Details

Time bar (total: 5.3s)

sample95.0ms

Algorithm
intervals
Results
49.0ms139×body1280valid
17.0ms20×body2560valid
16.0ms72×body640valid
3.0ms18×body320valid
1.0ms6×body160valid
0.0ms1×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: 40.2b

Counts
2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (cos (+ x eps)) (cos x))
3.8b
(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))

series65.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify73.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune112.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New341246
Fresh000
Picked101
Done000
Total351247

Merged error: 15.1b

Counts
47 → 12

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

rewrite29.0ms

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))
8.0ms
(- (* (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))

series297.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos x) (cos eps))
80.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms
(* (sin x) (sin eps))
127.0ms
(- (- (* (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

prune297.0ms

Filtered
105 candidates to 73 candidates (69.5%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New9015105
Fresh6511
Picked101
Done000
Total9720117

Merged error: 15.0b

Counts
117 → 20

localize15.0ms

Local error

Found 2 expressions with local error:

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

series191.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(fma (sin x) (sin eps) (cos x))
137.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))

simplify117.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
087209
1240182
2795182
33587180
45001180

prune127.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New22426
Fresh41519
Picked101
Done000
Total271946

Merged error: 14.9b

Counts
46 → 19

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

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:
5.0ms
(* (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:
39.0ms
(* (cos x) (cos eps))
53.0ms
(fma (sin x) (sin eps) (cos x))
128.0ms
(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify116.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0235486
1832409
24494407
35001406

prune130.0ms

Filtered
59 candidates to 43 candidates (72.9%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New57259
Fresh11718
Picked011
Done000
Total582078

Merged error: 14.8b

Counts
78 → 20

regimes197.0ms

Accuracy

85.2% (1.5b remaining)

Error of 16.2b against oracle of 14.8b and baseline of 24.6b

bsearch125.0ms

Steps
ItersRangePoint
10
6.5964766626641694e-24
4.551365472929582e-09
4.282729377320144e-09
9
-8.961399793617711e-18
-7.949661431150896e-23
-8.847627512437046e-18

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02913
12913

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s4479×body1280valid
548.0ms637×body2560valid
424.0ms1851×body640valid
105.0ms681×body320valid
29.0ms277×body160valid
4.0ms75×body80valid