Details

sample289.0ms

Algorithm: halfpoints

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	24
1	30	11
2	46	11
3	81	11
4	113	11
5	181	11
6	310	11
7	589	11
8	974	11
9	1495	11
10	1685	11
11	1822	11
12	1847	11
done	1847	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.7b	(- (exp x) (exp (- x)))

rewrite74.0ms

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:

6.0ms	(+ (exp x) (exp (- x)))
27.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
31.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series198.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (exp x) (exp (- x)))
56.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
79.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
40.0ms	(- (exp x) (exp (- x)))

simplify2.0s

Counts

111 → 111

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	200	1479
1	509	1449
2	1414	1277
3	4577	1273
done	5001	1273

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

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

rewrite60.0ms

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:

3.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
6.0ms	(* 1/60 (pow x 5))
41.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
7.0ms	(* 1/3 (pow x 3))

series312.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
52.0ms	(* 1/60 (pow x 5))
91.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
36.0ms	(* 1/3 (pow x 3))

simplify779.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (235.0ms)

Iter	Nodes	Cost
0	193	1563
1	479	1467
2	1446	1303
done	5000	1303

prune487.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize60.0ms

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))

rewrite133.0ms

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:

41.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
50.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
29.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms	(/ 1 (sqrt 2.0))

series494.0ms

Counts

4 → 10

Calls

4 calls:

154.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
219.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
121.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.1s

Counts

192 → 192

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	256	4878
1	686	4529
2	2316	3874
done	5000	3832

prune996.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

localize67.0ms

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))
0.3b	(* (pow 2.0 -1/2) (* (/ (+ (* 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))

rewrite129.0ms

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:

9.0ms	(* 1/3 (pow x 3))
42.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
42.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
30.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series537.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/3 (pow x 3))
156.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
225.0ms	(* (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))

simplify926.0ms

Counts

155 → 155

Iterations

Useful iterations: done (921.0ms)

Iter	Nodes	Cost
0	260	3877
1	660	3736
2	2211	3357
done	5000	3345

prune712.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes174.0ms

Accuracy

48.4% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.8b

bsearch110.0ms

Steps

Iters	Range		Point
8	-0.48869560230416215	-0.0008391074150366579	-0.015295351353249335

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	61
1	44	61
done	44	61

end0.0ms

sample6.0s

Algorithm: halfpoints