Details

sample94.0ms

Algorithm

intervals

Results

52.0ms	256×	body	80	valid
15.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	2000
3	1615
2	280
1	60
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.7b	(/ (/ (* (* 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))))

rewrite705.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

82.0ms	(* i (+ (+ alpha beta) i))
136.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
298.0ms	(/ (/ (* (* 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))
182.0ms	(/ (* (* 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:

30.0ms	(* i (+ (+ alpha beta) i))
127.0ms	(* (* 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))
303.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.5s

Counts

213 → 213

Iterations

Iter	Nodes
done	2006
2	2006
1	1299
0	359

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.3b	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
33.6b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite670.0ms

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:

283.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
170.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
156.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
56.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series1.0s

Counts

4 → 12

Calls

4 calls:

428.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
280.0ms	(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
180.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
122.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts

276 → 276

Iterations

Iter	Nodes
done	2011
2	2011
1	1146
0	409

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 32.9b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
33.6b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
145×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
22×	`associate-/r/`
21×	`add-cbrt-cube` `add-exp-log`
20×	`associate-/l*`
16×	`sqrt-prod` `distribute-lft-out--`
15×	`associate-/r*`
13×	`flip3-+` `flip-+`
11×	`div-inv`
8×	`cbrt-undiv` `div-exp`
7×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`
1×	`flip3--` `flip--`

Counts

4 → 221

Calls

4 calls:

287.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
143.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
66.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
63.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series799.0ms

Counts

4 → 12

Calls

4 calls:

437.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
146.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
119.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
96.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts

233 → 233

Iterations

Iter	Nodes
done	2000
2	2000
1	874
0	310

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.9b

localize97.0ms

Local error

Found 4 expressions with local error:

33.5b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.5b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `associate-/r*` `flip3-+` `times-frac` `sqrt-prod` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `sqrt-div` `div-exp` `associate-*r/` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 92

Calls

4 calls:

7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
70.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
64.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
69.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
131.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
95.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	2016
3	2016
2	1753
1	374
0	120

prune950.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 32.9b

regimes282.0ms

Accuracy

45.9% (1.5b remaining)

Error of 35.5b against oracle of 34.0b and baseline of 36.8b

bsearch94.0ms

Steps

Iters	Range		Point
8	4.618004300617091e+214	1.8668567131862295e+218	4.718881236776059e+214

simplify8.0ms

Iterations

Iter	Nodes
done	41
1	41
0	31

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
360.0ms	8000×	pre	80	true