Details

Time bar (total: 8.6s)

sample185.0ms

Algorithm
intervals
Results
100.0ms151×body1280valid
29.0ms19×body2560valid
24.0ms55×body640valid
6.0ms19×body320valid
2.0ms10×body160valid
0.0ms2×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0717
1717

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.2b

Counts
2 → 1

localize27.0ms

Local error

Found 2 expressions with local error:

1.4b
(- (cos (+ x eps)) (cos x))
4.5b
(cos (+ x eps))

rewrite20.0ms

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 → 24
Calls
2 calls:
11.0ms
(- (cos (+ x eps)) (cos x))
7.0ms
(cos (+ x eps))

series25.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(- (cos (+ x eps)) (cos x))
8.0ms
(cos (+ x eps))

simplify46.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
04999273
14999273

prune124.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New22830
Fresh000
Picked101
Done000
Total23831

Merged error: 0.3b

Counts
31 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b
(+ x (+ x eps))
0.2b
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
4.5b
(sin (/ (+ x (+ x eps)) 2))

rewrite69.0ms

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:
21.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
10.0ms
(+ x (+ x eps))
20.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
13.0ms
(sin (/ (+ x (+ x eps)) 2))

series71.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
7.0ms
(+ x (+ x eps))
26.0ms
(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
12.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify102.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
04907890
14907890

prune305.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New64872
Fresh527
Picked011
Done000
Total691180

Merged error: 0.3b

Counts
80 → 11

localize39.0ms

Local error

Found 4 expressions with local error:

4.5b
(sin (/ (+ x (+ x eps)) 2))
5.9b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.9b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
5.9b
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

rewrite64.0ms

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 sin-mult
Counts
4 → 37
Calls
4 calls:
13.0ms
(sin (/ (+ x (+ x eps)) 2))
16.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
18.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
16.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

series173.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sin (/ (+ x (+ x eps)) 2))
52.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
57.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
53.0ms
(cbrt (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))

simplify95.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
05057721

prune450.0ms

Filtered
45 candidates to 49 candidates (-8.9%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New49049
Fresh099
Picked011
Done011
Total491160

Merged error: 0.3b

Counts
60 → 11

localize34.0ms

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)))
4.5b
(sin (/ (+ x (+ x eps)) 2))

rewrite27.0ms

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)))
4.0ms
(cbrt (sin (/ eps 2)))
4.0ms
(cbrt (sin (/ eps 2)))
13.0ms
(sin (/ (+ x (+ x eps)) 2))

series112.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(cbrt (sin (/ eps 2)))
36.0ms
(cbrt (sin (/ eps 2)))
33.0ms
(cbrt (sin (/ eps 2)))
11.0ms
(sin (/ (+ x (+ x eps)) 2))

simplify58.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
05501442

prune318.0ms

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

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New52052
Fresh088
Picked011
Done022
Total521163

Merged error: 0.3b

Counts
63 → 11

regimes365.0ms

Accuracy

95.5% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 15.6b

bsearch144.0ms

Steps
ItersRangePoint
9
50227932113049.875
1.601522318771203e+21
51084485291333.914
8
-0.03637538406068891
-1.1294785154268786e-05
-5.4479956868733016e-05

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08151
18151

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.2s4568×body1280valid
916.0ms570×body2560valid
789.0ms1821×body640valid
209.0ms661×body320valid
60.0ms292×body160valid
9.0ms88×body80valid

Profiling

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