Details

Time bar (total: 4.3s)

analyze1.0ms

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

sample95.0ms

Algorithm
intervals
Results
46.0ms104×body1280valid
18.0ms68×body640valid
15.0ms16×body2560valid
4.0ms22×body320valid
2.0ms34×body80valid
1.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.9b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.8b
(- (sin (+ x eps)) (sin x))
2.4b
(sin (+ x eps))

rewrite11.0ms

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

series13.0ms

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

simplify42.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (39.0ms)

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 3 expressions with local error:

0.0b
(+ x (+ x eps))
0.2b
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
2.5b
(cos (/ (+ x (+ x eps)) 2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l* sum-log distribute-lft-out
1×+-commutative associate-+r+ flip3-+ pow-prod-down prod-exp *-commutative sin-cos-mult cbrt-unprod flip-+ unswap-sqr
Counts
3 → 41
Calls
3 calls:
5.0ms
(+ x (+ x eps))
5.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series20.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (+ x eps))
10.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify55.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
05169541

prune99.0ms

Filtered
38 candidates to 50 candidates (-31.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New46450
Fresh022
Picked011
Done000
Total46753

Merged error: 0.3b

Counts
53 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ x (+ x eps)) 2)))
0.2b
(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b
(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.5b
(cos (/ (+ x (+ x eps)) 2))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×distribute-rgt-in distribute-lft-in associate-*l*
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 61
Calls
4 calls:
7.0ms
(exp (cos (/ (+ x (+ x eps)) 2)))
12.0ms
(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
7.0ms
(log (exp (cos (/ (+ x (+ x eps)) 2))))
7.0ms
(cos (/ (+ x (+ x eps)) 2))

series30.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(exp (cos (/ (+ x (+ x eps)) 2)))
10.0ms
(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
5.0ms
(log (exp (cos (/ (+ x (+ x eps)) 2))))
5.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify46.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05064940

prune138.0ms

Filtered
53 candidates to 73 candidates (-37.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New73073
Fresh055
Picked011
Done011
Total73780

Merged error: 0.3b

Counts
80 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b
(* (cos x) (sin eps))
0.2b
(* (sin x) (cos eps))
2.5b
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
2×diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ sin-cos-mult flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
6.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
4.0ms
(* (cos x) (sin eps))
4.0ms
(* (sin x) (cos eps))
10.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series54.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
8.0ms
(* (cos x) (sin eps))
9.0ms
(* (sin x) (cos eps))
20.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify38.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
05096836

prune81.0ms

Filtered
54 candidates to 75 candidates (-38.9%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New631275
Fresh224
Picked101
Done112
Total671582

Merged error: 0.1b

Counts
82 → 15

regimes178.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01513
11513

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s3268×body1280valid
685.0ms1814×body640valid
613.0ms634×body2560valid
152.0ms805×body320valid
65.0ms1111×body80valid
46.0ms368×body160valid

Profiling

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