Details

Time bar (total: 17.5s)

sample182.0ms

Algorithm
intervals
Results
96.0ms91×body1280valid
33.0ms49×body640valid
19.0ms33×body320valid
10.0ms70×body80valid
4.0ms13×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune6.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
20×times-frac
18×add-cube-cbrt
11×add-exp-log add-cbrt-cube difference-of-squares
9×associate-*r*
8×pow1 sqrt-prod add-log-exp
6×distribute-lft-out--
4×sub-neg unswap-sqr
3×flip3-- prod-exp flip-- cbrt-unprod
2×distribute-rgt-in distribute-lft-in diff-log associate-*r/ pow-prod-down *-commutative
1×cbrt-undiv div-exp associate-*l/ div-inv diff-cos
Counts
4 → 102
Calls
4 calls:
10.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
11.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series226.0ms

Counts
4 → 10
Calls
4 calls:
84.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
85.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
56.0ms
(- (cos x) (cos y))

simplify53.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0584813
12075753
25001753

prune596.0ms

Filtered
112 candidates to 76 candidates (67.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10012112
Fresh000
Picked101
Done000
Total10112113

Merged error: 0.2b

Counts
113 → 12

localize38.0ms

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
23×times-frac
20×add-cube-cbrt
16×add-exp-log add-cbrt-cube
9×associate-*r* difference-of-squares
8×pow1
7×sqrt-prod
6×associate-*r/ add-log-exp
5×distribute-lft-out--
4×prod-exp associate-/r/ cbrt-unprod unswap-sqr
3×cbrt-undiv sub-neg flip3-+ div-exp associate-*l/ flip-+ associate-/l*
2×distribute-rgt-in flip3-- distribute-lft-in pow-prod-down frac-add *-commutative flip-- div-inv associate-/l/
1×frac-2neg diff-log clear-num associate-/r* diff-cos
Counts
4 → 114
Calls
4 calls:
11.0ms
(/ (+ 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)))))
10.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
11.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series2.0s

Counts
4 → 12
Calls
4 calls:
1.8s
(/ (+ 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)))))
85.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
85.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
56.0ms
(- (cos x) (cos y))

simplify113.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010292159
144041906
250011906

prune781.0ms

Filtered
126 candidates to 89 candidates (70.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1197126
Fresh9211
Picked101
Done000
Total1299138

Merged error: 0.0b

Counts
138 → 9

localize45.0ms

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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(/ 1 (sqrt 2.0))
2.0b
(- (cos x) (cos y))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
28×*-un-lft-identity
24×add-cube-cbrt
22×times-frac
16×sqrt-prod
15×add-exp-log
13×add-cbrt-cube
8×pow1
7×associate-/r*
6×associate-*r/ associate-*r* associate-*l* associate-/l* add-log-exp
4×div-exp associate-/r/
3×cbrt-undiv sub-neg pow-flip flip3-+ flip-+ difference-of-squares
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in associate-*l/ frac-add prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- unswap-sqr
1×rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down *-commutative diff-cos inv-pow
Counts
4 → 118
Calls
4 calls:
11.0ms
(/ (+ 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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
11.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(/ 1 (sqrt 2.0))
4.0ms
(- (cos x) (cos y))

series2.9s

Counts
4 → 10
Calls
4 calls:
2.8s
(/ (+ 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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(/ 1 (sqrt 2.0))
59.0ms
(- (cos x) (cos y))

simplify115.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
09542264
144511963
250011938

prune745.0ms

Filtered
128 candidates to 78 candidates (60.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1235128
Fresh268
Picked101
Done000
Total12611137

Merged error: 0.0b

Counts
137 → 11

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.4b
(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
1.0b
(/ 1 (sqrt 2.0))
2.0b
(- (cos x) (cos y))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×*-un-lft-identity
24×add-cube-cbrt
21×times-frac
16×sqrt-prod
15×add-exp-log
13×add-cbrt-cube
8×pow1
7×associate-/r*
6×associate-*r/ associate-*l* associate-/l* add-log-exp
4×div-exp associate-/r/
3×cbrt-undiv sub-neg pow-flip flip3-+ associate-*r* flip-+
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in associate-*l/ frac-add prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
1×rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down *-commutative diff-cos distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 115
Calls
4 calls:
11.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
7.0ms
(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
4.0ms
(/ 1 (sqrt 2.0))
5.0ms
(- (cos x) (cos y))

series3.1s

Counts
4 → 10
Calls
4 calls:
3.0s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
91.0ms
(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
0.0ms
(/ 1 (sqrt 2.0))
59.0ms
(- (cos x) (cos y))

simplify146.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
09292244
143831944
250011919

prune628.0ms

Filtered
125 candidates to 75 candidates (60.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1214125
Fresh4610
Picked011
Done000
Total12511136

Merged error: 0.0b

Counts
136 → 11

regimes216.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05538
15538

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.0s2706×body1280valid
1.3s1829×body640valid
402.0ms817×body320valid
343.0ms2316×body80valid
105.0ms332×body160valid