Details

Time bar (total: 5.9s)

sample87.0ms

Algorithm
intervals
Results
42.0ms133×body1280valid
19.0ms22×body2560valid
13.0ms67×body640valid
3.0ms19×body320valid
1.0ms13×body160valid
0.0ms2×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (cos (+ x eps)) (cos x))
4.0b
(cos (+ x eps))

rewrite13.0ms

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))

series68.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify71.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune120.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.4b

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

rewrite42.0ms

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)))
4.0ms
(* (sin x) (sin eps))
26.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series297.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos x) (cos eps))
82.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms
(* (sin x) (sin eps))
128.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0381988
11342837
25002822

prune317.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.3b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

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:
0.0ms
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
4.0ms
(* (sin eps) (sin x))
3.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

series263.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
48.0ms
(* (sin eps) (sin x))
131.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

simplify125.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0254758
1853610
24301593
35001546

prune238.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin eps) (sin x))
0.3b
(log1p (expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x))))))
0.5b
(expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))))
4.9b
(- (log1p (expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))))) (cos x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
7×add-log-exp
6×pow1 add-exp-log add-cbrt-cube
5×log1p-expm1-u
4×expm1-log1p-u
3×fma-neg associate-*r* associate-*l*
2×log1p-udef diff-log
1×sub-neg expm1-log1p flip3-- log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod sin-mult distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 72
Calls
4 calls:
4.0ms
(* (sin eps) (sin x))
0.0ms
(log1p (expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x))))))
0.0ms
(expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))))
4.0ms
(- (log1p (expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))))) (cos x))

series465.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin eps) (sin x))
119.0ms
(log1p (expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x))))))
115.0ms
(expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))))
181.0ms
(- (log1p (expm1 (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))))) (cos x))

simplify134.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
0300990
1978796
24756772
35001715

prune249.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.3b

regimes222.0ms

Accuracy

83.4% (1.6b remaining)

Error of 16.3b against oracle of 14.7b and baseline of 24.5b

bsearch101.0ms

Steps
ItersRangePoint
8
9.143643357499823e-08
5.968040026638966e-05
2.2379838828549683e-07
7
-9.091202463712598e-16
-2.574374193275519e-17
-8.911882491803393e-16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03624
13824
23824

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.7s4457×body1280valid
581.0ms686×body2560valid
403.0ms1837×body640valid
97.0ms656×body320valid
28.0ms292×body160valid
4.0ms72×body80valid