Details

Time bar (total: 5.4s)

sample94.0ms

Algorithm
intervals
Results
51.0ms144×body1280valid
17.0ms19×body2560valid
11.0ms51×body640valid
4.0ms24×body320valid
2.0ms16×body160valid
0.0ms2×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.1b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (cos (+ x eps)) (cos x))
5.1b
(cos (+ x eps))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u cos-sum add-cbrt-cube log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
7.0ms
(- (cos (+ x eps)) (cos x))
9.0ms
(cos (+ x eps))

series64.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune117.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New311546
Fresh000
Picked101
Done000
Total321547

Merged error: 14.3b

Counts
47 → 15

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(fma (sin x) (sin eps) (cos x))
3.0b
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube add-log-exp
3×expm1-log1p-u associate-*r* associate-*l* prod-diff log1p-expm1-u
2×fma-udef
1×sub-neg flip3-- fma-neg diff-log pow-prod-down prod-exp cos-mult *-commutative flip-- cbrt-unprod associate--r+ unswap-sqr
Counts
3 → 50
Calls
3 calls:
4.0ms
(* (cos x) (cos eps))
1.0ms
(fma (sin x) (sin eps) (cos x))
5.0ms
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series221.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(* (cos x) (cos eps))
54.0ms
(fma (sin x) (sin eps) (cos x))
128.0ms
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify119.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0235486
1832409
24494406
35001404

prune206.0ms

Filtered
59 candidates to 43 candidates (72.9%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New481159
Fresh7714
Picked101
Done000
Total561874

Merged error: 14.1b

Counts
74 → 18

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
3.0b
(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma (sin x) (sin eps) (cos x))
1.0ms
(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

series185.0ms

Counts
2 → 6
Calls
2 calls:
51.0ms
(fma (sin x) (sin eps) (cos x))
134.0ms
(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

simplify124.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
093210
1259183
2932182
34040180
45001180

prune136.0ms

Filtered
26 candidates to 22 candidates (84.6%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New22426
Fresh11617
Picked101
Done000
Total242044

Merged error: 14.1b

Counts
44 → 20

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
3.1b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×prod-diff add-log-exp
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u fma-neg diff-log log1p-expm1-u
3×sub-neg associate--l+ cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 93
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms
(* (sin x) (sin eps))
10.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series304.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos x) (cos eps))
85.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
50.0ms
(* (sin x) (sin eps))
129.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify50.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0381988
11342837
25002822

prune240.0ms

Filtered
105 candidates to 74 candidates (70.5%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1014105
Fresh51419
Picked101
Done000
Total10718125

Merged error: 14.1b

Counts
125 → 18

regimes193.0ms

Accuracy

79.4% (2.1b remaining)

Error of 16.5b against oracle of 14.5b and baseline of 24.5b

bsearch117.0ms

Steps
ItersRangePoint
8
6.3780966821006384e-18
1.0989223242724141e-13
1.0832738602013395e-13
7
-9.683097938158369e-25
-1.113797997846539e-26
-9.474781037984798e-25

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04348
14548
24548

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s4498×body1280valid
538.0ms613×body2560valid
438.0ms1825×body640valid
111.0ms679×body320valid
36.0ms295×body160valid
5.0ms90×body80valid

Profiling

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