Details

sample86.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
4	11139
3	1615
2	280
1	60
0	17

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.5b

localize57.0ms

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))))

rewrite631.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `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 → 212

Calls

4 calls:

155.0ms	(* (+ (+ 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))
136.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
178.0ms	(* (* 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))
277.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.1s

Counts

224 → 224

Iterations

Iter	Nodes
2	7473
1	1333
0	368

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.6b

localize55.0ms

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)))

rewrite773.0ms

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×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `associate-*r/` `cbrt-unprod`
1×	`flip3--` `flip--`

Counts

4 → 264

Calls

4 calls:

177.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
334.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
185.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
73.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.1s

Counts

4 → 12

Calls

4 calls:

320.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
493.0ms	(/ (/ (+ (* 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)))
92.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.7s

Counts

276 → 276

Iterations

Iter	Nodes
2	4177
1	1119
0	409

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 34.6b

localize71.0ms

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)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
35.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite622.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
62×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r/`
16×	`associate-/l*`
13×	`associate-/r*`
12×	`flip3-+` `flip-+`
10×	`distribute-lft-out`
9×	`cbrt-undiv` `div-exp` `div-inv`
7×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `associate-*r/` `cbrt-unprod`

Counts

4 → 167

Calls

4 calls:

186.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
185.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
154.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
94.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series841.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
220.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
154.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
128.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify915.0ms

Counts

179 → 179

Iterations

Iter	Nodes
2	2841
1	681
0	241

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.6b

localize114.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
0.3b	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite757.0ms

Algorithm

rewrite-expression-head

Rules

4016×	`times-frac`
2920×	`*-un-lft-identity`
1472×	`add-sqr-sqrt` `add-cube-cbrt`
810×	`distribute-lft-out`
164×	`div-inv`
133×	`associate-/r/`
98×	`associate-/r*`
62×	`flip3-+` `flip-+`
40×	`add-exp-log`
31×	`add-cbrt-cube`
27×	`div-exp`
24×	`associate-/l*`
18×	`cbrt-undiv`
7×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`1-exp`

Counts

4 → 1399

Calls

4 calls:

216.0ms	(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
97.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
208.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
162.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))))
93.0ms	(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2 i)))
151.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
138.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify14.4s

Counts

1411 → 1411

Iterations

Iter	Nodes
1	4980
0	1560

prune17.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 34.6b

regimes314.0ms

Accuracy

44.8% (1.5b remaining)

Error of 35.4b against oracle of 34.0b and baseline of 36.6b

bsearch126.0ms

Steps

Iters	Range		Point
10	2.51906495219307e+212	2.017553101079821e+224	2.5516067629565482e+212

simplify7.0ms

Iterations

Iter	Nodes
2	39
1	39
0	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
454.0ms	8000×	pre	80	true