Details

sample135.0ms

Algorithm

intervals

Results

73.0ms	52×	body	2560	valid
33.0ms	85×	body	1280	valid
14.0ms	63×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	14×	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: 28.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite29.0ms

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:

22.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series50.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify82.0ms

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

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

16.0ms	(/ (- 1.0 (cos x)) (sin x))
23.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
21.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms	(- 1.0 (cos x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
39.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
17.0ms	(- 1.0 (cos x))

simplify90.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune305.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
0.4b	(pow (cos x) 3)
0.4b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`difference-cubes` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

49.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
3.0ms	(pow (cos x) 3)
6.0ms	(+ (cos x) 1.0)
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series157.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
25.0ms	(pow (cos x) 3)
9.0ms	(+ (cos x) 1.0)
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	434	706
1	1921	654
2	5003	650

prune265.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(pow (pow (cos x) 3) 3)
0.4b	(+ (cos x) 1.0)
1.9b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
56×	`unpow-prod-down` `cube-prod`
44×	`difference-of-squares`
40×	`cbrt-prod`
27×	`sqr-pow`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
5×	`pow1` `pow-exp`
4×	`cube-mult` `unpow3`
3×	`pow-to-exp`
2×	`pow-pow` `rem-cube-cbrt`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 135

Calls

4 calls:

3.0ms	(pow (cos x) 3)
7.0ms	(pow (pow (cos x) 3) 3)
6.0ms	(+ (cos x) 1.0)
41.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (cos x) 3)
52.0ms	(pow (pow (cos x) 3) 3)
9.0ms	(+ (cos x) 1.0)
42.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify61.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	421	1014
1	1553	953
2	5002	916

prune251.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

regimes193.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 29.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	48
1	49	48

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1575×	body	2560	valid
1.2s	2854×	body	1280	valid
404.0ms	1846×	body	640	valid
156.0ms	906×	body	320	valid
46.0ms	442×	body	160	valid
23.0ms	374×	body	80	valid
8.0ms	3×	body	5120	valid