Details

sample266.0ms

Algorithm: halfpoints

simplify3.3s

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	597	11
8	982	11
9	1505	11
10	1702	11
11	1839	11
12	1865	11
done	1865	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.7b

localize38.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.4b	(- (exp x) (exp (- x)))

rewrite37.0ms

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:

29.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
39.0ms	(- (exp x) (exp (- x)))

simplify1.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (381.0ms)

Iter	Nodes	Cost
0	121	770
1	295	755
2	774	669
3	2499	668
done	5000	668

prune157.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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))
7.0ms	(* 1/3 (pow x 3))
40.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series305.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
47.0ms	(* 1/60 (pow x 5))
38.0ms	(* 1/3 (pow x 3))
89.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify579.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (210.0ms)

Iter	Nodes	Cost
0	193	1563
1	478	1469
2	1446	1303
done	5001	1303

prune319.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

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

rewrite142.0ms

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:

46.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
52.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
34.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms	(/ 1 (sqrt 2.0))

series507.0ms

Counts

4 → 10

Calls

4 calls:

161.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
218.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
128.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify949.0ms

Counts

192 → 192

Iterations

Useful iterations: done (943.0ms)

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

prune538.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize39.0ms

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

rewrite132.0ms

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:

7.0ms	(* 1/3 (pow x 3))
47.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
43.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
31.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series565.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 1/3 (pow x 3))
165.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
230.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
128.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify809.0ms

Counts

155 → 155

Iterations

Useful iterations: done (804.0ms)

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

prune503.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes81.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	20
1	24	20
done	24	20

end0.0ms

sample6.4s

Algorithm: halfpoints