Details

sample370.0ms

Algorithm: halfpoints

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	24
1	30	11
2	48	11
3	83	11
4	117	11
5	188	11
6	331	11
7	556	11
8	1006	11
9	1375	11
10	1691	11
11	1775	11
12	1795	11
done	1795	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize112.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.1b	(- (exp x) (exp (- x)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 99

Calls

4 calls:

86.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
15.0ms	(+ (exp x) (exp (- x)))
85.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
29.0ms	(- (exp x) (exp (- x)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
42.0ms	(+ (exp x) (exp (- x)))
129.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
54.0ms	(- (exp x) (exp (- x)))

simplify3.2s

Counts

111 → 111

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	200	1479
1	499	1449
2	1383	1277
3	4288	1273
done	5001	1273

prune473.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
22×	`associate-r`
21×	`*-un-lft-identity`
19×	`add-exp-log` `add-cube-cbrt` `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` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

16.0ms	(+ (exp x) (exp (- x)))
16.0ms	(* 1/60 (pow x 5))
132.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
23.0ms	(* 1/3 (pow x 3))

series280.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (exp x) (exp (- x)))
67.0ms	(* 1/60 (pow x 5))
143.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
45.0ms	(* 1/3 (pow x 3))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	209	1512
1	495	1430
2	1422	1264
done	5000	1263

prune987.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize127.0ms

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))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite376.0ms

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:

100.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
127.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
116.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
13.0ms	(/ 1 (sqrt 2.0))

series794.0ms

Counts

4 → 10

Calls

4 calls:

249.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
327.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
219.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.6s

Counts

192 → 192

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	256	4878
1	653	4529
2	2340	3872
done	5001	3848

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 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)))
0.4b	(/ (+ (* 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)))

rewrite519.0ms

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:

251.0ms	(* (/ (/ 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)))
131.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
45.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
10.0ms	(/ 1 (sqrt (sqrt 2.0)))

series797.0ms

Counts

4 → 8

Calls

4 calls:

313.0ms	(* (/ (/ 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)))
484.0ms	(/ (+ (* 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)))

simplify2.5s

Counts

775 → 775

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	616	20777
1	1672	17920
2	3912	16102
done	5000	15684

prune3.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes193.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	33
1	35	33
done	35	33

end0.0ms

sample12.3s

Algorithm: halfpoints