Details

sample453.0ms

Algorithm: halfpoints

simplify6.0s

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	127	11
5	200	11
6	373	11
7	608	11
8	1105	11
9	1521	11
10	1855	11
11	1939	11
12	1959	11
done	1959	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize52.0ms

Local error

Found 2 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-l`
16×	`times-frac`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`fma-neg` `associate-r`
2×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

2 → 68

Calls

2 calls:

114.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
21.0ms	(- (exp x) (exp (- x)))

series193.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
61.0ms	(- (exp x) (exp (- x)))

simplify2.9s

Counts

74 → 74

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	149	1156
1	348	1004
2	899	843
3	3520	788
done	5000	779

prune456.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-r`
2×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

2 → 44

Calls

2 calls:

1.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
35.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series192.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
127.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify2.5s

Counts

50 → 50

Iterations

Useful iterations: 3 (939.0ms)

Iter	Nodes	Cost
0	99	1049
1	219	1036
2	695	896
3	3306	894
done	5000	894

prune296.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite156.0ms

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×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Counts

4 → 188

Calls

4 calls:

48.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
78.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
6.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
7.0ms	(/ 1 (sqrt 2.0))

series726.0ms

Counts

4 → 10

Calls

4 calls:

236.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
287.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
203.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.8s

Counts

198 → 198

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	254	4584
1	601	4231
2	1984	3619
done	5001	3595

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (fma 1/3 (pow x 3) (fma 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)))

rewrite424.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `associate-*l/` `clear-num`
2×	`inv-pow`
1×	`frac-times` `associate-r/` `associate-r` `-commutative` `associate-/l/`

Counts

4 → 773

Calls

4 calls:

247.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
8.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
45.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
18.0ms	(/ 1 (sqrt (sqrt 2.0)))

series517.0ms

Counts

4 → 8

Calls

4 calls:

333.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
184.0ms	(/ (fma 1/3 (pow x 3) (fma 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)))

simplify2.4s

Counts

781 → 781

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	614	20031
1	1618	17143
2	3503	15388
done	5000	15100

prune2.9s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes172.0ms

Accuracy

42.7% (0.4b remaining)

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

bsearch144.0ms

Steps

Iters	Range		Point
8	-0.7718806003288846	-0.0008047768791668974	-0.012882299779342181

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	60
1	32	60
done	32	60

end0.0ms

sample12.0s

Algorithm: halfpoints