Details

sample465.0ms

Algorithm: halfpoints

simplify9.8s

Counts

1 → 1

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	16	24
1	38	11
2	74	11
3	148	11
4	380	11
5	4974	11
done	5000	11

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize58.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.7b	(- (exp x) (exp (- x)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`associate-l`
16×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

2 → 52

Calls

2 calls:

85.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
25.0ms	(- (exp x) (exp (- x)))

series198.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
62.0ms	(- (exp x) (exp (- x)))

simplify2.2s

Counts

58 → 58

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	121	770
1	863	753
done	5001	671

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/60 (pow x 5)) (* 2 x))
0.1b	(* 1/60 (pow x 5))
0.1b	(* 1/3 (pow x 3))
0.2b	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`add-cbrt-cube`
10×	`times-frac`
9×	`unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1` `add-log-exp`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `flip3-+` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 99

Calls

4 calls:

19.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
16.0ms	(* 1/60 (pow x 5))
14.0ms	(* 1/3 (pow x 3))
94.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series586.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
91.0ms	(* 1/60 (pow x 5))
71.0ms	(* 1/3 (pow x 3))
171.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify1.7s

Counts

111 → 111

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	193	1563
1	1408	1479
done	5000	1313

prune515.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow`

Counts

4 → 182

Calls

4 calls:

136.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
153.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
123.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
15.0ms	(/ 1 (sqrt 2.0))

series722.0ms

Counts

4 → 10

Calls

4 calls:

215.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
315.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
192.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify3.7s

Counts

192 → 192

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	256	4878
1	4302	4343
done	5001	3937

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

1128×	`sqrt-prod`
1116×	`times-frac`
592×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
79×	`add-exp-log`
49×	`add-cbrt-cube`
37×	`associate-/l*`
32×	`div-exp`
25×	`prod-exp`
24×	`associate-/r*`
23×	`pow1` `div-inv`
20×	`sqrt-pow1`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
14×	`pow-flip`
10×	`pow1/2` `pow-div`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/l/`
2×	`inv-pow`
1×	`frac-times` `flip3-+` `associate-r/` `associate-r` `-commutative` `flip-+`

Counts

4 → 767

Calls

4 calls:

265.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
90.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
30.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(/ 1 (sqrt (sqrt 2.0)))

series518.0ms

Counts

4 → 8

Calls

4 calls:

326.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
191.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify980.0ms

Counts

775 → 775

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	616	20777
done	5000	18878

prune4.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes175.0ms

Accuracy

42.7% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.8b

bsearch171.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.012882299779342181

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	62
1	38	62
done	38	62

end0.0ms

sample12.2s

Algorithm: halfpoints