Details

Time bar (total: 6.3s)

analyze7.0ms

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

sample241.0ms

Algorithm
intervals
Results
130.0ms153×body1280valid
39.0ms16×body2560valid
35.0ms54×body640valid
15.0ms27×body320valid
1.0ms6×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
07211
17211

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.3b

Counts
2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (cos (+ x eps)) (cos x))
2.4b
(cos (+ x eps))

rewrite82.0ms

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:
24.0ms
(- (cos (+ x eps)) (cos x))
57.0ms
(cos (+ x eps))

series31.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify68.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05000429

prune111.0ms

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

localize23.0ms

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)))
2.4b
(sin (/ (+ x (+ x eps)) 2))

rewrite70.0ms

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:
22.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
11.0ms
(+ x (+ x eps))
20.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
14.0ms
(sin (/ (+ x (+ x eps)) 2))

series72.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
7.0ms
(+ x (+ x eps))
22.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
12.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify130.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (101.0ms)

IterNodesCost
049101369
149101369

prune296.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New65772
Fresh145
Picked011
Done000
Total661278

Merged error: 0.2b

Counts
78 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

2.4b
(sin (/ (+ x (+ x eps)) 2))
6.7b
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))
6.7b
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))
6.7b
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod cbrt-div pow1/3 associate-*l/ sin-mult
Counts
4 → 37
Calls
4 calls:
14.0ms
(sin (/ (+ x (+ x eps)) 2))
19.0ms
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))
19.0ms
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))
19.0ms
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))

series213.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sin (/ (+ x (+ x eps)) 2))
60.0ms
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))
75.0ms
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))
72.0ms
(cbrt (* (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))) -2))

simplify151.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (126.0ms)

IterNodesCost
049021334
149021334

prune270.0ms

Filtered
42 candidates to 49 candidates (-16.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New48149
Fresh1910
Picked011
Done011
Total491261

Merged error: 0.2b

Counts
61 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))
0.6b
(cbrt (sin (/ eps 2)))
2.4b
(sin (/ (+ x (+ x eps)) 2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
Counts
4 → 40
Calls
4 calls:
4.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
2.0ms
(cbrt (sin (/ eps 2)))
8.0ms
(sin (/ (+ x (+ x eps)) 2))

series69.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(cbrt (sin (/ eps 2)))
19.0ms
(cbrt (sin (/ eps 2)))
20.0ms
(cbrt (sin (/ eps 2)))
8.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify70.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
05525701

prune285.0ms

Filtered
45 candidates to 52 candidates (-15.6%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New52052
Fresh099
Picked011
Done022
Total521264

Merged error: 0.2b

Counts
64 → 12

regimes395.0ms

Accuracy

97.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.0b

bsearch114.0ms

Steps
ItersRangePoint
10
1.2218550440895959e-08
426.91823734455465
2.3419086364105904e-05
10
-144.35439470067863
-2.5988527171649152e-14
-1.3830861607967381e-05

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
08281
18281

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s4367×body1280valid
531.0ms1894×body640valid
505.0ms659×body2560valid
162.0ms730×body320valid
37.0ms262×body160valid
7.0ms88×body80valid

Profiling

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