Details

sample65.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify4.3s

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize52.0ms

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))))
37.2b	(/ (/ (* (* 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))
45.9b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite660.0ms

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:

142.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
97.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
238.0ms	(/ (/ (* (* 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))
177.0ms	(/ (* (* 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:

79.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
134.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s	(/ (/ (* (* 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))
254.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.5s

Counts

216 → 216

Iterations

Iter	Nodes
2	7459
1	1304
0	360

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
35.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

216×	`times-frac`
163×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
99×	`add-cube-cbrt`
32×	`associate-/r/` `difference-of-squares`
28×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
17×	`flip3-+` `flip-+`
16×	`associate-/r*` `sqrt-prod` `div-inv` `distribute-lft-out--`
11×	`cbrt-undiv` `div-exp`
10×	`distribute-lft-out`
6×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`prod-exp` `associate-*r/` `cbrt-unprod`
1×	`flip3--` `flip--`

Counts

4 → 256

Calls

4 calls:

156.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
246.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
150.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
72.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts

4 → 12

Calls

4 calls:

316.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
409.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
202.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
135.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts

268 → 268

Iterations

Iter	Nodes
2	4048
1	1105
0	401

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 34.6b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite625.0ms

Algorithm

rewrite-expression-head

Rules

181×	`times-frac`
153×	`add-sqr-sqrt`
145×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`difference-of-squares`
24×	`associate-/l*`
22×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
16×	`associate-/r*` `sqrt-prod` `distribute-lft-out--`
14×	`distribute-lft-out`
12×	`flip3-+` `flip-+`
11×	`div-inv`
9×	`cbrt-undiv` `div-exp`
6×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`
1×	`flip3--` `associate-*r/` `flip--`

Counts

4 → 230

Calls

4 calls:

159.0ms	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
246.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
86.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
128.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
470.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
81.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
177.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts

242 → 242

Iterations

Iter	Nodes
2	3661
1	999
0	363

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
0.2b	(/ (+ (* 1/2 i) (* 1/4 (+ alpha beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
53×	`times-frac`
37×	`add-cube-cbrt`
23×	`distribute-lft-out`
22×	`add-cbrt-cube` `add-exp-log`
21×	`associate-r`
13×	`associate-/r*`
9×	`associate-/l*`
8×	`associate-/r/` `difference-of-squares`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
5×	`flip3-+` `flip-+` `associate-/l/`
4×	`prod-exp` `sqrt-prod` `cbrt-unprod` `insert-posit16` `div-inv` `distribute-lft-out--` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`associate-*r/` `unswap-sqr`
1×	`flip3--` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 154

Calls

4 calls:

145.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
129.0ms	(/ (+ (* 1/2 i) (* 1/4 (+ alpha beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
169.0ms	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
88.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

series798.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i))))
237.0ms	(/ (+ (* 1/2 i) (* 1/4 (+ alpha beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
333.0ms	(/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
114.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))

simplify1.0s

Counts

166 → 166

Iterations

Iter	Nodes
2	2836
1	701
0	252

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.6b

regimes338.0ms

Accuracy

48.2% (8.3b remaining)

Error of 10.3b against oracle of 2.0b and baseline of 18.0b

bsearch71.0ms

Steps

Iters	Range		Point
4	3.284463260365638e+137	6.4587449782834e+137	4.991681683367987e+137

simplify11.0ms

Iterations

Iter	Nodes
2	54
1	54
0	38

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
370.0ms	8000×	pre	80	true