Details

Time bar (total: 28.2s)

sample291.0ms

Algorithm
intervals
Results
159.0ms86×body1280valid
58.0ms55×body640valid
21.0ms80×body80valid
18.0ms26×body320valid
4.0ms9×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

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 (sqrt 5.0)) 2.0) (cos y)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.1b
(- (cos x) (cos y))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
15×*-un-lft-identity
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*r/ associate-*r* associate-*l*
5×sqrt-prod difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-- flip3-+ flip-- flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv distribute-rgt-in distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative div-inv diff-cos
Counts
4 → 88
Calls
4 calls:
74.0ms
(/ (+ 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 (sqrt 5.0)) 2.0) (cos y)))))
58.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series1.5s

Counts
4 → 10
Calls
4 calls:
1.4s
(/ (+ 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 (sqrt 5.0)) 2.0) (cos y)))))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify96.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08521769
135601553
250021553

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
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 2.0) (- (sin x) (/ (sin y) 16.0)))
2.1b
(- (cos x) (cos y))

rewrite190.0ms

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:
44.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
76.0ms
(/ (+ 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)))))
57.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- (cos x) (cos y))

series2.1s

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
1.9s
(/ (+ 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)))))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
60.0ms
(- (cos x) (cos y))

simplify123.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010292159
144041906
250011906

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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 (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (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 2.0) (- (sin x) (/ (sin y) 16.0)))
0.6b
(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
2.1b
(- (cos x) (cos y))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×associate-*l*
30×*-un-lft-identity
29×sqrt-prod
22×times-frac
20×add-cube-cbrt
16×add-exp-log add-cbrt-cube
11×pow1
9×difference-of-squares
7×associate-*r/ associate-*r*
6×add-log-exp
5×associate-*l/ prod-exp cbrt-unprod distribute-lft-out--
4×sqrt-div pow-prod-down associate-/r/
3×sub-neg flip3-+ flip-+ associate-/l*
2×cbrt-undiv distribute-rgt-in flip3-- distribute-lft-in div-exp frac-add *-commutative flip-- div-inv associate-/l/ unswap-sqr
1×frac-times frac-2neg diff-log clear-num associate-/r* diff-cos
Counts
4 → 116
Calls
4 calls:
76.0ms
(/ (+ 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 (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
54.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
94.0ms
(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
13.0ms
(- (cos x) (cos y))

series3.3s

Counts
4 → 12
Calls
4 calls:
3.0s
(/ (+ 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 (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
101.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
167.0ms
(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
61.0ms
(- (cos x) (cos y))

simplify130.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
010672645
144082236
250022233

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize277.0ms

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 (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (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 2.0) (- (sin x) (* 0.0625 (sin y))))
0.6b
(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
2.1b
(- (cos x) (cos y))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
31×associate-*l*
29×sqrt-prod
28×*-un-lft-identity
21×times-frac
20×add-cube-cbrt
16×add-exp-log add-cbrt-cube
11×pow1
7×associate-*r/ difference-of-squares
6×add-log-exp
5×associate-*l/ prod-exp cbrt-unprod
4×sqrt-div associate-*r* pow-prod-down associate-/r/ distribute-lft-out--
3×sub-neg flip3-+ flip-+ associate-/l*
2×cbrt-undiv distribute-rgt-in flip3-- distribute-lft-in div-exp frac-add *-commutative flip-- div-inv associate-/l/ unswap-sqr
1×frac-times frac-2neg diff-log clear-num associate-/r* diff-cos
Counts
4 → 113
Calls
4 calls:
77.0ms
(/ (+ 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 (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
30.0ms
(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
104.0ms
(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
8.0ms
(- (cos x) (cos y))

series3.2s

Counts
4 → 12
Calls
4 calls:
2.9s
(/ (+ 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 (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
100.0ms
(* (sqrt 2.0) (- (sin x) (* 0.0625 (sin y))))
159.0ms
(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
59.0ms
(- (cos x) (cos y))

simplify132.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
010422626
143402217
250012214

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes787.0ms

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
05140
15140

end0.0ms

sample8.8s

Algorithm
intervals
Results
5.1s2744×body1280valid
2.0s1820×body640valid
570.0ms732×body320valid
499.0ms2343×body80valid
177.0ms361×body160valid