Details

Time bar (total: 15.4s)

sample33.0ms

Algorithm
intervals
Results
15.0ms255×body80valid
0.0msbody160valid

simplify6.0s

Counts
1 → 1
Iterations
IterNodes
done5001
64908
5557
4115
345
221
114
08

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)
15.4b
(sqrt (+ 1.0 (pow x 2.0)))
15.4b
(/ (pow x 2.0) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
28×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt
15×unpow-prod-down
10×distribute-lft-out
add-exp-log
associate-/l*
add-cbrt-cube add-log-exp sqr-pow
pow1 associate-/r* sqrt-prod
flip3-+ div-exp flip-+
sqrt-div associate-/r/
pow-to-exp cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 pow-exp div-inv
Counts
3 → 83
Calls
3 calls:
100.0ms
(+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)
24.0ms
(sqrt (+ 1.0 (pow x 2.0)))
132.0ms
(/ (pow x 2.0) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0))

series557.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)
91.0ms
(sqrt (+ 1.0 (pow x 2.0)))
389.0ms
(/ (pow x 2.0) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0))

simplify2.3s

Counts
92 → 92
Iterations
IterNodes
done5000
21860
1436
0195

prune609.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)
0.0b
(* (pow x (/ 2.0 2)) (/ (pow x (/ 2.0 2)) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)))
0.0b
(/ (pow x (/ 2.0 2)) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0))
15.4b
(sqrt (+ 1.0 (pow x 2.0)))

rewrite554.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
68×add-sqr-sqrt
65×times-frac
41×add-cube-cbrt
37×unpow-prod-down
35×add-exp-log
34×associate-*r*
17×distribute-lft-out sqr-pow
12×div-exp prod-exp unswap-sqr
11×add-cbrt-cube
pow-to-exp pow-exp
associate-*l* associate-/l*
add-log-exp
pow1
associate-/r* flip3-+ associate-/r/ sqrt-prod flip-+
cbrt-undiv sqrt-div cbrt-unprod div-inv
+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 associate-*r/ *-commutative
Counts
4 → 159
Calls
4 calls:
96.0ms
(+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)
289.0ms
(* (pow x (/ 2.0 2)) (/ (pow x (/ 2.0 2)) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)))
132.0ms
(/ (pow x (/ 2.0 2)) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0))
24.0ms
(sqrt (+ 1.0 (pow x 2.0)))

series955.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)
392.0ms
(* (pow x (/ 2.0 2)) (/ (pow x (/ 2.0 2)) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0)))
386.0ms
(/ (pow x (/ 2.0 2)) (+ (sqrt (+ 1.0 (pow x 2.0))) 1.0))
92.0ms
(sqrt (+ 1.0 (pow x 2.0)))

simplify1.7s

Counts
171 → 171
Iterations
IterNodes
done5000
1746
0287

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes82.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.8b

bsearch214.0ms

Steps
ItersRangePoint
11
6.39684937763006e-15
11427567992489.943
101112.92887628924
9
-3.4298688938742986e+159
-8.648518336606113e+153
-1.3418761783167835e+154

simplify13.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample906.0ms

Algorithm
intervals
Results
644.0ms7995×body80valid
1.0msbody160valid