Details

analyze744.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

sample198.0ms

Algorithm

intervals

Results

112.0ms	92×	body	1280	valid
43.0ms	49×	body	640	valid
14.0ms	81×	body	80	valid
10.0ms	18×	body	320	valid
6.0ms	16×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4955	50
1	4955	50

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.4b

Counts

2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 88

Calls

4 calls:

18.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series46.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

simplify38.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5070	1524

prune304.0ms

Filtered

72 candidates to 98 candidates (-36.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 0.3b

Counts

100 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.8b	(- (cos x) (cos y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
14×	`associate-*r/`
12×	`associate-r`
11×	`pow1`
10×	`add-cube-cbrt`
8×	`flip3--` `flip--`
7×	`associate-l`
6×	`add-log-exp`
5×	`sub-neg` `times-frac` `prod-exp` `cbrt-unprod` `difference-of-squares`
4×	`frac-times` `pow-prod-down` `associate-*l/` `sqrt-prod` `associate-/r/`
3×	`flip3-+` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `frac-add` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/r*` `div-inv` `diff-cos`

Counts

4 → 101

Calls

4 calls:

12.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
17.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- (cos x) (cos y))

series291.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
22.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
12.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms	(- (cos x) (cos y))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4992	3393
1	4992	3393

prune443.0ms

Filtered

84 candidates to 113 candidates (-34.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.8b	(- (cos x) (cos y))
2.8b	(- (cos x) (cos y))
2.8b	(- (cos x) (cos y))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`sub-neg` `difference-of-squares`
4×	`flip3--` `sqrt-prod` `flip--` `distribute-lft-out--`
3×	`diff-log` `diff-cos`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

14.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- (cos x) (cos y))
4.0ms	(- (cos x) (cos y))
5.0ms	(- (cos x) (cos y))

series40.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms	(- (cos x) (cos y))
9.0ms	(- (cos x) (cos y))
9.0ms	(- (cos x) (cos y))

simplify40.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4927	852
1	4927	852

prune382.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	83	11	94

Merged error: 0.0b

Counts

94 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ 2.0 (* (- (cos x) (cos y)) (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0)))))) 3.0) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
0.3b	(* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))
2.8b	(- (cos x) (cos y))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

77×	`times-frac`
64×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
50×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`flip3--` `flip--` `associate-/l*`
12×	`associate-r/` `associate-l*`
11×	`pow1`
8×	`frac-times`
7×	`sub-neg` `associate-r`
6×	`associate-*l/` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `div-inv` `difference-of-squares`
4×	`pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod`
3×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `distribute-lft-out--`
2×	`flip3-+` `frac-add` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `diff-cos` `associate-/l/` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

13.0ms	(/ (/ (+ 2.0 (* (- (cos x) (cos y)) (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0)))))) 3.0) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
19.0ms	(* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0)))
19.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))
4.0ms	(- (cos x) (cos y))

series297.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (/ (+ 2.0 (* (- (cos x) (cos y)) (* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0)))))) 3.0) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y))))
18.0ms	(* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0)))
23.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))
9.0ms	(- (cos x) (cos y))

simplify70.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4993	8531
1	4993	8531

prune728.0ms

Filtered

125 candidates to 167 candidates (-33.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	168	10	178

Merged error: 0.0b

Counts

178 → 10

regimes211.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify27.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	928	110
1	928	110

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.5s	2720×	body	1280	valid
1.5s	1825×	body	640	valid
459.0ms	777×	body	320	valid
419.0ms	2310×	body	80	valid
140.0ms	368×	body	160	valid

Details

analyze744.0ms

sample198.0ms

simplify21.0ms

prune19.0ms

localize35.0ms

rewrite42.0ms

series46.0ms

simplify38.0ms

prune304.0ms

localize36.0ms

rewrite50.0ms

series291.0ms

simplify44.0ms

prune443.0ms

localize47.0ms

rewrite29.0ms

series40.0ms

simplify40.0ms

prune382.0ms

localize36.0ms

rewrite61.0ms

series297.0ms

simplify70.0ms

prune728.0ms

regimes211.0ms

bsearch0.0ms

simplify27.0ms

end0.0ms

sample6.2s

Profiling