Details

Time bar (total: 4.5s)

analyze2.0ms

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

sample97.0ms

Algorithm
intervals
Results
49.0ms139×body1280valid
20.0ms62×body640valid
14.0ms16×body2560valid
4.0ms24×body320valid
1.0ms10×body160valid
0.0ms5×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: 39.3b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
3.5b
(cos (+ x eps))

rewrite10.0ms

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:
6.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series15.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

simplify25.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
04999270
14999270

prune67.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New20929
Fresh000
Picked101
Done000
Total21930

Merged error: 0.4b

Counts
30 → 9

localize12.0ms

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)))
3.7b
(sin (/ (+ x (+ x eps)) 2))

rewrite37.0ms

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))))
8.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

series36.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms
(+ x (+ x eps))
11.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify55.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
04907890
14907890

prune159.0ms

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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New621072
Fresh448
Picked101
Done000
Total671481

Merged error: 0.3b

Counts
81 → 14

localize11.0ms

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))))
3.7b
(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)))))
8.0ms
(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
4.0ms
(sin (+ x (* eps 1/2)))

series32.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(* -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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New52961
Fresh8513
Picked101
Done000
Total611475

Merged error: 0.1b

Counts
75 → 14

localize19.0ms

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)))
0.1b
(* (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)))
6.0ms
(* (sin x) (cos (* eps 1/2)))
10.0ms
(* (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

prune158.0ms

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

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New75782
Fresh4913
Picked101
Done000
Total801696

Merged error: 0.0b

Counts
96 → 16

regimes307.0ms

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

sample3.0s

Algorithm
intervals
Results
1.7s4508×body1280valid
572.0ms629×body2560valid
428.0ms1862×body640valid
100.0ms641×body320valid
32.0ms277×body160valid
5.0ms83×body80valid

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