Details

sample296.0ms

Algorithm: halfpoints

simplify3.4s

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	123	11
5	193	11
6	337	11
7	617	11
8	1035	11
9	1587	11
10	1802	11
11	1942	11
12	1969	11
done	1969	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize53.0ms

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)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`associate-l`
31×	`add-cube-cbrt`
29×	`times-frac`
14×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`fma-def` `fma-neg`
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 → 122

Calls

4 calls:

5.0ms	(+ (exp x) (exp (- x)))
25.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
26.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
7.0ms	(- (exp x) (exp (- x)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (exp x) (exp (- x)))
62.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
82.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
37.0ms	(- (exp x) (exp (- x)))

simplify939.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (256.0ms)

Iter	Nodes	Cost
0	232	1903
1	571	1734
2	1645	1486
done	5001	1486

prune473.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
29×	`associate-l`
23×	`times-frac`
22×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `unswap-sqr`
3×	`fma-def`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef`

Counts

4 → 98

Calls

4 calls:

0.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
5.0ms	(+ (exp x) (exp (- x)))
25.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
8.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series233.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
22.0ms	(+ (exp x) (exp (- x)))
62.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
90.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify867.0ms

Counts

110 → 110

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	199	1796
1	488	1766
2	1503	1539
done	5002	1538

prune579.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite53.0ms

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:

14.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
26.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
3.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
3.0ms	(/ 1 (sqrt 2.0))

series501.0ms

Counts

4 → 10

Calls

4 calls:

160.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
224.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
115.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.1s

Counts

198 → 198

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	254	4584
1	634	4231
2	1981	3621
done	5001	3579

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize64.0ms

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))
0.3b	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (* 2.0 (sqrt 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-l`
31×	`add-exp-log`
22×	`sqrt-prod` `add-cbrt-cube`
17×	`pow1`
10×	`prod-exp`
8×	`cbrt-unprod`
7×	`cbrt-prod` `div-exp` `associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv` `pow-flip` `pow-prod-down`
4×	`expm1-log1p-u` `associate-r` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`rec-exp` `cbrt-div` `frac-2neg` `1-exp` `clear-num` `*-commutative` `pow-prod-up`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `pow3` `inv-pow`

Counts

4 → 150

Calls

4 calls:

14.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
20.0ms	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
3.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
6.0ms	(/ 1 (* 2.0 (sqrt 2.0)))

series814.0ms

Counts

4 → 10

Calls

4 calls:

156.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
544.0ms	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
113.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (* 2.0 (sqrt 2.0)))

simplify1.1s

Counts

160 → 160

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	260	3772
1	607	3626
2	1798	3253
done	5000	3237

prune837.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes118.0ms

Accuracy

48.4% (0.4b remaining)

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

bsearch115.0ms

Steps

Iters	Range		Point
8	-0.48869560230416215	-0.0008391074150366579	-0.01665691799395379

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	64
1	40	64
done	40	64

end0.0ms

sample6.0s

Algorithm: halfpoints