Details

sample424.0ms

Algorithm: halfpoints

simplify5.3s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize49.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.9b	(- (exp x) (exp (- x)))

rewrite99.0ms

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:

68.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
29.0ms	(- (exp x) (exp (- x)))

series191.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
66.0ms	(- (exp x) (exp (- x)))

simplify2.4s

Counts

58 → 58

Iterations

Useful iterations: 3 (734.0ms)

Iter	Nodes	Cost
0	121	770
1	290	755
2	749	669
3	2404	668
done	5001	668

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

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))
0.2b	(* 1/3 (pow x 3))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
22×	`associate-r`
19×	`associate-l`
18×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
12×	`add-cbrt-cube`
10×	`times-frac`
9×	`unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
5×	`pow1`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`*-commutative` `add-log-exp`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `cube-mult` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `div-inv`

Counts

3 → 88

Calls

3 calls:

12.0ms	(* 1/60 (pow x 5))
96.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
13.0ms	(* 1/3 (pow x 3))

series252.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(* 1/60 (pow x 5))
123.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
40.0ms	(* 1/3 (pow x 3))

simplify1.0s

Counts

97 → 97

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	174	1355
1	402	1282
2	1181	1134
done	5001	1133

prune408.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ (* 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)))
0.5b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite390.0ms

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:

107.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
168.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
99.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
8.0ms	(/ 1 (sqrt 2.0))

series794.0ms

Counts

4 → 10

Calls

4 calls:

271.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
318.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
204.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.4s

Counts

192 → 192

Iterations

Useful iterations: done (1.4s)

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

prune922.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(* (sin y) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)))
0.5b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ (sqrt 1) (sqrt (sqrt 2.0)))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

220×	`sqrt-prod`
164×	`times-frac`
149×	`add-sqr-sqrt`
118×	`*-un-lft-identity`
115×	`add-cube-cbrt`
61×	`associate-l`
45×	`add-exp-log` `add-cbrt-cube`
35×	`associate-r`
15×	`cbrt-undiv` `div-exp` `associate-/r*`
14×	`prod-exp` `cbrt-unprod`
13×	`unswap-sqr`
9×	`associate-/l*`
8×	`pow1`
5×	`div-inv`
4×	`add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`
1×	`frac-times` `sqrt-undiv` `flip3-+` `associate-*l/` `flip-+`

Counts

4 → 274

Calls

4 calls:

162.0ms	(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0))))
123.0ms	(* (sin y) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)))
89.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
13.0ms	(/ (sqrt 1) (sqrt (sqrt 2.0)))

series1.1s

Counts

4 → 10

Calls

4 calls:

479.0ms	(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))) (sqrt (sqrt 2.0))))
365.0ms	(* (sin y) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)))
215.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ (sqrt 1) (sqrt (sqrt 2.0)))

simplify2.3s

Counts

284 → 284

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	346	8294
1	895	7288
2	3292	6273
done	5000	6267

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample11.7s

Algorithm: halfpoints