Details

sample138.0ms

Algorithm

intervals

Results

68.0ms	50×	body	2560	valid
37.0ms	87×	body	1280	valid
12.0ms	51×	body	640	valid
6.0ms	20×	body	160	valid
6.0ms	38×	body	320	valid
1.0ms	10×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.5b	(- 1.0 (cos x))

rewrite14.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune181.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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

rewrite1.0ms

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)))
0.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

series178.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
126.0ms	(fma 1/240 (pow x 5) (* 1/2 x))

simplify35.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	61	148
1	188	130
2	1009	130
3	5002	130

prune94.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize8.0ms

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)))
2.5b	(- 1.0 (cos x))

rewrite28.0ms

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:

10.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series91.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms	(/ (sin x) (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify74.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	572	1779
1	2636	1549
2	5001	1441

prune283.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(/ 1 (- 1.0 (cos x)))
0.2b	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
2.5b	(- 1.0 (cos x))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

705×	`times-frac`
403×	`add-sqr-sqrt` `*-un-lft-identity`
309×	`add-cube-cbrt`
52×	`add-exp-log`
47×	`distribute-lft-out--` `difference-of-squares`
39×	`div-inv`
36×	`div-exp`
31×	`associate-/r/`
29×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-/l*`
16×	`flip3--` `flip--`
10×	`cbrt-undiv` `rec-exp` `1-exp`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `fma-neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `associate-/l/`

Counts

4 → 445

Calls

4 calls:

2.0ms	(/ 1 (sin x))
5.0ms	(/ 1 (- 1.0 (cos x)))
17.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
7.0ms	(- 1.0 (cos x))

series106.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (sin x))
27.0ms	(/ 1 (- 1.0 (cos x)))
34.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
26.0ms	(- 1.0 (cos x))

simplify86.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1705	5786
1	5001	5085

prune598.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.3b

regimes123.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.5b

bsearch77.0ms

Steps

Iters	Range		Point
10	7.712829756242493e-08	8770343.893451896	0.020393739459838457
9	-1827977.1926269082	-0.00043085380315138777	-0.022144219019054306

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	24
1	38	24

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.4s	1613×	body	2560	valid
1.2s	2670×	body	1280	valid
456.0ms	1933×	body	640	valid
152.0ms	941×	body	320	valid
61.0ms	478×	body	160	valid
24.0ms	363×	body	80	valid
11.0ms	2×	body	5120	valid