Details

sample132.0ms

Algorithm

intervals

Results

61.0ms	52×	body	2560	valid
45.0ms	104×	body	1280	valid
11.0ms	48×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	13×	body	160	valid
0.0ms	7×	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: 29.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.9b	(- 1.0 (cos x))

rewrite12.0ms

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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(- 1.0 (cos x))

simplify84.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

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

prune161.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

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)))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
0.8b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite80.0ms

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:

51.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
1.0ms	(pow (cos x) 3)
3.0ms	(+ (cos x) 1.0)
15.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series223.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)))
28.0ms	(pow (cos x) 3)
10.0ms	(+ (cos x) 1.0)
52.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify97.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (72.0ms)

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

prune471.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.4b	(+ (cos x) 1.0)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- 1.0 (cos x))

rewrite17.0ms

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:

4.0ms	(* (cos x) (cos x))
6.0ms	(+ (cos x) 1.0)
4.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series93.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cos x) (cos x))
10.0ms	(+ (cos x) 1.0)
42.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify44.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (38.0ms)

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

prune259.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1.0 (cos x)))
0.4b	(+ (cos x) 1.0)
0.5b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.9b	(- 1.0 (cos x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `log-prod`
4×	`add-cbrt-cube`
2×	`+-commutative` `log-div` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `sqr-cos` `associate-+l+` `distribute-rgt-out` `diff-log` `rem-log-exp` `log-pow` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

2.0ms	(log (- 1.0 (cos x)))
3.0ms	(+ (cos x) 1.0)
4.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series152.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(log (- 1.0 (cos x)))
10.0ms	(+ (cos x) 1.0)
47.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify88.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	276	390
1	909	342
2	2915	338
3	5001	338

prune227.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes87.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.5b

bsearch96.0ms

Steps

Iters	Range		Point
8	0.003342748024832997	13.582308112339199	0.024127924279373096
9	-118.89002763209811	-0.00028315217264546786	-0.015504801539486723

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	34
1	53	34

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1585×	body	2560	valid
1.2s	2776×	body	1280	valid
448.0ms	1876×	body	640	valid
150.0ms	933×	body	320	valid
65.0ms	465×	body	160	valid
23.0ms	360×	body	80	valid
23.0ms	5×	body	5120	valid