Details

Time bar (total: 7.5s)

sample48.0ms

Algorithm
intervals
Results
23.0ms103×body1280valid
6.0ms125×body80valid
3.0ms16×body640valid
1.0msbody320valid
0.0msbody160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
198
2108
done108

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize11.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (sqrt (+ (* x x) 1.0)) 1.0)
15.4b
(sqrt (+ (* x x) 1.0))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
*-un-lft-identity
sqrt-prod add-log-exp
pow1 add-cube-cbrt
add-cbrt-cube sqrt-div add-exp-log difference-of-squares
rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out--
Counts
2 → 30
Calls
2 calls:
116.0ms
(- (sqrt (+ (* x x) 1.0)) 1.0)
18.0ms
(sqrt (+ (* x x) 1.0))

series175.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(- (sqrt (+ (* x x) 1.0)) 1.0)
93.0ms
(sqrt (+ (* x x) 1.0))

simplify810.0ms

Counts
36 → 36
Iterations

Useful iterations: 2 (228.0ms)

IterNodesCost
085472
1199421
2852391
done5001391

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ (* x x) 1.0)) 1.0)
1.1b
(- (+ (* x x) 1.0) (* 1.0 1.0))
15.4b
(sqrt (+ (* x x) 1.0))
15.4b
(/ (- (+ (* x x) 1.0) (* 1.0 1.0)) (+ (sqrt (+ (* x x) 1.0)) 1.0))

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
16×times-frac
15×add-cube-cbrt
11×add-log-exp
add-cbrt-cube add-exp-log distribute-lft-out difference-of-squares
pow1
associate-/r* associate-/l*
flip3-+ sqrt-prod flip-+
sum-log flip3-- sqrt-div diff-log associate-/r/ flip-- associate-/l/
cbrt-undiv +-commutative rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 div-sub div-exp associate--l+ div-inv
Counts
4 → 83
Calls
4 calls:
68.0ms
(+ (sqrt (+ (* x x) 1.0)) 1.0)
95.0ms
(- (+ (* x x) 1.0) (* 1.0 1.0))
18.0ms
(sqrt (+ (* x x) 1.0))
258.0ms
(/ (- (+ (* x x) 1.0) (* 1.0 1.0)) (+ (sqrt (+ (* x x) 1.0)) 1.0))

series456.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (sqrt (+ (* x x) 1.0)) 1.0)
44.0ms
(- (+ (* x x) 1.0) (* 1.0 1.0))
89.0ms
(sqrt (+ (* x x) 1.0))
244.0ms
(/ (- (+ (* x x) 1.0) (* 1.0 1.0)) (+ (sqrt (+ (* x x) 1.0)) 1.0))

simplify2.4s

Counts
95 → 95
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01761920
14821826
229511698
done50021693

prune477.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes303.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.0b

bsearch263.0ms

Steps
ItersRangePoint
11
6.39684937763006e-15
11427567992489.943
1.1488253575026786
9
-170.1724623506855
-7.250512869097592e-05
-1.165295338898229

simplify26.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04380
15980
26480
36680
done6680

end0.0ms

sample1.7s

Algorithm
intervals
Results
863.0ms2845×body1280valid
217.0ms4088×body80valid
171.0ms595×body640valid
159.0ms305×body320valid
15.0ms167×body160valid