Details

sample179.0ms

Algorithm

intervals

Results

94.0ms	58×	body	2560	valid
42.0ms	75×	body	1280	valid
20.0ms	65×	body	640	valid
8.0ms	33×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	12×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

55.0ms	(/ (- 1.0 (cos x)) (sin x))
14.0ms	(- 1.0 (cos x))

series80.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- 1.0 (cos x)) (sin x))
22.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	134	964
1	309	834
2	1215	733
done	5001	692

prune331.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.2b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
1.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series215.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
156.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify1.6s

Counts

26 → 26

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	36	358
1	69	349
2	285	307
3	1930	307
done	5000	307

prune173.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

26.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(/ (- 1.0 (cos x)) (sin x))
52.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
14.0ms	(- 1.0 (cos x))

series152.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
42.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
24.0ms	(- 1.0 (cos x))

simplify1.0s

Counts

144 → 144

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	195	1743
1	392	1512
2	1395	1374
done	5002	1333

prune517.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (cos x) 1.0)
0.2b	(* (cos x) (+ (cos x) 1.0))
0.3b	(pow (cos x) 3)
2.0b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
111×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-l`
2×	`flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

7.0ms	(+ (cos x) 1.0)
37.0ms	(* (cos x) (+ (cos x) 1.0))
4.0ms	(pow (cos x) 3)
42.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series199.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (cos x) 1.0)
47.0ms	(* (cos x) (+ (cos x) 1.0))
61.0ms	(pow (cos x) 3)
73.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify7.2s

Counts

271 → 271

Iterations

Useful iterations: done (7.1s)

Iter	Nodes	Cost
0	276	7533
1	732	4394
2	4482	3248
done	5000	3247

prune514.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.2b

regimes297.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.2b

bsearch97.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.02174222265971262
8	-0.031678663534995	-9.641814872486784e-07	-0.021849564525527353

simplify23.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	76
1	38	76
done	38	76

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.5s	1541×	body	2560	valid
3.3s	2807×	body	1280	valid
905.0ms	1887×	body	640	valid
317.0ms	933×	body	320	valid
94.0ms	373×	body	80	valid
88.0ms	455×	body	160	valid
27.0ms	4×	body	5120	valid