Details

sample93.0ms

Algorithm

intervals

Results

52.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.0b

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))))
35.3b	(/ (/ (* (* 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))
46.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite810.0ms

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:

153.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
159.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
356.0ms	(/ (/ (* (* 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))
135.0ms	(/ (* (* 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)))
136.0ms	(* (* 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))
258.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.3s

Counts

224 → 224

Iterations

Iter	Nodes
2	7476
1	1333
0	368

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.9b

localize60.0ms

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))))
36.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 376

Calls

4 calls:

323.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
865.0ms	(* (/ (/ (* 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))))
73.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
141.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.0s

Counts

4 → 12

Calls

4 calls:

531.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.2s	(* (/ (/ (* 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))))
130.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
158.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.3s

Counts

388 → 388

Iterations

Iter	Nodes
2	7224
1	1714
0	511

prune6.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.8b

localize81.0ms

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))) (/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))))
0.1b	(/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
36.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

1669×	`times-frac`
1103×	`add-sqr-sqrt`
864×	`*-un-lft-identity`
630×	`add-cube-cbrt`
290×	`associate-r`
220×	`add-exp-log`
210×	`difference-of-squares`
128×	`div-exp`
107×	`associate-/r/`
105×	`sqrt-prod` `distribute-lft-out--`
101×	`associate-/r*`
100×	`add-cbrt-cube`
58×	`div-inv`
53×	`cbrt-undiv`
51×	`flip3-+` `prod-exp` `flip-+`
42×	`associate-l`
21×	`cbrt-unprod`
15×	`rec-exp` `1-exp`
14×	`unswap-sqr`
9×	`distribute-lft-out`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-*r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 891

Calls

4 calls:

839.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))))
191.0ms	(/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
98.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
189.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.9s

Counts

4 → 12

Calls

4 calls:

3.1s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))))))
434.0ms	(/ 1 (/ (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))))
141.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
160.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.8s

Counts

903 → 903

Iterations

Iter	Nodes
1	3759
0	1054

prune16.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 33.8b

localize101.0ms

Local error

Found 4 expressions with local error:

36.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
36.5b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

63.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
97.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
145.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
135.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
118.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
162.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
148.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.9s

Counts

136 → 136

Iterations

Iter	Nodes
3	9698
2	1614
1	377
0	130

prune3.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 33.8b

regimes326.0ms

Accuracy

20.9% (2.3b remaining)

Error of 36.4b against oracle of 34.1b and baseline of 37.0b

bsearch59.0ms

Steps

Iters	Range		Point
5	1.0399753874323529e+154	2.918761046225584e+154	2.8543550670306893e+154

simplify23.0ms

Iterations

Iter	Nodes
2	38
1	38
0	28

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
401.0ms	8000×	pre	80	true