Details

Time bar (total: 5.7s)

sample98.0ms

Algorithm
intervals
Results
49.0ms141×body1280valid
23.0ms26×body2560valid
12.0ms54×body640valid
4.0ms27×body320valid
1.0ms7×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: 40.8b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (cos (+ x eps)) (cos x))
4.6b
(cos (+ x eps))

rewrite18.0ms

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))
9.0ms
(cos (+ x eps))

series63.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify74.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0192385
1523285
22519275
35001220

prune125.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New311546
Fresh000
Picked101
Done000
Total321547

Merged error: 14.7b

Counts
47 → 15

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))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
7.0ms
(* (sin x) (sin eps))
10.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series295.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cos x) (cos eps))
83.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
47.0ms
(* (sin x) (sin eps))
125.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify51.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0381988
11342837
25002822

prune314.0ms

Filtered
105 candidates to 73 candidates (69.5%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New9015105
Fresh11314
Picked101
Done000
Total10218120

Merged error: 14.5b

Counts
120 → 18

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

rewrite12.0ms

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))

series261.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(fma (cos x) (cos eps) (- (* (sin eps) (sin x))))
47.0ms
(* (sin eps) (sin x))
131.0ms
(- (fma (cos x) (cos eps) (- (* (sin eps) (sin x)))) (cos x))

simplify122.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (116.0ms)

IterNodesCost
0254758
1853610
24301593
35001546

prune224.0ms

Filtered
69 candidates to 49 candidates (71.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New67269
Fresh11617
Picked101
Done000
Total691887

Merged error: 14.5b

Counts
87 → 18

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
0.1b
(fma (sin x) (sin eps) (cos x))
2.3b
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
2.4b
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×pow1 add-log-exp
4×add-exp-log expm1-log1p-u log-prod log-pow add-cbrt-cube fma-udef log1p-expm1-u
2×exp-sum
1×rem-log-exp rem-exp-log
Counts
4 → 52
Calls
4 calls:
2.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
1.0ms
(fma (sin x) (sin eps) (cos x))
1.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
2.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x)))))
54.0ms
(fma (sin x) (sin eps) (cos x))
132.0ms
(fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))
137.0ms
(log (exp (fma (cos eps) (cos x) (- (fma (sin x) (sin eps) (cos x))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
0137627
1357554
21340554
35002551

prune206.0ms

Filtered
64 candidates to 52 candidates (81.3%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New60464
Fresh21517
Picked101
Done000
Total631982

Merged error: 14.5b

Counts
82 → 19

regimes204.0ms

Accuracy

82.7% (1.7b remaining)

Error of 15.6b against oracle of 13.9b and baseline of 23.7b

bsearch135.0ms

Steps
ItersRangePoint
7
6.574427863770428e-26
6.36136280187789e-24
6.275401615665634e-24
10
-0.1948919490089863
-1.6822503097093667e-15
-3.0852323357979476e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04548
14748
24748

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.6s4435×body1280valid
531.0ms603×body2560valid
439.0ms1877×body640valid
109.0ms692×body320valid
33.0ms307×body160valid
5.0ms86×body80valid