Details

Time bar (total: 4.3s)

analyze2.0ms

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

sample106.0ms

Algorithm
intervals
Results
60.0ms153×body1280valid
22.0ms25×body2560valid
11.0ms49×body640valid
3.0ms20×body320valid
1.0ms7×body160valid
0.0ms2×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: 41.5b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
3.8b
(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))

series14.0ms

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

simplify23.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
04999270
14999270

prune57.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New23629
Fresh000
Picked101
Done000
Total24630

Merged error: 0.3b

Counts
30 → 6

localize15.0ms

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)))
3.8b
(sin (/ (+ x (+ x eps)) 2))

rewrite35.0ms

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))

series36.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms
(+ x (+ x eps))
12.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04907890
14907890

prune162.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New611172
Fresh145
Picked101
Done000
Total631578

Merged error: 0.2b

Counts
78 → 15

localize12.0ms

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))))
3.8b
(sin (+ x (* eps 1/2)))

rewrite23.0ms

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:
10.0ms
(* -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))))
5.0ms
(sin (+ x (* eps 1/2)))

simplify71.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04816851
14816851

prune154.0ms

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

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New511061
Fresh9514
Picked101
Done000
Total611576

Merged error: 0.1b

Counts
76 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×associate-*l*
10×add-cube-cbrt *-un-lft-identity
8×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×*-commutative add-log-exp
2×sin-mult unswap-sqr
1×associate-*r/
Counts
4 → 74
Calls
4 calls:
7.0ms
(* (cos x) (* (sin (* eps 1/2)) (sin (/ eps 2))))
5.0ms
(* (cos (* eps 1/2)) (sin (/ eps 2)))
7.0ms
(* (sin x) (* (cos (* eps 1/2)) (sin (/ eps 2))))
6.0ms
(* (sin (* eps 1/2)) (sin (/ eps 2)))

series39.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (cos x) (* (sin (* eps 1/2)) (sin (/ eps 2))))
5.0ms
(* (cos (* eps 1/2)) (sin (/ eps 2)))
17.0ms
(* (sin x) (* (cos (* eps 1/2)) (sin (/ eps 2))))
4.0ms
(* (sin (* eps 1/2)) (sin (/ eps 2)))

simplify68.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
04944880
14944880

prune180.0ms

Filtered
66 candidates to 86 candidates (-30.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New79786
Fresh5914
Picked101
Done000
Total8516101

Merged error: 0.0b

Counts
101 → 16

regimes199.0ms

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
02322
12322

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s4476×body1280valid
610.0ms667×body2560valid
420.0ms1825×body640valid
108.0ms674×body320valid
34.0ms276×body160valid
5.0ms82×body80valid

Profiling

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