Details

sample144.0ms

Algorithm

intervals

Results

71.0ms	49×	body	2560	valid
40.0ms	88×	body	1280	valid
17.0ms	62×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	20×	body	160	valid
1.0ms	13×	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: 31.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite27.0ms

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:

17.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune179.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

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)))
0.3b	(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))

series179.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
124.0ms	(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

prune101.0ms

Pruning

16 alts after pruning (15 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)))
1.8b	(- 1.0 (cos x))

rewrite50.0ms

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:

17.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
18.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series97.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
41.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify66.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (52.0ms)

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

prune279.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x))))
0.1b	(fma 1/360 (pow x 3) (* 1/6 x))
0.3b	(* 1/6 x)
0.5b	(/ 1 (fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `fma-udef`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

0.0ms	(fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x))))
0.0ms	(fma 1/360 (pow x 3) (* 1/6 x))
6.0ms	(* 1/6 x)
5.0ms	(/ 1 (fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x)))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x))))
82.0ms	(fma 1/360 (pow x 3) (* 1/6 x))
14.0ms	(* 1/6 x)
63.0ms	(/ 1 (fma 2 (/ 1 x) (- (fma 1/360 (pow x 3) (* 1/6 x)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	235	606
1	827	541
2	2618	526
3	5001	526

prune167.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes65.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.0b

bsearch64.0ms

Steps

Iters	Range		Point
8	1.317141247235427e-05	0.43775957865898985	0.024292261377200218
9	-3096.4512561506854	-0.0006592480666379122	-0.022439059113539255

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	17
1	32	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1566×	body	2560	valid
1.2s	2753×	body	1280	valid
439.0ms	1901×	body	640	valid
145.0ms	963×	body	320	valid
49.0ms	464×	body	160	valid
22.0ms	351×	body	80	valid
5.0ms	2×	body	5120	valid