Details

sample2.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.15564%

Results

69.0ms	45×	body	2560	valid
42.0ms	85×	body	1280	valid
17.0ms	64×	body	640	valid
7.0ms	38×	body	320	valid
1.0ms	11×	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

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite11.0ms

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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 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	2640	373
3	5002	373

prune128.0ms

Filtered

42 candidates to 58 candidates (-38.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	44	14	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	14	59

Merged error: 0.1b

Counts

59 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
1.5b	(- 1.0 (cos x))

rewrite20.0ms

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:

4.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms	(- 1.0 (cos x))

series15.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1 (sin x))
8.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
4.0ms	(- 1.0 (cos x))

simplify45.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	320	546
1	1393	480
2	5001	454

prune116.0ms

Filtered

56 candidates to 96 candidates (-71.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	96	14	110

Merged error: 0.1b

Counts

110 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.3b	(pow (cos x) 3)
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
12×	`pow1`
11×	`add-cube-cbrt`
9×	`sqr-pow`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out--`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`sqr-cos`
1×	`difference-cubes` `+-commutative` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-pow` `flip3-+` `pow-plus` `diff-log` `unpow3` `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 → 97

Calls

4 calls:

4.0ms	(* (cos x) (cos x))
2.0ms	(pow (cos x) 3)
5.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series23.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (cos x) (cos x))
5.0ms	(pow (cos x) 3)
6.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
10.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	380	592
1	1866	548
2	5001	523

prune193.0ms

Filtered

63 candidates to 109 candidates (-73.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	107	16	123

Merged error: 0.1b

Counts

123 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.3b	(- (pow 1.0 3) (pow (cos x) 3))
1.4b	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
29×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`pow-unpow`
2×	`difference-cubes` `sub-neg` `exp-sum`
1×	`+-commutative` `cube-mult` `pow-to-exp` `log-div` `sqr-cos` `associate-+l+` `distribute-rgt-out` `flip3--` `pow-pow` `flip3-+` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `flip-+` `rem-cube-cbrt`

Counts

4 → 110

Calls

4 calls:

3.0ms	(pow (cos x) 3)
5.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))
16.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos x) 3)
6.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))
8.0ms	(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	398	736
1	1608	687
2	5001	659

prune186.0ms

Filtered

71 candidates to 122 candidates (-71.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	123	15	138

Merged error: 0.1b

Counts

138 → 15

regimes99.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.4b

bsearch46.0ms

Steps

Iters	Range		Point
10	2.0625668874781664e-15	7.128324467637312	0.020122061786894047
9	-807.5111341838605	-0.0015569508820097735	-0.0229491805501743

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	37
1	48	37

end0.0ms

sample6.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.15564%

Results

2.2s	1500×	body	2560	valid
1.4s	2768×	body	1280	valid
499.0ms	1870×	body	640	valid
185.0ms	1024×	body	320	valid
62.0ms	450×	body	160	valid
29.0ms	386×	body	80	valid
8.0ms	2×	body	5120	valid

Details

sample2.0s

simplify6.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series12.0ms

simplify82.0ms

prune128.0ms

localize9.0ms

rewrite20.0ms

series15.0ms

simplify45.0ms

prune116.0ms

localize17.0ms

rewrite26.0ms

series23.0ms

simplify84.0ms

prune193.0ms

localize20.0ms

rewrite40.0ms

series26.0ms

simplify69.0ms

prune186.0ms

regimes99.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling