Details

sample149.0ms

Algorithm

intervals

Results

52.0ms	274×	body	80	valid
38.0ms	23×	body	1280	valid
19.0ms	25×	body	640	valid
14.0ms	23×	body	320	valid
4.0ms	11×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2531
6	2531
5	1352
4	542
3	196
2	66
1	28
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
0.3b	(* (* x (* sin cos)) (* x (* sin cos)))
6.1b	(* x (* sin cos))
6.1b	(* x (* sin cos))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-r` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `cos-2` `div-inv`

Counts

4 → 138

Calls

4 calls:

99.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
82.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
30.0ms	(* x (* sin cos))
26.0ms	(* x (* sin cos))

series217.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
66.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
27.0ms	(* x (* sin cos))
38.0ms	(* x (* sin cos))

simplify1.0s

Counts

150 → 150

Iterations

Iter	Nodes
done	2012
2	2012
1	399
0	141

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* x 2)) (* (* (* x cos) sin) (* (* x cos) sin)))
0.3b	(* (* (* x cos) sin) (* (* x cos) sin))
5.2b	(* (* x cos) sin)
5.2b	(* (* x cos) sin)

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-l` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `swap-sqr` `div-inv`

Counts

4 → 137

Calls

4 calls:

92.0ms	(/ (cos (* x 2)) (* (* (* x cos) sin) (* (* x cos) sin)))
104.0ms	(* (* (* x cos) sin) (* (* x cos) sin))
20.0ms	(* (* x cos) sin)
14.0ms	(* (* x cos) sin)

series270.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (cos (* x 2)) (* (* (* x cos) sin) (* (* x cos) sin)))
79.0ms	(* (* (* x cos) sin) (* (* x cos) sin))
42.0ms	(* (* x cos) sin)
31.0ms	(* (* x cos) sin)

simplify1.2s

Counts

149 → 149

Iterations

Iter	Nodes
done	2000
3	2000
2	1881
1	406
0	139

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* x 2)) (* (* x cos) sin))
0.3b	(/ 1 (* (* x cos) sin))
5.2b	(* (* x cos) sin)
5.2b	(* (* x cos) sin)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
32×	`add-cbrt-cube`
20×	`pow1`
18×	`prod-exp`
12×	`cbrt-unprod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`div-exp` `pow-prod-down`
6×	`cbrt-undiv` `times-frac` `associate-r` `associate-/l*`
4×	`insert-posit16` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-l` `-commutative` `div-inv`
1×	`inv-pow`

Counts

4 → 96

Calls

4 calls:

21.0ms	(/ (cos (* x 2)) (* (* x cos) sin))
23.0ms	(/ 1 (* (* x cos) sin))
19.0ms	(* (* x cos) sin)
14.0ms	(* (* x cos) sin)

series133.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (cos (* x 2)) (* (* x cos) sin))
23.0ms	(/ 1 (* (* x cos) sin))
27.0ms	(* (* x cos) sin)
27.0ms	(* (* x cos) sin)

simplify776.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2006
3	2006
2	1084
1	295
0	118

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (* x cos) sin))
0.7b	(/ 1 (* x cos))
5.0b	(* (/ 1 (* x cos)) (/ (cos (* x 2)) sin))
5.2b	(* (* x cos) sin)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
44×	`add-cbrt-cube`
35×	`prod-exp`
25×	`div-exp`
23×	`add-sqr-sqrt`
20×	`pow1`
19×	`times-frac`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-r`
15×	`cbrt-unprod`
12×	`cbrt-undiv`
9×	`rec-exp` `1-exp`
8×	`associate-l` `pow-prod-down`
6×	`associate-/l*`
5×	`pow-flip`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `-commutative` `inv-pow` `unswap-sqr`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 137

Calls

4 calls:

33.0ms	(/ 1 (* (* x cos) sin))
12.0ms	(/ 1 (* x cos))
44.0ms	(* (/ 1 (* x cos)) (/ (cos (* x 2)) sin))
20.0ms	(* (* x cos) sin)

series124.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1 (* (* x cos) sin))
13.0ms	(/ 1 (* x cos))
45.0ms	(* (/ 1 (* x cos)) (/ (cos (* x 2)) sin))
38.0ms	(* (* x cos) sin)

simplify738.0ms

Counts

149 → 149

Iterations

Iter	Nodes
done	2000
2	2000
1	533
0	188

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes478.0ms

Accuracy

11.9% (2.4b remaining)

Error of 2.5b against oracle of 0.1b and baseline of 2.9b

bsearch119.0ms

Steps

Iters	Range		Point
7	-6.716582716219829e-270	-3.9880362675029046e-272	-6.606769180032518e-270

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.9s	8910×	body	80	valid
806.0ms	830×	body	1280	valid
775.0ms	995×	body	640	valid
421.0ms	295×	body	160	valid
419.0ms	630×	body	320	valid