Details

Time bar (total: 10.6s)

sample224.0ms

Algorithm
intervals
Results
121.0ms96×body1280valid
58.0ms65×body640valid
15.0ms25×body320valid
12.0ms65×body80valid
3.0ms5×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
0518050

prune15.0ms

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

localize37.0ms

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) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.3b
(- (cos x) (cos y))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*r/
29×flip3-- flip--
28×frac-times
24×distribute-rgt-in distribute-lft-in
13×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×sub-neg *-un-lft-identity add-log-exp
8×associate-*l/
6×add-cube-cbrt associate-*l* pow-prod-down prod-exp cbrt-unprod
4×sqrt-prod
3×difference-of-squares
2×diff-log distribute-lft-out--
1×+-commutative flip3-+ associate-*r* frac-add sum-log *-commutative flip-+ diff-cos
Counts
4 → 108
Calls
4 calls:
26.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
10.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series74.0ms

Counts
4 → 10
Calls
4 calls:
35.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
29.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
0.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

simplify38.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
055402967

prune373.0ms

Filtered
82 candidates to 118 candidates (-43.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10810118
Fresh011
Picked101
Done000
Total10911120

Merged error: 0.2b

Counts
120 → 11

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

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*r/
28×frac-times flip3-- flip--
24×distribute-rgt-in distribute-lft-in
18×add-exp-log add-cbrt-cube
13×pow1
12×add-sqr-sqrt
10×*-un-lft-identity
9×sub-neg
8×add-cube-cbrt associate-*l/ add-log-exp
7×prod-exp cbrt-unprod
6×associate-*l* pow-prod-down
4×times-frac associate-/l*
3×flip3-+ sqrt-prod flip-+
2×cbrt-undiv div-exp associate-/r/ associate-/l/ distribute-lft-out
1×+-commutative frac-2neg diff-log associate-*r* frac-add clear-num associate-/r* sum-log *-commutative div-inv diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
15.0ms
(/ (+ 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 (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0))))))
26.0ms
(* (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) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
4.0ms
(- (cos x) (cos y))

series318.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ (+ 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 (+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0))))))
36.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
27.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
9.0ms
(- (cos x) (cos y))

simplify84.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
054284853

prune536.0ms

Filtered
94 candidates to 132 candidates (-40.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1248132
Fresh7310
Picked101
Done000
Total13211143

Merged error: 0.0b

Counts
143 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
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) 2.0)) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ (sqrt 5.0) 3.0)))))
1.3b
(- (cos x) (cos y))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
43×associate-*r/
36×add-sqr-sqrt
28×frac-times flip3-- flip--
25×*-un-lft-identity
24×distribute-rgt-in distribute-lft-in
23×associate-*r*
19×times-frac
18×add-exp-log add-cbrt-cube
17×add-cube-cbrt
15×pow1
9×sub-neg associate-*l*
8×associate-*l/ prod-exp cbrt-unprod add-log-exp
7×pow-prod-down difference-of-squares
6×sqrt-prod
4×distribute-lft-out--
2×*-commutative unswap-sqr
1×cbrt-undiv +-commutative flip3-+ diff-log div-exp frac-add sum-log flip-+ div-inv diff-cos
Counts
4 → 134
Calls
4 calls:
11.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
26.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
10.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ (sqrt 5.0) 3.0)))))
5.0ms
(- (cos x) (cos y))

series77.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
35.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
23.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ (sqrt 5.0) 3.0)))))
12.0ms
(- (cos x) (cos y))

simplify58.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049823416
149823416

prune484.0ms

Filtered
99 candidates to 146 candidates (-47.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1451146
Fresh1910
Picked011
Done000
Total14611157

Merged error: 0.0b

Counts
157 → 11

localize41.0ms

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 (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ (sqrt 5.0) 3.0)))))
0.6b
(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
1.3b
(- (cos x) (cos y))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
55×associate-*r/
36×add-sqr-sqrt
32×frac-times flip3-- associate-*r* flip--
30×*-un-lft-identity
27×times-frac
25×add-exp-log add-cbrt-cube
24×distribute-rgt-in distribute-lft-in sqrt-prod
22×add-cube-cbrt
18×pow1
12×associate-*l/ prod-exp cbrt-unprod
9×sub-neg pow-prod-down
8×sqrt-div add-log-exp
7×associate-*l* difference-of-squares
5×frac-add
4×distribute-lft-out--
2×cbrt-undiv div-exp *-commutative
1×+-commutative flip3-+ diff-log sum-log flip-+ div-inv diff-cos
Counts
4 → 152
Calls
4 calls:
31.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
16.0ms
(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ (sqrt 5.0) 3.0)))))
18.0ms
(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
4.0ms
(- (cos x) (cos y))

series78.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
23.0ms
(+ (* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0)) (* (cos y) (/ (- (* 3.0 3.0) 5.0) (* 2.0 (+ (sqrt 5.0) 3.0)))))
6.0ms
(* (* (cos x) (sqrt (- (sqrt 5.0) 1.0))) (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0))
9.0ms
(- (cos x) (cos y))

simplify73.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049864001
149864001

prune707.0ms

Filtered
107 candidates to 164 candidates (-53.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1640164
Fresh099
Picked011
Done011
Total16411175

Merged error: 0.0b

Counts
175 → 11

regimes332.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05058
15058

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.7s2716×body1280valid
1.6s1873×body640valid
477.0ms758×body320valid
453.0ms2318×body80valid
138.0ms335×body160valid

Profiling

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