Details

sample150.0ms

Algorithm

intervals

Results

57.0ms	314×	body	80	valid
34.0ms	25×	body	1280	valid
26.0ms	35×	body	640	valid
9.0ms	17×	body	320	valid
4.0ms	10×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5009
6	4062
5	1352
4	542
3	196
2	66
1	28
0	12

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
4.7b	(* sin (* x cos))
4.7b	(* sin (* x cos))

rewrite207.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 146

Calls

4 calls:

73.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
89.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
20.0ms	(* sin (* x cos))
22.0ms	(* sin (* x cos))

series259.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (cos (* 2 x)) (* (* sin (* x cos)) (* sin (* x cos))))
85.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
35.0ms	(* sin (* x cos))
35.0ms	(* sin (* x cos))

simplify1.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5136
2	1843
1	425
0	147

prune390.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (* sin (* x cos)) (* sin (* x cos))))
0.3b	(* (* sin (* x cos)) (* sin (* x cos)))
4.7b	(* sin (* x cos))
4.7b	(* sin (* x cos))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

243×	`pow1`
171×	`add-exp-log`
138×	`pow-prod-down`
114×	`prod-exp`
97×	`add-cbrt-cube`
60×	`cbrt-unprod`
32×	`pow-flip`
20×	`div-exp`
18×	`pow-sqr` `pow-prod-up`
10×	`cbrt-undiv` `rec-exp` `1-exp`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
6×	`pow-plus`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `-commutative` `associate-/l`
2×	`pow2`
1×	`clear-num` `associate-/r*` `frac-2neg` `swap-sqr` `div-inv` `inv-pow`

Counts

4 → 198

Calls

4 calls:

174.0ms	(/ 1 (* (* sin (* x cos)) (* sin (* x cos))))
92.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
14.0ms	(* sin (* x cos))
18.0ms	(* sin (* x cos))

series225.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (* (* sin (* x cos)) (* sin (* x cos))))
94.0ms	(* (* sin (* x cos)) (* sin (* x cos)))
42.0ms	(* sin (* x cos))
33.0ms	(* sin (* x cos))

simplify1.6s

Counts

210 → 210

Iterations

Iter	Nodes
done	5069
2	1376
1	422
0	150

prune501.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos (* 2 x)) (pow (* sin (* x cos)) -2))
0.3b	(pow (* sin (* x cos)) -2)
4.7b	(* sin (* x cos))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`pow1` `prod-exp`
10×	`add-sqr-sqrt` `add-cbrt-cube`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `associate-l` `pow-prod-down` `pow-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-unpow` `pow-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `*-commutative` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

29.0ms	(* (cos (* 2 x)) (pow (* sin (* x cos)) -2))
19.0ms	(pow (* sin (* x cos)) -2)
24.0ms	(* sin (* x cos))

series161.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(* (cos (* 2 x)) (pow (* sin (* x cos)) -2))
47.0ms	(pow (* sin (* x cos)) -2)
31.0ms	(* sin (* x cos))

simplify2.2s

Counts

79 → 79

Iterations

Iter	Nodes
done	5011
3	4118
2	928
1	285
0	117

prune389.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos (* 2 x)) (pow (* x (* cos sin)) -2))
0.3b	(pow (* x (* cos sin)) -2)
5.5b	(* x (* cos sin))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
14×	`pow1` `prod-exp`
10×	`add-sqr-sqrt` `add-cbrt-cube`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `associate-l` `pow-prod-down` `pow-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-unpow` `pow-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `*-commutative` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

27.0ms	(* (cos (* 2 x)) (pow (* x (* cos sin)) -2))
24.0ms	(pow (* x (* cos sin)) -2)
22.0ms	(* x (* cos sin))

series158.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(* (cos (* 2 x)) (pow (* x (* cos sin)) -2))
48.0ms	(pow (* x (* cos sin)) -2)
32.0ms	(* x (* cos sin))

simplify2.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4859
2	978
1	283
0	117

prune298.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

regimes596.0ms

Accuracy

-1.5% (2.8b remaining)

Error of 2.9b against oracle of 0.1b and baseline of 2.8b

bsearch111.0ms

Steps

Iters	Range		Point
6	-9.784660488848261e-110	-2.3239832428417497e-110	-9.175790255859891e-110

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.3s	9202×	body	80	valid
973.0ms	827×	body	1280	valid
811.0ms	922×	body	640	valid
426.0ms	619×	body	320	valid
149.0ms	326×	body	160	valid