Details

Time bar (total: 11.4s)

analyze761.0ms (6.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
50%50%0.1%4
74.9%25%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
74.9%25%0.1%8
74.9%25%0.1%9
74.9%25%0.1%10
74.9%25%0.1%11
74.9%25%0.1%12
74.9%25%0.1%13
74.9%25%0.1%14

sample209.0ms (1.8%)

Algorithm
intervals
Results
111.0ms88×body1280valid
46.0ms54×body640valid
22.0ms31×body320valid
14.0ms72×body80valid
4.0ms11×body160valid

simplify20.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0495550
1495550

prune19.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2

localize34.0ms (0.3%)

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)) (- (cos x) (cos y)))))
0.4b
(+ (* (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))
2.0b
(- (cos x) (cos y))

rewrite255.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
42×associate-*r/
29×flip3-- flip--
28×frac-times
13×pow1 add-exp-log add-cbrt-cube
12×distribute-rgt-in add-sqr-sqrt distribute-lft-in
10×sub-neg *-un-lft-identity add-log-exp
associate-*l/
add-cube-cbrt associate-*l* pow-prod-down prod-exp cbrt-unprod
sqrt-prod
difference-of-squares
diff-log distribute-lft-out--
+-commutative flip3-+ associate-*r* frac-add sum-log *-commutative flip-+ diff-cos
Counts
4 → 98
Calls

4 calls:

230.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
11.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0)))
5.0ms
(- (cos x) (cos y))
4.0ms
(- 3.0 (sqrt 5.0))

series76.0ms (0.7%)

Counts
4 → 10
Calls

4 calls:

40.0ms
(* (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 (sqrt 5.0)) 2.0)))
10.0ms
(- (cos x) (cos y))
0.0ms
(- 3.0 (sqrt 5.0))

simplify51.0ms (0.4%)

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049972617
149972617

prune474.0ms (4.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New9810108
Fresh011
Picked101
Done000
Total9911110

Merged error: 0.2b

Counts
110 → 11

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite61.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
43×associate-*r/
36×add-sqr-sqrt
28×frac-times flip3-- flip--
25×*-un-lft-identity
23×associate-*r*
19×times-frac
18×add-exp-log add-cbrt-cube
17×add-cube-cbrt
15×pow1
12×distribute-rgt-in distribute-lft-in
sub-neg associate-*l*
associate-*l/ prod-exp cbrt-unprod add-log-exp
pow-prod-down difference-of-squares
sqrt-prod
distribute-lft-out--
*-commutative unswap-sqr
cbrt-undiv +-commutative flip3-+ diff-log div-exp frac-add sum-log flip-+ div-inv diff-cos
Counts
4 → 125
Calls

4 calls:

27.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
12.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
12.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
5.0ms
(- (cos x) (cos y))

series77.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

36.0ms
(* (sqrt 2.0) (* (- (sin x) (/ (sin y) 16.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))))
26.0ms
(+ (* (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))
7.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))

simplify57.0ms (0.5%)

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
050043062

prune716.0ms (6.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New12710137
Fresh4610
Picked101
Done000
Total13216148

Merged error: 0.1b

Counts
148 → 16

localize43.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
0.5b
(cbrt (pow (- (cos x) (cos y)) 3))
0.6b
(pow (- (cos x) (cos y)) 3)
2.0b
(- (cos x) (cos y))

rewrite28.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
18×cbrt-prod
12×unpow-prod-down cube-prod
10×add-cube-cbrt
add-log-exp
pow1 add-exp-log add-cbrt-cube diff-cos distribute-lft-out-- difference-of-squares
cube-div
pow-unpow flip3-- flip--
cube-mult cbrt-div unpow3 associate-*r/ sqr-pow
+-commutative pow-to-exp sub-neg pow-pow flip3-+ pow1/3 diff-log frac-add pow-exp sum-log rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 86
Calls

4 calls:

11.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
5.0ms
(cbrt (pow (- (cos x) (cos y)) 3))
5.0ms
(pow (- (cos x) (cos y)) 3)
5.0ms
(- (cos x) (cos y))

series89.0ms (0.8%)

Counts
4 → 12
Calls

4 calls:

42.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
21.0ms
(cbrt (pow (- (cos x) (cos y)) 3))
16.0ms
(pow (- (cos x) (cos y)) 3)
9.0ms
(- (cos x) (cos y))

simplify32.0ms (0.3%)

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
050711317

prune479.0ms (4.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New98098
Fresh01515
Picked011
Done000
Total9816114

Merged error: 0.1b

Counts
114 → 16

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite61.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
32×associate-*l/
28×frac-times flip3-- flip--
26×*-un-lft-identity
23×associate-*r*
20×times-frac
18×add-exp-log add-cbrt-cube
17×associate-*r/
16×add-cube-cbrt
15×pow1
associate-*l* difference-of-squares
prod-exp cbrt-unprod add-log-exp
pow-prod-down
distribute-lft-out--
sqrt-prod
*-commutative unswap-sqr
cbrt-undiv +-commutative sub-neg flip3-+ diff-log div-exp frac-add sum-log flip-+ div-inv diff-cos
Counts
4 → 117
Calls

4 calls:

29.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) (sqrt (sqrt 2.0))))
11.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))
11.0ms
(+ (* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0)) (* (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0)))
5.0ms
(- (cos x) (cos y))

series85.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

44.0ms
(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (- (sin y) (/ (sin x) 16.0))) (sqrt (sqrt 2.0))))
24.0ms
(+ (* (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))
8.0ms
(* (cos x) (/ (- (sqrt 5.0) 1.0) 2.0))

simplify68.0ms (0.6%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049853271
149853271

prune690.0ms (6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1281129
Fresh01414
Picked011
Done101
Total12916145

Merged error: 0.1b

Counts
145 → 16

regimes443.0ms (3.9%)

Accuracy

Total 0.3b remaining (62.9%)

Threshold costs 0.3b (62.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010461
110461

end0.0ms (0%)

sample6.5s (57.1%)

Algorithm
intervals
Results
3.7s2798×body1280valid
1.6s1789×body640valid
455.0ms745×body320valid
442.0ms2321×body80valid
143.0ms347×body160valid

Profiling

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