Details

sample288.0ms

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	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: 46.4b

localize56.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.8b	(- (exp x) (exp (- x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 105

Calls

3 calls:

26.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
27.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
7.0ms	(- (exp x) (exp (- x)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
85.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
42.0ms	(- (exp x) (exp (- x)))

simplify910.0ms

Counts

114 → 114

Iterations

Useful iterations: done (902.0ms)

Iter	Nodes	Cost
0	218	1732
1	538	1573
2	1560	1344
done	5001	1343

prune406.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`associate-l`
27×	`*-un-lft-identity`
23×	`times-frac`
21×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

0.0ms	(fma 1/60 (pow x 5) (* 2 x))
0.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
27.0ms	(* (/ (+ (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))

series345.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(fma 1/60 (pow x 5) (* 2 x))
61.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
64.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
92.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify810.0ms

Counts

103 → 103

Iterations

Useful iterations: done (807.0ms)

Iter	Nodes	Cost
0	186	1765
1	435	1742
2	1373	1518
done	5000	1517

prune559.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

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))

rewrite55.0ms

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:

13.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
29.0ms	(* (/ 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))

series507.0ms

Counts

4 → 10

Calls

4 calls:

165.0ms	(* (/ (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)))
117.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.3s

Counts

198 → 198

Iterations

Useful iterations: done (1.3s)

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

prune839.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize70.0ms

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	(* (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)))
0.5b	(/ (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)))

rewrite51.0ms

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:

13.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
24.0ms	(* (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)))

series844.0ms

Counts

4 → 10

Calls

4 calls:

169.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
556.0ms	(* (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)))
119.0ms	(/ (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

prune856.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes115.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	31
1	29	31
done	29	31

end0.0ms

sample6.4s

Algorithm: halfpoints