Details

Time bar (total: 5.9s)

sample91.0ms

Algorithm
intervals
Results
52.0ms147×body1280valid
15.0ms18×body2560valid
11.0ms55×body640valid
3.0ms23×body320valid
1.0ms9×body160valid
0.0ms4×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: 39.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.5b
(- (cos (+ x eps)) (cos x))
4.4b
(cos (+ x eps))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×cos-sum add-log-exp
3×fma-neg
2×pow1 add-exp-log +-commutative associate--l- expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 42
Calls
2 calls:
8.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series73.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify69.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0193395
1504295
22368285
35001230

prune101.0ms

Filtered
48 candidates to 32 candidates (66.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New351348
Fresh000
Picked101
Done000
Total361349

Merged error: 13.0b

Counts
49 → 13

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (cos eps) (cos x))
0.1b
(fma (sin eps) (sin x) (cos x))
3.9b
(- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
36×prod-diff
33×*-un-lft-identity
29×add-cube-cbrt
16×associate-*l*
15×associate-*r*
12×fma-neg
6×unswap-sqr
5×pow1 add-exp-log *-commutative add-cbrt-cube add-log-exp
3×expm1-log1p-u log1p-expm1-u
2×fma-udef distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- diff-log pow-prod-down prod-exp cos-mult flip-- cbrt-unprod associate--r+
Counts
3 → 98
Calls
3 calls:
4.0ms
(* (cos eps) (cos x))
1.0ms
(fma (sin eps) (sin x) (cos x))
11.0ms
(- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x)))

series252.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* (cos eps) (cos x))
66.0ms
(fma (sin eps) (sin x) (cos x))
143.0ms
(- (* (cos eps) (cos x)) (fma (sin eps) (sin x) (cos x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03101796
19111138
250011064

prune241.0ms

Filtered
107 candidates to 59 candidates (55.1%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New8819107
Fresh9312
Picked101
Done000
Total9822120

Merged error: 12.8b

Counts
120 → 22

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (sin eps) (sin x) (cos x))
3.9b
(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (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 eps) (sin x) (cos x))
1.0ms
(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))

series197.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(fma (sin eps) (sin x) (cos x))
135.0ms
(fma (cos x) (cos eps) (- (fma (sin eps) (sin x) (cos x))))

simplify118.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
094210
1254183
2901182
33875180
45001180

prune154.0ms

Filtered
26 candidates to 24 candidates (92.3%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New22426
Fresh31821
Picked101
Done000
Total262248

Merged error: 12.8b

Counts
48 → 22

localize14.0ms

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))
3.9b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
334×add-sqr-sqrt
321×prod-diff
224×*-un-lft-identity
177×associate-*l*
170×add-cube-cbrt
153×associate-*r*
146×associate--l+
71×unswap-sqr
51×*-commutative
29×distribute-lft-out--
23×fma-neg
21×difference-of-squares
11×add-log-exp
8×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u diff-log log1p-expm1-u
3×sub-neg cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod
1×associate--l- frac-sub sub-div
Counts
4 → 434
Calls
4 calls:
5.0ms
(* (cos x) (cos eps))
24.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms
(* (sin x) (sin eps))
37.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series319.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (cos x) (cos eps))
88.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
46.0ms
(* (sin x) (sin eps))
139.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify121.0ms

Algorithm
egg-herbie
Counts
446 → 446
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07918207
122855411
250015137

prune762.0ms

Filtered
446 candidates to 221 candidates (49.6%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New4397446
Fresh61521
Picked101
Done000
Total44622468

Merged error: 12.8b

Counts
468 → 22

regimes239.0ms

Accuracy

86.8% (1.4b remaining)

Error of 15.6b against oracle of 14.2b and baseline of 24.5b

bsearch132.0ms

Steps
ItersRangePoint
10
2.622148067335985e-09
2370348158.537013
3.237071340470319e-06
9
-450.37044368271705
-0.0037838497803388085
-0.0038159350625846396

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03840
13840

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.6s4494×body1280valid
521.0ms603×body2560valid
380.0ms1876×body640valid
92.0ms669×body320valid
32.0ms276×body160valid
4.0ms82×body80valid