Details

sample132.0ms

Algorithm

intervals

Results

70.0ms	54×	body	2560	valid
34.0ms	83×	body	1280	valid
12.0ms	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))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

16.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series54.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
16.0ms	(- 1.0 (cos x))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune153.0ms

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))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`flip3--` `associate-/r` `flip--` `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 → 87

Calls

3 calls:

6.0ms	(/ 1 (sin x))
30.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
6.0ms	(- 1.0 (cos x))

series63.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1 (sin x))
31.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
20.0ms	(- 1.0 (cos x))

simplify40.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	320	548
1	1393	482
2	5001	456

prune172.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
0.3b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

75.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
4.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series195.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
24.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
47.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify100.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	617	2953
1	2699	2889
2	5001	2810

prune450.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(+ (cos x) 1.0)
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1`
10×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`+-commutative` `sqr-cos` `flip3-+` `sum-log` `flip-+`
1×	`pow2` `sub-neg` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

10.0ms	(* (cos x) (cos x))
6.0ms	(+ (cos x) 1.0)
13.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series81.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (cos x) (cos x))
9.0ms	(+ (cos x) 1.0)
37.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
21.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	293	370
1	1182	322
2	5001	313

prune216.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes69.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.2b

bsearch75.0ms

Steps

Iters	Range		Point
11	1.661404138935296e-22	2.5556453819330236	0.02165047000055947
9	-0.04331797882383785	-2.2082264187638084e-10	-0.024280922068190693

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	19
1	34	19

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	1569×	body	2560	valid
1.4s	2804×	body	1280	valid
417.0ms	1904×	body	640	valid
144.0ms	930×	body	320	valid
49.0ms	472×	body	160	valid
19.0ms	318×	body	80	valid
8.0ms	3×	body	5120	valid