
done	5001	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize12.0ms

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))

1.6b

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

20.5b

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

rewrite789.0ms

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:

182.0ms

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

551.0ms

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

52.0ms

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

series633.0ms

Counts

3 → 9

Calls

3 calls:

251.0ms

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

301.0ms

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

81.0ms

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

simplify89.0ms

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5003	1789
done	5003	1789

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize13.0ms

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))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.3b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite703.0ms

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-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
179.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
363.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
100.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series815.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
172.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
254.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
306.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify69.0ms

Counts

307 → 307

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605
done	5001	4605

prune763.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.3b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite843.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
137×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
90×	`associate-r`
69×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`div-inv`
4×	`cube-div` `associate-l`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-mult` `frac-times` `cbrt-div` `unpow3` `associate-*l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `pow-prod-down` `pow-exp` `sum-log` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 176

Calls

4 calls:

189.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
184.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
360.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
101.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.7s

Counts

4 → 12

Calls

4 calls:

823.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
306.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
254.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
305.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify51.0ms

Counts

188 → 188

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	973	3074
1	5001	2918
done	5001	2918

prune543.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize18.0ms

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)))
0.3b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.1b	(+ (* (/ (+ 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)

rewrite1.2s

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:

681.0ms	(* (/ (+ 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))))
188.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
134.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
165.0ms	(+ (* (/ (+ 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)

series944.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (/ (+ 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))))
240.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
143.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
306.0ms	(+ (* (/ (+ 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)

simplify116.0ms

Counts

497 → 497

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1727	10548
1	5001	10067
done	5001	10067

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

regimes212.0ms

Accuracy

16.5% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.6b

bsearch83.0ms

Steps

Iters	Range		Point
9	2.57588219440865e+170	5.648441501904801e+176	1.73042538274464e+174

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	50
1	55	50
done	55	50

end0.0ms

sample868.0ms

Algorithm

intervals

Results

247.0ms	6330×	body	80	valid
114.0ms	523×	body	1280	valid
113.0ms	8000×	pre	80	true
94.0ms	576×	body	640	valid
46.0ms	391×	body	320	valid
14.0ms	180×	body	160	valid