Details

sample277.0ms

Algorithm: halfpoints

simplify4.8s

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	621	11
8	1040	11
9	1629	11
10	1957	11
11	2143	11
12	2163	11
done	2163	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.4b

localize51.0ms

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)))

rewrite70.0ms

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:

30.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
28.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
8.0ms	(- (exp x) (exp (- x)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
99.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
37.0ms	(- (exp x) (exp (- x)))

simplify1.1s

Counts

114 → 114

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	218	1732
1	542	1573
2	1565	1344
done	5002	1343

prune377.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

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))

rewrite43.0ms

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)))
31.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
9.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series338.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(fma 1/60 (pow x 5) (* 2 x))
59.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
58.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
91.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	186	1765
1	435	1742
2	1373	1518
done	5001	1517

prune530.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

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))

rewrite57.0ms

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))
28.0ms	(* (/ 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))

series504.0ms

Counts

4 → 10

Calls

4 calls:

164.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
222.0ms	(* (/ 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))

simplify1.4s

Counts

198 → 198

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	254	4584
1	634	4285
2	2180	3619
done	5000	3579

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize67.0ms

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)))

rewrite52.0ms

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)))

series831.0ms

Counts

4 → 10

Calls

4 calls:

162.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
552.0ms	(* (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)))
117.0ms	(/ (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)))

simplify1.2s

Counts

160 → 160

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	260	3772
1	607	3642
2	1799	3255
done	5001	3239

prune838.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes110.0ms

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

sample6.1s

Algorithm: halfpoints