Details

Time bar (total: 4.3s)

analyze2.0ms

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

sample92.0ms

Algorithm
intervals
Results
42.0ms98×body1280valid
16.0ms60×body640valid
15.0ms16×body2560valid
7.0ms35×body320valid
2.0ms34×body80valid
2.0ms13×body160valid

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: 37.9b

Counts
2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (sin (+ x eps)) (sin x))
3.6b
(sin (+ x eps))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt sin-sum add-cbrt-cube
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 23
Calls
2 calls:
7.0ms
(- (sin (+ x eps)) (sin x))
5.0ms
(sin (+ x eps))

series13.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(- (sin (+ x eps)) (sin x))
5.0ms
(sin (+ x eps))

simplify43.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
05348268

prune45.0ms

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

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New26329
Fresh000
Picked101
Done000
Total27330

Merged error: 0.3b

Counts
30 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
0.0b
(+ x (+ x eps))
0.3b
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.6b
(cos (/ (+ x (+ x eps)) 2))

rewrite27.0ms

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-cos-mult
1×+-commutative associate-+r+ flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 60
Calls
4 calls:
7.0ms
(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
6.0ms
(+ x (+ x eps))
5.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
8.0ms
(cos (/ (+ x (+ x eps)) 2))

series33.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
4.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify48.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
05222886

prune138.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New66672
Fresh022
Picked101
Done000
Total67875

Merged error: 0.2b

Counts
75 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2 (sin (/ eps 2)))
0.0b
(+ x (+ x eps))
0.3b
(* (* 2 (sin (/ eps 2))) (cos (/ (+ x (+ x eps)) 2)))
3.6b
(cos (/ (+ x (+ x eps)) 2))

rewrite26.0ms

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-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sum-log distribute-lft-out
2×*-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 58
Calls
4 calls:
5.0ms
(* 2 (sin (/ eps 2)))
6.0ms
(+ x (+ x eps))
7.0ms
(* (* 2 (sin (/ eps 2))) (cos (/ (+ x (+ x eps)) 2)))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series26.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* 2 (sin (/ eps 2)))
4.0ms
(+ x (+ x eps))
12.0ms
(* (* 2 (sin (/ eps 2))) (cos (/ (+ x (+ x eps)) 2)))
5.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify42.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05041700

prune123.0ms

Filtered
48 candidates to 70 candidates (-45.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New69170
Fresh077
Picked011
Done000
Total69978

Merged error: 0.2b

Counts
78 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2)))
0.4b
(* (sin (/ eps 2)) (sqrt 2))
0.5b
(* (sqrt 2) (* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2))))
3.6b
(cos (/ (+ x (+ x eps)) 2))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×associate-*l*
10×add-cube-cbrt *-un-lft-identity pow-prod-down prod-exp cbrt-unprod
8×associate-*r*
7×sqrt-prod
4×add-log-exp
3×*-commutative
2×unswap-sqr
Counts
4 → 71
Calls
4 calls:
7.0ms
(* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2)))
6.0ms
(* (sin (/ eps 2)) (sqrt 2))
10.0ms
(* (sqrt 2) (* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2))))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series51.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2)))
5.0ms
(* (sin (/ eps 2)) (sqrt 2))
21.0ms
(* (sqrt 2) (* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2))))
5.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify55.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049271100
149271100

prune142.0ms

Filtered
60 candidates to 83 candidates (-38.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh167
Picked011
Done011
Total83992

Merged error: 0.2b

Counts
92 → 9

regimes177.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.3b

bsearch83.0ms

Steps
ItersRangePoint
9
5.381829064577836e-17
2.062238816387472e-10
2.0374182041794392e-10
10
-7.036382079572536e-05
-2.176989237525133e-17
-1.4223670267152646e-08

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04538
14538

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s3316×body1280valid
596.0ms629×body2560valid
511.0ms1844×body640valid
149.0ms770×body320valid
64.0ms1091×body80valid
44.0ms350×body160valid

Profiling

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