Details

sample272.0ms

Algorithm

intervals

Results

138.0ms	51×	body	2560	valid
74.0ms	92×	body	1280	valid
25.0ms	45×	body	640	valid
12.0ms	39×	body	320	valid
4.0ms	1×	body	5120	valid
4.0ms	20×	body	160	valid
1.0ms	8×	body	80	valid

simplify8.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
10.0ms	(- 1.0 (cos x))

series95.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/ (- 1.0 (cos x)) (sin x))
37.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

74 → 74

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune228.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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:

0.0ms	(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))

series240.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
171.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify1.1s

Counts

26 → 26

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	36	358
1	62	349
2	177	307
3	967	307
done	5001	307

prune131.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (+ 1.0 (cos x)))
0.3b	(+ 1.0 (cos x))
0.3b	(pow (cos x) 3)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite95.0ms

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:

38.0ms	(* (cos x) (+ 1.0 (cos x)))
7.0ms	(+ 1.0 (cos x))
4.0ms	(pow (cos x) 3)
33.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series178.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cos x) (+ 1.0 (cos x)))
12.0ms	(+ 1.0 (cos x))
36.0ms	(pow (cos x) 3)
97.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.0s

Counts

271 → 271

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	273	7533
1	612	4117
2	1963	3101
done	5001	2379

prune590.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 177

Calls

3 calls:

30.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
22.0ms	(/ (sin x) (- 1.0 (cos x)))
15.0ms	(- 1.0 (cos x))

series138.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
65.0ms	(/ (sin x) (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify2.7s

Counts

186 → 186

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	269	3021
1	561	2564
2	1226	2279
3	3472	2188
done	5000	2178

prune411.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes84.0ms

Accuracy

98.9% (0.4b remaining)

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

bsearch105.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.020706483323998073
8	-11.923248480236845	-0.0008047768791668974	-0.024087893247376972

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	57
1	42	57
done	42	57

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.4s	1581×	body	2560	valid
2.9s	2788×	body	1280	valid
947.0ms	1866×	body	640	valid
507.0ms	334×	body	80	valid
496.0ms	960×	body	320	valid
92.0ms	464×	body	160	valid
60.0ms	7×	body	5120	valid