Details

Time bar (total: 16.6s)

sample160.0ms

Algorithm
intervals
Results
53.0ms59×body2560valid
53.0ms92×body1280valid
25.0ms59×body640valid
7.0ms22×body320valid
2.0ms12×body160valid
1.0ms12×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
188
2128
done128

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(sqrt (- 1.0 (* (cos x) (cos x))))
0.2b
(* (cos x) (cos x))
1.7b
(- 1.0 (* (cos x) (cos x)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×pow1
*-un-lft-identity add-cube-cbrt
add-cbrt-cube add-exp-log add-log-exp
sqrt-prod
swap-sqr associate-*r* associate-*l*
sqr-cos flip3-- sqrt-div flip-- difference-of-squares
pow2 rem-sqrt-square sub-neg sqrt-pow1 pow-plus pow1/2 diff-log pow-prod-down prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod associate--r+ unswap-sqr
Counts
3 → 57
Calls
3 calls:
15.0ms
(sqrt (- 1.0 (* (cos x) (cos x))))
64.0ms
(* (cos x) (cos x))
11.0ms
(- 1.0 (* (cos x) (cos x)))

series210.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(sqrt (- 1.0 (* (cos x) (cos x))))
33.0ms
(* (cos x) (cos x))
63.0ms
(- 1.0 (* (cos x) (cos x)))

simplify2.8s

Counts
66 → 66
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0106671
1260543
21577483
done5002480

prune367.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b
(sqrt (- (- 1.0 1/2) (* 1/2 (cos (* 2 x)))))
1.6b
(- (- 1.0 1/2) (* 1/2 (cos (* 2 x))))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
add-log-exp
add-sqr-sqrt
pow1 *-un-lft-identity diff-log add-cube-cbrt sqrt-prod
sub-neg flip3-- add-cbrt-cube sqrt-div associate--l+ add-exp-log flip--
associate--l- rem-sqrt-square sqrt-pow1 pow1/2
Counts
2 → 31
Calls
2 calls:
82.0ms
(sqrt (- (- 1.0 1/2) (* 1/2 (cos (* 2 x)))))
134.0ms
(- (- 1.0 1/2) (* 1/2 (cos (* 2 x))))

series208.0ms

Counts
2 → 6
Calls
2 calls:
128.0ms
(sqrt (- (- 1.0 1/2) (* 1/2 (cos (* 2 x)))))
80.0ms
(- (- 1.0 1/2) (* 1/2 (cos (* 2 x))))

simplify2.7s

Counts
37 → 37
Iterations

Useful iterations: 2 (152.0ms)

IterNodesCost
077591
1170538
2578509
32807509
done5000509

prune167.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

regimes291.0ms

Accuracy

98.9% (0.2b remaining)

Error of 7.6b against oracle of 7.3b and baseline of 29.7b

bsearch542.0ms

Steps
ItersRangePoint
11
6.39684937763006e-15
11427567992489.943
0.019180148720016048
10
-1.6163600377583066e-291
6.121941968471993e-308
6.00683692990105e-310
9
-170.1724623506855
-7.250512869097592e-05
-0.01582460057993371

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
048123
159123
done59123

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.7s1864×body640valid
2.1s2756×body1280valid
2.0s1582×body2560valid
363.0ms934×body320valid
165.0ms478×body160valid
43.0ms386×body80valid