Details

Time bar (total: 16.9s)

analyze761.0ms

Algorithm
search
Search
TrueOtherFalseIter
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

sample205.0ms

Algorithm
intervals
Results
106.0ms84×body1280valid
51.0ms54×body640valid
19.0ms32×body320valid
14.0ms76×body80valid
4.0ms10×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0158948
1158948

prune16.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (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)) (* (cos y) (- 3.0 (sqrt 5.0))))
1.0b
(- 3.0 (sqrt 5.0))
1.9b
(- (cos x) (cos y))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
48×associate-*r/
33×flip3-- flip--
28×frac-times
14×distribute-rgt-in sub-neg distribute-lft-in
13×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
8×associate-*l/
6×add-cube-cbrt associate-*l* pow-prod-down prod-exp cbrt-unprod
4×frac-add sqrt-prod
3×difference-of-squares
2×associate-+l+ associate-+r+ diff-log distribute-lft-out--
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ diff-cos
Counts
4 → 105
Calls
4 calls:
24.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
9.0ms
(+ (* (cos x) (- (sqrt 5.0) 1.0)) (* (cos y) (- 3.0 (sqrt 5.0))))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series74.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
28.0ms
(+ (* (cos x) (- (sqrt 5.0) 1.0)) (* (cos y) (- 3.0 (sqrt 5.0))))
0.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

simplify43.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
050752769

prune424.0ms

Filtered
89 candidates to 115 candidates (-29.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1069115
Fresh011
Picked101
Done000
Total10710117

Merged error: 0.2b

Counts
117 → 10

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))
0.3b
(+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0))))
0.4b
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
1.9b
(- (cos x) (cos y))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
214×associate-*r/
120×frac-times
103×flip3-- flip--
64×frac-add
49×flip3-+ flip-+
48×associate-*l/
24×distribute-rgt-in distribute-lft-in
18×pow1 add-exp-log add-cbrt-cube
17×sub-neg
14×add-sqr-sqrt
12×associate-*l*
11×*-un-lft-identity
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
7×add-cube-cbrt
4×associate-+l+ associate-+r+
3×sqrt-prod difference-of-squares
2×associate-*r* *-commutative distribute-lft-out--
1×+-commutative times-frac diff-log sum-log diff-cos
Counts
4 → 206
Calls
4 calls:
20.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))
18.0ms
(+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0))))
25.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
4.0ms
(- (cos x) (cos y))

series126.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))))
42.0ms
(+ (* (cos x) (* (+ 5.0 (* 3.0 (+ 3.0 (sqrt 5.0)))) (- 5.0 (* 1.0 1.0)))) (* (cos y) (* (- (pow 3.0 3) (* 5.0 (sqrt 5.0))) (+ (sqrt 5.0) 1.0))))
42.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
9.0ms
(- (cos x) (cos y))

simplify96.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0501411840

prune2.8s

Filtered
185 candidates to 218 candidates (-17.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2153218
Fresh189
Picked101
Done000
Total21711228

Merged error: 0.1b

Counts
228 → 11

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (* (cos x) (* (+ 3.0 (sqrt 5.0)) (- (* 5.0 (sqrt 5.0)) (pow 1.0 3)))) (* (cos y) (* (- (* 3.0 3.0) 5.0) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0)))))) (* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0)))))
0.4b
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
1.0b
(* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0))))
1.9b
(- (cos x) (cos y))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
204×associate-*r/
100×frac-times
76×flip3-- flip--
66×associate-/l/
64×frac-add
61×flip3-+ flip-+
44×associate-*l/
20×add-exp-log add-cbrt-cube
15×pow1
14×add-sqr-sqrt *-un-lft-identity
13×distribute-rgt-in distribute-lft-in
10×add-cube-cbrt associate-*l*
9×sub-neg
8×prod-exp associate-/r/ cbrt-unprod
7×pow-prod-down
6×add-log-exp
4×associate-*r*
3×times-frac sqrt-prod associate-/l*
2×cbrt-undiv div-exp *-commutative
1×frac-2neg diff-log clear-num associate-/r* div-inv diff-cos distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 196
Calls
4 calls:
32.0ms
(/ (+ (* (cos x) (* (+ 3.0 (sqrt 5.0)) (- (* 5.0 (sqrt 5.0)) (pow 1.0 3)))) (* (cos y) (* (- (* 3.0 3.0) 5.0) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0)))))) (* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0)))))
27.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
8.0ms
(* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0))))
5.0ms
(- (cos x) (cos y))

series131.0ms

Counts
4 → 10
Calls
4 calls:
77.0ms
(/ (+ (* (cos x) (* (+ 3.0 (sqrt 5.0)) (- (* 5.0 (sqrt 5.0)) (pow 1.0 3)))) (* (cos y) (* (- (* 3.0 3.0) 5.0) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0)))))) (* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0)))))
44.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
0.0ms
(* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0))))
9.0ms
(- (cos x) (cos y))

simplify56.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
061407652

prune3.0s

Filtered
177 candidates to 206 candidates (-16.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2006206
Fresh4610
Picked101
Done000
Total20512217

Merged error: 0.1b

Counts
217 → 12

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (- (sin x) (/ (sin y) 16.0)) 3)
0.6b
(pow (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) 3)
1.0b
(* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0))))
1.9b
(- (cos x) (cos y))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×*-un-lft-identity
10×pow1 add-exp-log cube-div add-cube-cbrt add-cbrt-cube
8×frac-times flip3-- flip--
7×unpow-prod-down cube-prod
6×pow-unpow flip3-+ flip-+ add-log-exp
5×difference-of-squares
4×associate-*r/ associate-*l* associate-*l/
3×pow-pow associate-*r* pow-exp distribute-lft-out-- rem-cube-cbrt
2×cube-mult pow-to-exp times-frac unpow3 pow-prod-down prod-exp cbrt-unprod sqr-pow
1×distribute-rgt-in sub-neg distribute-lft-in diff-log *-commutative diff-cos distribute-lft-out unswap-sqr
Counts
4 → 104
Calls
4 calls:
8.0ms
(pow (- (sin x) (/ (sin y) 16.0)) 3)
15.0ms
(pow (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) 3)
8.0ms
(* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0))))
5.0ms
(- (cos x) (cos y))

series75.0ms

Counts
4 → 10
Calls
4 calls:
20.0ms
(pow (- (sin x) (/ (sin y) 16.0)) 3)
45.0ms
(pow (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) 3)
0.0ms
(* (+ 3.0 (sqrt 5.0)) (+ 5.0 (* 1.0 (+ (sqrt 5.0) 1.0))))
9.0ms
(- (cos x) (cos y))

simplify49.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
051121927

prune638.0ms

Filtered
78 candidates to 114 candidates (-46.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1131114
Fresh01111
Picked101
Done000
Total11412126

Merged error: 0.1b

Counts
126 → 12

regimes445.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06283
16283

end0.0ms

analyze763.0ms

Algorithm
search
Search
TrueOtherFalseIter
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

sample6.7s

Algorithm
intervals
Results
3.8s2695×body1280valid
1.6s1852×body640valid
484.0ms785×body320valid
425.0ms2305×body80valid
148.0ms363×body160valid

Profiling

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