Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.15564%

Results

71.0ms	51×	body	2560	valid
46.0ms	97×	body	1280	valid
12.0ms	51×	body	640	valid
6.0ms	35×	body	320	valid
2.0ms	17×	body	160	valid
0.0ms	5×	body	80	valid

simplify5.0ms

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: 30.2b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.8b	(- 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))
3.0ms	(- 1.0 (cos x))

series11.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 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	2640	373
3	5002	373

prune126.0ms

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: 0.2b

Counts

59 → 14

localize11.0ms

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)))
2.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.8b	(- 1.0 (cos x))

rewrite27.0ms

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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series31.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

simplify91.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

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

prune202.0ms

Filtered

88 candidates to 124 candidates (-40.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	121	17	138

Merged error: 0.2b

Counts

138 → 17

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
2.8b	(- 1.0 (cos x))

rewrite19.0ms

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:

3.0ms	(/ 1 (sin x))
10.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

series16.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ 1 (sin x))
8.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

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

prune127.0ms

Filtered

56 candidates to 96 candidates (-71.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	94	19	113

Merged error: 0.2b

Counts

113 → 19

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)) (sin x)))
0.4b	(pow (cos x) 3)
0.5b	(+ (cos x) 1.0)
2.6b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
48×	`difference-of-squares`
41×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
25×	`times-frac` `associate-/l*` `sqr-pow`
15×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
3×	`difference-cubes` `pow-unpow`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-*l/` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 139

Calls

4 calls:

21.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
2.0ms	(pow (cos x) 3)
4.0ms	(+ (cos x) 1.0)
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series51.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x)))
5.0ms	(pow (cos x) 3)
5.0ms	(+ (cos x) 1.0)
8.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify81.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	566	1663
1	2538	1547
2	5001	1503

prune201.0ms

Filtered

85 candidates to 151 candidates (-77.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	6	11	17
Picked	1	0	1
Done	0	1	1
Total	151	19	170

Merged error: 0.1b

Counts

170 → 19

regimes256.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.9b

bsearch58.0ms

Steps

Iters	Range		Point
10	1.7311255617291425e-13	3907.5625149473053	0.022000626003212953
9	-74.69332681057587	-1.0689829255659151e-07	-0.02331583925925036

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	27
1	49	27

end0.0ms

sample6.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 50.15564%

Results

2.3s	1571×	body	2560	valid
1.4s	2793×	body	1280	valid
489.0ms	1871×	body	640	valid
174.0ms	971×	body	320	valid
56.0ms	454×	body	160	valid
25.0ms	337×	body	80	valid
16.0ms	3×	body	5120	valid

Details

sample1.8s

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series11.0ms

simplify79.0ms

prune126.0ms

localize11.0ms

rewrite27.0ms

series31.0ms

simplify91.0ms

prune202.0ms

localize9.0ms

rewrite19.0ms

series16.0ms

simplify43.0ms

prune127.0ms

localize15.0ms

rewrite44.0ms

series51.0ms

simplify81.0ms

prune201.0ms

regimes256.0ms

bsearch58.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling