Details

sample490.0ms

Algorithm: halfpoints

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.7b	(- (exp x) (exp (- x)))

rewrite200.0ms

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:

98.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
14.0ms	(+ (exp x) (exp (- x)))
68.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
15.0ms	(- (exp x) (exp (- x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
36.0ms	(+ (exp x) (exp (- x)))
114.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.0ms	(- (exp x) (exp (- x)))

simplify2.9s

Counts

111 → 111

Iterations

Useful iterations: 3 (1.6s)

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

prune658.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow x 3)) (+ (* 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))

rewrite153.0ms

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×	`add-log-exp` `unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`sum-log` `*-commutative`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

25.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
14.0ms	(* 1/60 (pow x 5))
15.0ms	(* 1/3 (pow x 3))
95.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series313.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
60.0ms	(* 1/60 (pow x 5))
65.0ms	(* 1/3 (pow x 3))
126.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	192	1718
1	467	1618
2	1503	1442
done	5000	1441

prune763.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize104.0ms

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))

rewrite509.0ms

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:

148.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
155.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
162.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
28.0ms	(/ 1 (sqrt 2.0))

series757.0ms

Counts

4 → 10

Calls

4 calls:

232.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
352.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
173.0ms	(/ (+ (* 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 (1.6s)

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

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow x 3))
0.2b	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b	(* (pow 2.0 -1/2) (* (/ (+ (* 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))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`add-exp-log`
39×	`add-cube-cbrt` `*-un-lft-identity`
38×	`times-frac`
32×	`associate-l`
22×	`sqrt-prod` `add-cbrt-cube`
20×	`prod-exp`
16×	`associate-r`
8×	`cbrt-unprod`
7×	`unpow-prod-down` `unswap-sqr`
6×	`pow1` `associate-/r*`
5×	`div-exp`
4×	`pow-to-exp` `cube-prod` `pow-exp` `add-log-exp`
3×	`cbrt-undiv` `-commutative` `associate-/l` `sqr-pow`
2×	`associate-*l/` `div-inv` `associate-/l/`
1×	`cube-mult` `frac-2neg` `flip3-+` `unpow3` `associate-*r/` `pow-prod-down` `clear-num` `flip-+`

Counts

4 → 143

Calls

4 calls:

28.0ms	(* 1/3 (pow x 3))
93.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
110.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
120.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series811.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 1/3 (pow x 3))
202.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
351.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
216.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify1.3s

Counts

155 → 155

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	260	3877
1	648	3736
2	2235	3357
done	5000	3356

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes623.0ms

Accuracy

42.7% (0.4b remaining)

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

bsearch149.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.012882299779342181

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	88
1	48	88
done	48	88

end0.0ms

sample12.1s

Algorithm: halfpoints