Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	26
1	283	26
2	1620	26
3	5003	26
done	5003	26

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.4b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.7b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

137.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
101.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
228.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
136.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.2s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
109.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
828.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
185.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify67.0ms

Counts

212 → 212

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1249	5670
1	5001	5161
done	5001	5161

prune632.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.7b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-exp-log` `add-cbrt-cube`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 364

Calls

4 calls:

263.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
769.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
64.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
131.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.0s

Counts

4 → 12

Calls

4 calls:

330.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
89.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
330.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify109.0ms

Counts

376 → 376

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1683	10749
1	5001	9903
done	5001	9903

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.3b

localize28.0ms

Local error

Found 4 expressions with local error:

7.7b	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
34.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite841.0ms

Algorithm

rewrite-expression-head

Rules

11777×	`times-frac`
6537×	`add-sqr-sqrt`
5431×	`*-un-lft-identity`
4327×	`add-cube-cbrt`
3150×	`sqrt-prod`
1104×	`difference-of-squares`
552×	`distribute-lft-out--`
313×	`div-inv`
302×	`associate-/r/`
152×	`associate-/r*`
142×	`flip3-+` `flip-+`
39×	`add-exp-log`
30×	`add-cbrt-cube`
26×	`div-exp`
23×	`associate-/l*`
17×	`cbrt-undiv`
6×	`pow1`
4×	`sqrt-div` `add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 3531

Calls

4 calls:

262.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
65.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
91.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
63.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
58.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.3s

Counts

3543 → 3543

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5001	182857
done	5001	182857

prune9.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))))
7.7b	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
34.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.6b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

23343×	`times-frac`
12948×	`add-sqr-sqrt`
10701×	`*-un-lft-identity`
8531×	`add-cube-cbrt`
6220×	`sqrt-prod`
3283×	`associate-r`
2160×	`difference-of-squares`
1080×	`distribute-lft-out--`
617×	`div-inv`
589×	`associate-/r/`
273×	`flip3-+` `flip-+`
258×	`add-exp-log`
183×	`add-cbrt-cube`
160×	`div-exp`
149×	`associate-/r*`
103×	`cbrt-undiv`
60×	`prod-exp`
42×	`cbrt-unprod`
22×	`associate-/l*`
21×	`unswap-sqr`
15×	`1-exp`
10×	`associate-l`
8×	`pow1`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/` `distribute-lft-out`

Counts

4 → 6900

Calls

4 calls:

1.8s	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))))
260.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series2.9s

Counts

4 → 12

Calls

4 calls:

2.5s	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))))
329.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
63.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
58.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify2.4s

Counts

6912 → 6912

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5063	334506
done	5063	334506

prune21.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.3b

regimes169.0ms

Accuracy

35.9% (2.4b remaining)

Error of 36.6b against oracle of 34.3b and baseline of 38.0b

bsearch57.0ms

Steps

Iters	Range		Point
8	1.395872028693069e+203	2.4154738403318782e+207	1.4174577998254982e+203

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	55
1	44	55
done	44	55

end0.0ms

sample705.0ms

Algorithm

intervals

Results

343.0ms	8000×	body	80	valid
109.0ms	8000×	pre	80	true