Details

Time bar (total: 8.3s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1

sample245.0ms

Algorithm
intervals
Results
49.0ms140×body1280valid
20.0ms23×body2560valid
12.0ms57×body640valid
3.0ms20×body320valid
1.0ms13×body160valid
0.0ms3×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.2b

Counts
2 → 1

localize45.0ms

Local error

Found 2 expressions with local error:

14.4b
(cos (+ x eps))
23.5b
(- (cos (+ x eps)) (cos x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 23
Calls
2 calls:
4.0ms
(cos (+ x eps))
10.0ms
(- (cos (+ x eps)) (cos x))

series15.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(cos (+ x eps))
11.0ms
(- (cos (+ x eps)) (cos x))

simplify24.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
04999270
14999270

prune60.0ms

Filtered
23 candidates to 29 candidates (-26.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New22729
Fresh000
Picked101
Done000
Total23730

Merged error: 0.3b

Counts
30 → 7

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b
(+ x (+ x eps))
0.3b
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
14.4b
(sin (/ (+ x (+ x eps)) 2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l*
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×sum-log distribute-lft-out
2×*-commutative sin-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 60
Calls
4 calls:
11.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
5.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

series38.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms
(+ x (+ x eps))
14.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify54.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04907890
14907890

prune155.0ms

Filtered
53 candidates to 72 candidates (-35.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New64872
Fresh336
Picked101
Done000
Total681179

Merged error: 0.2b

Counts
79 → 11

localize69.0ms

Local error

Found 3 expressions with local error:

0.0b
(* -2 (* (sin (/ eps 2)) (sin (+ x (* eps 1/2)))))
0.3b
(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
14.4b
(sin (+ x (* eps 1/2)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×sin-sum
6×add-cube-cbrt *-un-lft-identity associate-*l*
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×add-log-exp
2×*-commutative sin-mult
1×associate-*r/ unswap-sqr
Counts
3 → 52
Calls
3 calls:
9.0ms
(* -2 (* (sin (/ eps 2)) (sin (+ x (* eps 1/2)))))
7.0ms
(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
4.0ms
(sin (+ x (* eps 1/2)))

series30.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(* -2 (* (sin (/ eps 2)) (sin (+ x (* eps 1/2)))))
11.0ms
(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
6.0ms
(sin (+ x (* eps 1/2)))

simplify73.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
04816851
14816851

prune148.0ms

Filtered
45 candidates to 61 candidates (-35.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New55661
Fresh4610
Picked101
Done000
Total601272

Merged error: 0.1b

Counts
72 → 12

localize163.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
0.1b
(* (cos x) (sin (* eps 1/2)))
0.2b
(* (sin x) (cos (* eps 1/2)))
0.3b
(* (sin (/ eps 2)) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×flip3-+ associate-*r/ flip-+
1×+-commutative distribute-rgt-in distribute-lft-in sum-log sin-cos-mult
Counts
4 → 70
Calls
4 calls:
7.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
5.0ms
(* (cos x) (sin (* eps 1/2)))
5.0ms
(* (sin x) (cos (* eps 1/2)))
12.0ms
(* (sin (/ eps 2)) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
9.0ms
(* (cos x) (sin (* eps 1/2)))
9.0ms
(* (sin x) (cos (* eps 1/2)))
25.0ms
(* (sin (/ eps 2)) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
050301237

prune172.0ms

Filtered
58 candidates to 82 candidates (-41.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh7411
Picked101
Done000
Total811394

Merged error: 0.0b

Counts
94 → 13

regimes201.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02527
12527

end0.0ms

sample6.5s

Algorithm
intervals
Results
1.6s4403×body1280valid
595.0ms653×body2560valid
412.0ms1878×body640valid
105.0ms703×body320valid
30.0ms290×body160valid
4.0ms73×body80valid

Profiling

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