Details

Time bar (total: 5.2s)

sample97.0ms

Algorithm
intervals
Results
45.0ms134×body1280valid
19.0ms22×body2560valid
18.0ms61×body640valid
5.0ms31×body320valid
1.0ms6×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: 38.6b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (cos (+ x eps)) (cos x))
2.8b
(cos (+ x eps))

rewrite12.0ms

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))
4.0ms
(cos (+ x eps))

series69.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune107.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New351146
Fresh000
Picked101
Done000
Total361147

Merged error: 14.5b

Counts
47 → 11

localize17.0ms

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))
2.2b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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))
9.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series290.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos x) (cos eps))
81.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms
(* (sin x) (sin eps))
124.0ms
(- (- (* (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

prune279.0ms

Filtered
105 candidates to 73 candidates (69.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New9312105
Fresh5510
Picked101
Done000
Total9917116

Merged error: 14.3b

Counts
116 → 17

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
0.2b
(* (sin eps) (sin x))
2.2b
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
9×prod-diff
5×pow1 add-exp-log add-cbrt-cube add-log-exp
3×expm1-log1p-u fma-neg associate-*r* associate-*l* log1p-expm1-u
2×fma-udef
1×sub-neg flip3-- diff-log pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 60
Calls
3 calls:
1.0ms
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
5.0ms
(* (sin eps) (sin x))
4.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

series259.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
47.0ms
(* (sin eps) (sin x))
130.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

simplify127.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
0254758
1853610
24301593
35001546

prune199.0ms

Filtered
69 candidates to 47 candidates (68.1%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh21416
Picked101
Done000
Total691786

Merged error: 14.3b

Counts
86 → 17

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin x) (sin eps) (cos x))
2.2b
(fma (cos eps) (cos x) (- (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 eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

series187.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(fma (sin x) (sin eps) (cos x))
134.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify118.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune71.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New21526
Fresh61016
Picked101
Done000
Total281543

Merged error: 14.3b

Counts
43 → 15

regimes158.0ms

Accuracy

85.9% (1.4b remaining)

Error of 15.7b against oracle of 14.3b and baseline of 24.5b

bsearch127.0ms

Steps
ItersRangePoint
8
1.6633021246357823e-21
3.8324351575410724e-17
3.754279903285256e-17
10
-0.2811373454017632
-5.543039065948379e-18
-1.7161493361231751e-06

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02913
12913

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s4386×body1280valid
557.0ms641×body2560valid
432.0ms1838×body640valid
113.0ms740×body320valid
31.0ms302×body160valid
6.0ms93×body80valid