Details

sample54.0ms

Algorithm

intervals

Results

31.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	11034
3	1567
2	267
1	58
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.2b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
44.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite722.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`*-un-lft-identity` `add-cube-cbrt`
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` `insert-posit16` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 204

Calls

4 calls:

156.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
91.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
293.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
176.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.5s

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
139.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.0s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
262.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify2.8s

Counts

216 → 216

Iterations

Iter	Nodes
2	7740
1	1304
0	360

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.3b

localize427.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
32.0b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
32.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

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-cbrt-cube` `add-exp-log`
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×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 368

Calls

4 calls:

251.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
632.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
68.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
142.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.9s

Counts

4 → 12

Calls

4 calls:

473.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.1s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
110.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
152.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.8s

Counts

380 → 380

Iterations

Iter	Nodes
2	7064
1	1693
0	503

prune6.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 30.2b

localize62.0ms

Local error

Found 4 expressions with local error:

6.0b	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
32.0b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
32.3b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.3b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite585.0ms

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` `insert-posit16` `add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 3535

Calls

4 calls:

192.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
65.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
12.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
9.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series782.0ms

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
120.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
82.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
119.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify13.3s

Counts

3547 → 3547

Iterations

Iter	Nodes
1	11533
0	3258

prune1.3m

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 30.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i))))))
6.0b	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
32.3b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
32.3b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite1.8s

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` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out` `associate-/l/`

Counts

4 → 6904

Calls

4 calls:

909.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i))))))
179.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
12.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.8s

Counts

4 → 12

Calls

4 calls:

3.1s	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i))))))
480.0ms	(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2 i)))))
90.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
78.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify39.3s

Counts

6916 → 6916

Iterations

Iter	Nodes
1	20985
0	5063

prune2.4m

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 30.2b

regimes149.0ms

Accuracy

37.6% (1.6b remaining)

Error of 35.3b against oracle of 33.7b and baseline of 36.3b

bsearch59.0ms

Steps

Iters	Range		Point
6	1.2746295619568668e+189	8.90793562400218e+189	1.2994741600183278e+189

simplify9.0ms

Iterations

Iter	Nodes
2	43
1	43
0	31

end0.0ms

sample1.6s

Algorithm

intervals

Results

901.0ms	8000×	body	80	valid
527.0ms	8000×	pre	80	true