Details

analyze779.0ms

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

sample222.0ms

Algorithm

intervals

Results

121.0ms	90×	body	1280	valid
53.0ms	57×	body	640	valid
16.0ms	27×	body	320	valid
14.0ms	74×	body	80	valid
3.0ms	8×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4955	50
1	4955	50

prune16.0ms

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

localize41.0ms

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)) (- (cos x) (cos y)))))
0.5b	(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.0b	(- (cos x) (cos y))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
29×	`flip3--` `flip--`
28×	`frac-times`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`distribute-rgt-in` `add-sqr-sqrt` `distribute-lft-in`
10×	`sub-neg` `*-un-lft-identity` `add-log-exp`
8×	`associate-*l/`
6×	`add-cube-cbrt` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`sqrt-prod`
3×	`difference-of-squares`
2×	`diff-log` `distribute-lft-out--`
1×	`+-commutative` `flip3-+` `associate-r` `frac-add` `sum-log` `*-commutative` `flip-+` `diff-cos`

Counts

4 → 98

Calls

4 calls:

28.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
11.0ms	(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
4.0ms	(- 3.0 (sqrt 5.0))
5.0ms	(- (cos x) (cos y))

series82.0ms

Counts

4 → 10

Calls

4 calls:

39.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
33.0ms	(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
0.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4997	2617
1	4997	2617

prune389.0ms

Filtered

82 candidates to 108 candidates (-31.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	11	110

Merged error: 0.2b

Counts

110 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
0.3b	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
0.5b	(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
2.0b	(- (cos x) (cos y))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

43×	`associate-*r/`
36×	`add-sqr-sqrt`
28×	`frac-times` `flip3--` `flip--`
25×	`*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
18×	`add-exp-log` `add-cbrt-cube`
17×	`add-cube-cbrt`
15×	`pow1`
12×	`distribute-rgt-in` `distribute-lft-in`
9×	`sub-neg` `associate-l`
8×	`associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
7×	`pow-prod-down` `difference-of-squares`
6×	`sqrt-prod`
4×	`distribute-lft-out--`
2×	`*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `diff-log` `div-exp` `frac-add` `sum-log` `flip-+` `div-inv` `diff-cos`

Counts

4 → 125

Calls

4 calls:

11.0ms	(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
28.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
13.0ms	(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
5.0ms	(- (cos x) (cos y))

series85.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
43.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
26.0ms	(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
9.0ms	(- (cos x) (cos y))

simplify63.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5004	3062

prune531.0ms

Filtered

99 candidates to 137 candidates (-38.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	137	11	148

Merged error: 0.1b

Counts

148 → 11

localize42.0ms

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)) (- (cos x) (cos y)))))
0.5b	(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
0.6b	(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
2.0b	(- (cos x) (cos y))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

55×	`associate-*r/`
36×	`add-sqr-sqrt`
32×	`frac-times` `flip3--` `associate-r` `flip--`
30×	`*-un-lft-identity`
27×	`times-frac`
25×	`add-exp-log` `add-cbrt-cube`
24×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`pow1`
12×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `prod-exp` `cbrt-unprod`
9×	`sub-neg` `pow-prod-down`
8×	`sqrt-div` `add-log-exp`
7×	`associate-l` `difference-of-squares`
5×	`frac-add`
4×	`distribute-lft-out--`
2×	`cbrt-undiv` `div-exp` `*-commutative`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `div-inv` `diff-cos`

Counts

4 → 143

Calls

4 calls:

33.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
17.0ms	(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
26.0ms	(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
5.0ms	(- (cos x) (cos y))

series84.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
26.0ms	(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
7.0ms	(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
9.0ms	(- (cos x) (cos y))

simplify69.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5011	3627

prune671.0ms

Filtered

106 candidates to 155 candidates (-46.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 0.1b

Counts

166 → 11

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
0.5b	(pow (* (sqrt 2.0) (* (- (cos x) (cos y)) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))) 3)
0.6b	(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
2.0b	(- (cos x) (cos y))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

55×	`associate-*r/`
35×	`add-sqr-sqrt`
32×	`frac-times` `flip3--` `flip--`
31×	`associate-r`
29×	`*-un-lft-identity`
27×	`times-frac`
26×	`add-exp-log` `cube-div` `add-cbrt-cube`
21×	`add-cube-cbrt` `sqrt-prod`
19×	`pow1`
12×	`associate-*l/` `prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
8×	`sqrt-div` `add-log-exp`
7×	`difference-of-squares`
5×	`frac-add`
4×	`pow-pow` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt`
3×	`pow-unpow`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `flip3-+` `diff-log` `unpow3` `cube-prod` `associate-l` `sum-log` `*-commutative` `flip-+` `div-inv` `diff-cos` `sqr-pow`

Counts

4 → 139

Calls

4 calls:

22.0ms	(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
29.0ms	(pow (* (sqrt 2.0) (* (- (cos x) (cos y)) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))) 3)
18.0ms	(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
5.0ms	(- (cos x) (cos y))

series207.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
164.0ms	(pow (* (sqrt 2.0) (* (- (cos x) (cos y)) (* (- (sin x) (/ (sin y) 16.0)) (- (sin y) (/ (sin x) 16.0))))) 3)
7.0ms	(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
10.0ms	(- (cos x) (cos y))

simplify63.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5007	4031

prune710.0ms

Filtered

108 candidates to 151 candidates (-39.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	150	12	162

Merged error: 0.1b

Counts

162 → 12

regimes380.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	66
1	107	66

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	2682×	body	1280	valid
1.6s	1853×	body	640	valid
480.0ms	780×	body	320	valid
448.0ms	2342×	body	80	valid
145.0ms	343×	body	160	valid

Details

analyze779.0ms

sample222.0ms

simplify23.0ms

prune16.0ms

localize41.0ms

rewrite53.0ms

series82.0ms

simplify56.0ms

prune389.0ms

localize37.0ms

rewrite63.0ms

series85.0ms

simplify63.0ms

prune531.0ms

localize42.0ms

rewrite89.0ms

series84.0ms

simplify69.0ms

prune671.0ms

localize46.0ms

rewrite82.0ms

series207.0ms

simplify63.0ms

prune710.0ms

regimes380.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.6s

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