Details

Time bar (total: 15.9s)

sample191.0ms

Algorithm
intervals
Results
107.0ms96×body1280valid
41.0ms62×body640valid
9.0ms67×body80valid
7.0ms16×body320valid
5.0ms15×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize58.0ms

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))
1.3b
(- (cos x) (cos y))

rewrite155.0ms

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:
67.0ms
(/ (+ 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)))))
60.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms
(- 3.0 (sqrt 5.0))
13.0ms
(- (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)))))
95.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify87.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
08521769
135601553
250021553

prune549.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.0b
(- 3.0 (sqrt 5.0))
1.3b
(- (cos x) (cos y))
3.6b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×*-un-lft-identity
12×associate-*r/
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*l* frac-sub sin-mult
5×sqrt-prod associate-/l/
4×sub-neg flip3-- times-frac associate-*r* associate-/r* flip-- difference-of-squares
2×cbrt-undiv distribute-rgt-in frac-times distribute-lft-in diff-log div-exp associate-*l/ prod-exp associate-/r/ cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-+ div-inv diff-cos associate-/l*
Counts
4 → 92
Calls
4 calls:
48.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
7.0ms
(- 3.0 (sqrt 5.0))
7.0ms
(- (cos x) (cos y))
56.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

series363.0ms

Counts
4 → 10
Calls
4 calls:
119.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
0.0ms
(- 3.0 (sqrt 5.0))
55.0ms
(- (cos x) (cos y))
189.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05731299
124171122
250011105

prune682.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (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 x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.3b
(- (cos x) (cos y))
3.6b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
16×add-exp-log associate-*r/ add-cbrt-cube
11×add-cube-cbrt
7×times-frac associate-/l/
6×pow1 associate-*l* associate-/r/ frac-sub sin-mult add-log-exp
5×associate-/r*
4×cbrt-undiv flip3-+ div-exp associate-*r* associate-*l/ sqrt-prod flip-+ associate-/l*
3×sub-neg flip3-- prod-exp flip-- cbrt-unprod
2×distribute-rgt-in frac-times frac-2neg distribute-lft-in frac-add clear-num div-inv distribute-lft-out difference-of-squares unswap-sqr
1×diff-log pow-prod-down *-commutative diff-cos distribute-lft-out--
Counts
4 → 104
Calls
4 calls:
64.0ms
(/ (+ 2.0 (* (* (/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (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)))))
48.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
7.0ms
(- (cos x) (cos y))
57.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

series3.2s

Counts
4 → 12
Calls
4 calls:
2.8s
(/ (+ 2.0 (* (* (/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (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)))))
117.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
61.0ms
(- (cos x) (cos y))
187.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011263165
150022728

prune821.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (cos x) (cos y))
3.6b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
3.6b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
3.6b
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-exp-log add-cbrt-cube
18×associate-*r/
15×associate-/l/
12×add-sqr-sqrt times-frac associate-/r*
10×add-cube-cbrt
9×frac-sub sin-mult
6×cbrt-undiv div-exp associate-/r/ distribute-lft-out add-log-exp
4×pow1 flip3-- flip--
3×frac-times frac-2neg flip3-+ associate-*l/ prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l*
1×sub-neg diff-log diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 105
Calls
4 calls:
7.0ms
(- (cos x) (cos y))
54.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
54.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
58.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

series617.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (cos x) (cos y))
187.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
188.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))
187.0ms
(/ (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (+ (sin x) (/ (sin y) 16.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03831984
115771635
250011584

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes174.0ms

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
05698
15698

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.0s2733×body1280valid
1.3s1834×body640valid
365.0ms741×body320valid
327.0ms2311×body80valid
119.0ms381×body160valid