Details

Time bar (total: 16.1s)

sample176.0ms

Algorithm
intervals
Results
88.0ms88×body1280valid
38.0ms61×body640valid
17.0ms28×body320valid
9.0ms69×body80valid
3.0ms10×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize33.0ms

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))
1.7b
(- (cos x) (cos y))

rewrite97.0ms

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×distribute-rgt-in frac-times distribute-lft-in pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 94
Calls
4 calls:
55.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
32.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))

series281.0ms

Counts
4 → 10
Calls
4 calls:
139.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
89.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
52.0ms
(- (cos x) (cos y))

simplify71.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06221094
126431002
250031002

prune582.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

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)))
1.7b
(- (cos x) (cos y))

rewrite117.0ms

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×distribute-rgt-in frac-times distribute-lft-in pow-prod-down associate-*l/ sqrt-prod associate-/r/
3×flip3-+ flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv div-exp frac-add *-commutative associate-/l/ unswap-sqr
1×frac-2neg diff-log clear-num associate-/r* div-inv diff-cos
Counts
4 → 106
Calls
4 calls:
24.0ms
(/ (+ 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))) (- (sin y) (/ (sin x) 16.0)))
28.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- (cos x) (cos y))

series2.1s

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)))))
137.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
59.0ms
(- (cos x) (cos y))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010752447
150012151

prune780.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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 (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
1.7b
(- (cos x) (cos y))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
22×associate-*r/
18×pow1
17×add-sqr-sqrt
14×*-un-lft-identity
10×distribute-rgt-in add-cube-cbrt distribute-lft-in associate-*l* prod-exp cbrt-unprod
9×pow-prod-down sqrt-prod
8×flip3-- flip--
7×sub-neg associate-*r*
6×add-log-exp
4×frac-times times-frac associate-*l/ associate-/r/
3×flip3-+ flip-+ associate-/l* difference-of-squares
2×cbrt-undiv div-exp frac-add *-commutative associate-/l/ distribute-lft-out--
1×frac-2neg diff-log clear-num associate-/r* div-inv diff-cos
Counts
4 → 112
Calls
4 calls:
25.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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)))))
145.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
42.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
3.0ms
(- (cos x) (cos y))

series2.3s

Counts
4 → 12
Calls
4 calls:
2.0s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (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)))))
140.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
95.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
60.0ms
(- (cos x) (cos y))

simplify49.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011172834
150012349

prune773.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 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 (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
1.7b
(- (cos x) (cos y))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×add-exp-log *-un-lft-identity add-cbrt-cube
18×pow1 associate-*r/
16×add-cube-cbrt
10×distribute-rgt-in distribute-lft-in times-frac associate-*l*
9×pow-prod-down prod-exp sqrt-prod cbrt-unprod
8×flip3-- flip--
7×sub-neg associate-*r*
6×add-log-exp
4×frac-times associate-*l/ associate-/r/
3×flip3-+ associate-/r* flip-+ associate-/l* difference-of-squares
2×frac-add *-commutative associate-/l/ distribute-lft-out--
1×cbrt-undiv frac-2neg diff-log div-exp clear-num div-inv diff-cos
Counts
4 → 118
Calls
4 calls:
28.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 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))))
145.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
38.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
3.0ms
(- (cos x) (cos y))

series1.9s

Counts
4 → 12
Calls
4 calls:
1.6s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 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))))
139.0ms
(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
93.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
55.0ms
(- (cos x) (cos y))

simplify125.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
010473259
146262841
250022833

prune789.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes188.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05463
15463

end0.0ms

sample5.2s

Algorithm
intervals
Results
3.0s2801×body1280valid
1.3s1817×body640valid
328.0ms2321×body80valid
327.0ms726×body320valid
99.0ms335×body160valid