Details

Time bar (total: 5.7s)

sample92.0ms

Algorithm
intervals
Results
50.0ms153×body1280valid
21.0ms25×body2560valid
9.0ms45×body640valid
3.0ms23×body320valid
1.0ms9×body160valid
0.0ms1×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (cos (+ x eps)) (cos x))
3.6b
(cos (+ x eps))

rewrite19.0ms

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:
8.0ms
(- (cos (+ x eps)) (cos x))
10.0ms
(cos (+ x eps))

series67.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify78.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune117.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.0b

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))
2.4b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

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))

series300.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos x) (cos eps))
84.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
50.0ms
(* (sin x) (sin eps))
127.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0381988
11342837
25002822

prune311.0ms

Filtered
105 candidates to 72 candidates (68.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.9b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
0.2b
(* (sin eps) (sin x))
2.4b
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

rewrite15.0ms

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))
8.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

series267.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
49.0ms
(* (sin eps) (sin x))
133.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

simplify125.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (119.0ms)

IterNodesCost
0254758
1853610
24301593
35001546

prune235.0ms

Filtered
69 candidates to 48 candidates (69.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps)))))
0.2b
(* (sin x) (sin eps))
2.4b
(- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×*-un-lft-identity
17×add-cube-cbrt
15×prod-diff
14×add-log-exp
8×pow1 add-exp-log add-cbrt-cube
7×diff-log
6×associate-*r* associate-*l*
5×associate--l+
4×expm1-log1p-u fma-neg log1p-expm1-u
3×sub-neg
2×log1p-udef flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- cos-mult sin-mult distribute-lft-out-- difference-of-squares
Counts
4 → 97
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps)))))
5.0ms
(* (sin x) (sin eps))
8.0ms
(- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))

series379.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos x) (cos eps))
123.0ms
(- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps)))))
44.0ms
(* (sin x) (sin eps))
173.0ms
(- (- (* (cos x) (cos eps)) (log1p (expm1 (* (sin x) (sin eps))))) (cos x))

simplify56.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04001255
11471937
25001922

prune304.0ms

Filtered
109 candidates to 75 candidates (68.8%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.9b

regimes197.0ms

Accuracy

84.2% (1.6b remaining)

Error of 16.4b against oracle of 14.9b and baseline of 24.8b

bsearch137.0ms

Steps
ItersRangePoint
10
5.168885000514563e-20
2.7581197155588776e-09
2.466932298927087e-09
8
-3.484100988050835e-05
-1.4570494276460042e-08
-4.620864681058517e-08

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04638
14838
24838

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4450×body1280valid
568.0ms672×body2560valid
400.0ms1823×body640valid
97.0ms694×body320valid
26.0ms275×body160valid
4.0ms86×body80valid