Details

sample129.0ms

Algorithm

intervals

Results

67.0ms	54×	body	2560	valid
34.0ms	83×	body	1280	valid
13.0ms	58×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	11×	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: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.1b	(- 1.0 (cos x))

rewrite33.0ms

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:

24.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series56.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify34.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (7.0ms)

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

prune173.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.1b	(- 1.0 (cos x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-/r` `flip--` `log1p-expm1-u` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (sin x))
31.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
7.0ms	(- 1.0 (cos x))

series72.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ 1 (sin x))
35.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
23.0ms	(- 1.0 (cos x))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	728
1	1613	574
2	5002	548

prune191.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.1b	(/ (cos x) (sin x))
1.2b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
222×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
210×	`add-cube-cbrt`
169×	`prod-diff`
31×	`div-inv`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 265

Calls

3 calls:

8.0ms	(/ 1.0 (sin x))
9.0ms	(/ (cos x) (sin x))
42.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series122.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ 1.0 (sin x))
20.0ms	(/ (cos x) (sin x))
84.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify89.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	810	7180
1	2234	5060
2	5001	4434

prune338.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(pow (cos x) 3)
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
112×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
86×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`pow1` `fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos`
1×	`difference-cubes` `+-commutative` `pow2` `pow-to-exp` `sub-neg` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-pow` `fma-def` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 262

Calls

4 calls:

13.0ms	(* (cos x) (cos x))
3.0ms	(pow (cos x) 3)
12.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
30.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series137.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (cos x) (cos x))
28.0ms	(pow (cos x) 3)
46.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify146.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	656	2815
1	2754	1911
2	5001	1872

prune311.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes68.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.3b

bsearch72.0ms

Steps

Iters	Range		Point
11	1.661404138935296e-22	2.5556453819330236	0.021088117470294238
9	-0.04331797882383785	-2.2082264187638084e-10	-0.024280922068190693

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	19
1	29	19

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.0s	1569×	body	2560	valid
1.4s	2804×	body	1280	valid
443.0ms	1904×	body	640	valid
149.0ms	930×	body	320	valid
52.0ms	472×	body	160	valid
20.0ms	318×	body	80	valid
8.0ms	3×	body	5120	valid