Details

Time bar (total: 4.4s)

analyze2.0ms

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

sample101.0ms

Algorithm
intervals
Results
55.0ms139×body1280valid
18.0ms21×body2560valid
13.0ms60×body640valid
4.0ms24×body320valid
1.0ms10×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: 39.3b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b
(- (cos (+ x eps)) (cos x))
2.6b
(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:
10.0ms
(- (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

prune61.0ms

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: 0.4b

Counts
30 → 7

localize13.0ms

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))

rewrite36.0ms

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:
13.0ms
(* -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))

series37.0ms

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)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify52.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04907890
14907890

prune144.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New66672
Fresh336
Picked011
Done000
Total691079

Merged error: 0.3b

Counts
79 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin (/ (+ x (+ x eps)) 2)))
2.4b
(sin (/ (+ x (+ x eps)) 2))
2.4b
(sin (/ (+ x (+ x eps)) 2))
2.4b
(sin (/ (+ x (+ x eps)) 2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 32
Calls
4 calls:
6.0ms
(cbrt (sin (/ (+ x (+ x eps)) 2)))
7.0ms
(sin (/ (+ x (+ x eps)) 2))
7.0ms
(sin (/ (+ x (+ x eps)) 2))
7.0ms
(sin (/ (+ x (+ x eps)) 2))

series40.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(cbrt (sin (/ (+ x (+ x eps)) 2)))
6.0ms
(sin (/ (+ x (+ x eps)) 2))
6.0ms
(sin (/ (+ x (+ x eps)) 2))
6.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify48.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
05090468

prune159.0ms

Filtered
38 candidates to 44 candidates (-15.8%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New43144
Fresh088
Picked011
Done011
Total431154

Merged error: 0.3b

Counts
54 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin (/ eps 2)) (cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3)))
0.5b
(pow (sin (/ (+ x (+ x eps)) 2)) 3)
2.4b
(sin (/ (+ x (+ x eps)) 2))
6.5b
(cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
24×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity associate-*r*
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×unswap-sqr
4×add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3 associate-*l*
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 85
Calls
4 calls:
13.0ms
(* (sin (/ eps 2)) (cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3)))
7.0ms
(pow (sin (/ (+ x (+ x eps)) 2)) 3)
9.0ms
(sin (/ (+ x (+ x eps)) 2))
7.0ms
(cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3))

series40.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (sin (/ eps 2)) (cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3)))
15.0ms
(pow (sin (/ (+ x (+ x eps)) 2)) 3)
6.0ms
(sin (/ (+ x (+ x eps)) 2))
6.0ms
(cbrt (pow (sin (/ (+ x (+ x eps)) 2)) 3))

simplify38.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
055111267

prune137.0ms

Filtered
56 candidates to 97 candidates (-73.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New94397
Fresh178
Picked011
Done112
Total9612108

Merged error: 0.3b

Counts
108 → 12

regimes202.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.1b

bsearch57.0ms

Steps
ItersRangePoint
5
6.615862107880164
26.418166781782844
6.740685226435875
9
-4.5309087082570456e-08
-1.6657409484079213e-16
-4.449359907394579e-08

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06938
16938

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s4470×body1280valid
624.0ms675×body2560valid
433.0ms1809×body640valid
119.0ms672×body320valid
33.0ms294×body160valid
5.0ms80×body80valid

Profiling

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