Details

sample14.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	15	11
2	22	11
3	25	11
4	26	11
done	26	11

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
6.2b	(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`times-frac`
11×	`add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-/r/` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 48

Calls

2 calls:

16.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
8.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
64.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify2.2s

Counts

54 → 54

Iterations

Useful iterations: 3 (373.0ms)

Iter	Nodes	Cost
0	116	913
1	274	865
2	928	811
3	4649	807
done	5000	807

prune109.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0))))
0.2b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
3.6b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
14.9b	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log` `add-cbrt-cube`
39×	`add-sqr-sqrt`
37×	`times-frac`
32×	`*-un-lft-identity`
30×	`add-cube-cbrt`
25×	`associate-l`
17×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`pow1`
12×	`associate-r`
8×	`difference-of-squares`
7×	`swap-sqr`
6×	`div-inv` `add-log-exp`
5×	`sub-neg` `flip3--` `flip--`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*` `associate-/r/` `associate--r+`
3×	`frac-times` `associate-r/` `associate-/l` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`pow2` `frac-2neg` `pow-plus` `diff-log` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

3.0ms	(- x (* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0))))
15.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
32.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- x (* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0))))
40.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
55.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
124.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- 1.0 (/ (* x y) 2.0)))

simplify1.6s

Counts

164 → 164

Iterations

Useful iterations: 2 (264.0ms)

Iter	Nodes	Cost
0	271	4153
1	774	3787
2	4028	3335
done	5001	3335

prune338.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
3.6b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
3.6b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
15.0b	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- (/ (* x y) 2.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

55×	`times-frac`
50×	`add-sqr-sqrt`
49×	`add-exp-log` `add-cbrt-cube`
43×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r` `associate-l`
17×	`prod-exp` `cbrt-unprod`
15×	`cbrt-undiv` `div-exp`
13×	`pow1`
11×	`difference-of-squares`
9×	`div-inv`
8×	`associate-/r*`
7×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `swap-sqr`
6×	`associate-/r/` `associate-/l*`
4×	`add-log-exp`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `distribute-neg-frac`
1×	`pow2` `neg-mul-1` `pow-plus` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out`

Counts

4 → 177

Calls

4 calls:

15.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
25.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- (/ (* x y) 2.0)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
55.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
59.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
63.0ms	(* (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))) (- (/ (* x y) 2.0)))

simplify1.6s

Counts

189 → 189

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	238	4328
1	722	4106
2	4042	3522
done	5000	3521

prune476.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
0.2b	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
3.6b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
17.8b	(/ (* y (- (* x y))) (* (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))) 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-exp-log` `add-cbrt-cube`
37×	`times-frac`
34×	`prod-exp` `cbrt-unprod`
33×	`add-sqr-sqrt`
29×	`cbrt-undiv` `add-cube-cbrt` `*-un-lft-identity` `div-exp`
18×	`pow1`
14×	`swap-sqr` `associate-r` `associate-l`
10×	`div-inv`
5×	`associate-/r*`
4×	`associate-l/` `associate-/r/` `associate-/l` `add-log-exp` `difference-of-squares`
2×	`pow2` `frac-times` `flip3--` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `clear-num` `pow-sqr` `-commutative` `pow-prod-up` `flip--` `unswap-sqr`
1×	`distribute-frac-neg` `distribute-rgt-neg-out`

Counts

4 → 169

Calls

4 calls:

14.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
18.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
8.0ms	(/ (* y (- (* x y))) (* (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))) 2.0))

series194.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
39.0ms	(* (/ (* x y) 2.0) (/ (* x y) 2.0))
54.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
65.0ms	(/ (* y (- (* x y))) (* (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))) 2.0))

simplify1.5s

Counts

181 → 181

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	213	3741
1	627	3370
2	3558	2512
done	5000	2512

prune389.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes43.0ms

Accuracy

65.8% (5.4b remaining)

Error of 5.4b against oracle of 0.0b and baseline of 15.8b

bsearch89.0ms

Steps

Iters	Range		Point
6	9.69163245006952e+130	1.3927480203233686e+132	1.2105836526692892e+131
10	-1.9838605160624203e+101	-6.360096683844279e+82	-1.0316187449465748e+92

simplify13.0ms

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	25	104
1	38	80
2	44	80
3	45	80
done	45	80

end0.0ms

sample333.0ms

Algorithm

intervals

Results

206.0ms	7998×	body	80	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid