Details

sample64.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1753
2	282
1	58
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.0b	(/ (/ (* (* 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))
45.8b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite583.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
38×	`add-sqr-sqrt`
32×	`frac-times`
28×	`associate-*r/`
24×	`*-un-lft-identity` `add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
9×	`pow1` `associate-/l/`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
3×	`associate-r` `pow-prod-down`
2×	`distribute-rgt-in` `associate-+r+` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `flip3--` `associate-l` `*-commutative` `flip--`

Counts

4 → 178

Calls

4 calls:

24.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
141.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
260.0ms	(/ (/ (* (* 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))
141.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
151.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s	(/ (/ (* (* 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))
321.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.8s

Counts

190 → 190

Iterations

Iter	Nodes
done	5001
1	1224
0	339

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.3b

localize46.0ms

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))))
35.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.4s

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

Counts

4 → 364

Calls

4 calls:

336.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
827.0ms	(* (/ (/ (* 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))))
56.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
127.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.0s

Counts

4 → 12

Calls

4 calls:

467.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.2s	(* (/ (/ (* 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))))
132.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
176.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.2s

Counts

376 → 376

Iterations

Iter	Nodes
done	5000
1	1786
0	501

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
0.0b	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
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))))
36.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
166×	`add-sqr-sqrt`
159×	`*-un-lft-identity`
117×	`associate-r`
92×	`add-cube-cbrt`
67×	`add-cbrt-cube` `add-exp-log`
30×	`difference-of-squares`
27×	`cbrt-undiv` `div-exp`
22×	`associate-/r/` `distribute-lft-out`
20×	`prod-exp` `cbrt-unprod`
15×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-l`
12×	`flip3-+` `flip-+`
11×	`div-inv`
8×	`pow1` `associate-/l*`
6×	`associate-/r*`
5×	`unswap-sqr`
4×	`add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`
1×	`frac-times` `flip3--` `associate-*l/` `flip--`

Counts

4 → 255

Calls

4 calls:

115.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
141.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
803.0ms	(* (/ (* 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))))
125.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.7s

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
152.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
3.3s	(* (/ (* 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))))
164.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.9s

Counts

267 → 267

Iterations

Iter	Nodes
done	5000
1	1429
0	399

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 (+ alpha beta)) (* 0.5 i)) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
0.0b	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.0b	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
0.0b	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
58×	`times-frac`
52×	`add-cbrt-cube` `add-exp-log`
45×	`associate-r`
38×	`add-cube-cbrt`
24×	`distribute-lft-out`
18×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
13×	`associate-l`
10×	`associate-/r/`
8×	`pow1`
7×	`associate-/r*`
6×	`associate-/l*` `difference-of-squares`
5×	`flip3-+` `flip-+` `div-inv`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-*r/` `sqrt-prod` `distribute-lft-out--` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `associate-*l/` `flip--`

Counts

4 → 171

Calls

4 calls:

844.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 (+ alpha beta)) (* 0.5 i)) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
173.0ms	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
76.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
155.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))

series1.3s

Counts

4 → 12

Calls

4 calls:

678.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 (+ alpha beta)) (* 0.5 i)) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
343.0ms	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
104.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
144.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))

simplify1.6s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
1	898
0	270

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.2b

regimes438.0ms

Accuracy

38.4% (9.4b remaining)

Error of 11.3b against oracle of 1.9b and baseline of 17.2b

bsearch104.0ms

Steps

Iters	Range		Point
6	3.710562679513184e+121	1.5715503341522111e+122	1.557956856149691e+122

simplify17.0ms

Iterations

Iter	Nodes
done	47
1	47
0	33

end0.0ms

sample1.4s

Algorithm

intervals

Results

758.0ms	8000×	body	80	valid
369.0ms	8000×	pre	80	true