Details

Time bar (total: 4.4s)

sample100.0ms

Algorithm
intervals
Results
55.0ms113×body1280valid
13.0ms49×body640valid
11.0ms12×body2560valid
5.0ms30×body320valid
2.0ms43×body80valid
1.0ms9×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0107
1107

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 38.1b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.2b
(- (sin (+ x eps)) (sin x))
4.1b
(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 → 24
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))

simplify52.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
05212271

prune50.0ms

Filtered
23 candidates to 30 candidates (-30.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New27330
Fresh000
Picked101
Done000
Total28331

Merged error: 0.3b

Counts
31 → 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)))
4.0b
(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))

series21.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (+ x eps))
11.0ms
(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
6.0ms
(cos (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
05118541

prune123.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New44650
Fresh022
Picked101
Done000
Total45853

Merged error: 0.2b

Counts
53 → 8

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (sin (/ eps 2)) (cos (+ x (* eps 1/2))))
4.0b
(cos (+ x (* eps 1/2)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×associate-*r* associate-*l*
2×add-log-exp
1×cos-sum pow-prod-down prod-exp *-commutative sin-cos-mult cbrt-unprod unswap-sqr
Counts
2 → 27
Calls
2 calls:
6.0ms
(* (sin (/ eps 2)) (cos (+ x (* eps 1/2))))
4.0ms
(cos (+ x (* eps 1/2)))

series18.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(* (sin (/ eps 2)) (cos (+ x (* eps 1/2))))
7.0ms
(cos (+ x (* eps 1/2)))

simplify45.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
05247380

prune102.0ms

Filtered
27 candidates to 33 candidates (-22.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New27633
Fresh527
Picked101
Done000
Total33841

Merged error: 0.1b

Counts
41 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
6×add-log-exp
5×cos-mult sin-mult
4×associate-*r/
3×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-rgt-in flip3-- distribute-lft-in frac-sub flip-- sub-div
1×diff-log
Counts
4 → 78
Calls
4 calls:
5.0ms
(* (cos x) (cos (* eps 1/2)))
6.0ms
(- (* (cos x) (cos (* eps 1/2))) (* (sin x) (sin (* eps 1/2))))
5.0ms
(* (sin x) (sin (* eps 1/2)))
12.0ms
(* (sin (/ eps 2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin x) (sin (* eps 1/2)))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos x) (cos (* eps 1/2)))
18.0ms
(- (* (cos x) (cos (* eps 1/2))) (* (sin x) (sin (* eps 1/2))))
10.0ms
(* (sin x) (sin (* eps 1/2)))
25.0ms
(* (sin (/ eps 2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin x) (sin (* eps 1/2)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049931351
149931351

prune191.0ms

Filtered
63 candidates to 90 candidates (-42.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New83790
Fresh527
Picked101
Done000
Total89998

Merged error: 0.0b

Counts
98 → 9

regimes162.0ms

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
02425
12425

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.6s3354×body1280valid
622.0ms613×body2560valid
497.0ms1834×body640valid
160.0ms758×body320valid
65.0ms1097×body80valid
44.0ms344×body160valid

Profiling

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