Details

Time bar (total: 10.4s)

sample63.0ms

Algorithm
intervals
Results
30.0ms78×body1280valid
12.0ms53×body640valid
6.0ms24×body2560valid
4.0ms27×body320valid
2.0ms60×body80valid
1.0ms14×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1108
done108

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.7b

localize8.0ms

Local error

Found 3 expressions with local error:

1.1b
(+ (sqrt (fma x x 1.0)) x)
2.2b
(log (+ (sqrt (fma x x 1.0)) x))
15.0b
(sqrt (fma x x 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×fma-def sqrt-prod
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 52
Calls
3 calls:
9.0ms
(+ (sqrt (fma x x 1.0)) x)
7.0ms
(log (+ (sqrt (fma x x 1.0)) x))
2.0ms
(sqrt (fma x x 1.0))

series293.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(+ (sqrt (fma x x 1.0)) x)
180.0ms
(log (+ (sqrt (fma x x 1.0)) x))
50.0ms
(sqrt (fma x x 1.0))

simplify1.1s

Counts
61 → 61
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune164.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series142.0ms

Counts
1 → 3
Calls
1 calls:
142.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify609.0ms

Counts
13 → 13
Iterations

Useful iterations: done (608.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune40.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
13.4b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
19.2b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
480×*-un-lft-identity
367×times-frac
244×add-sqr-sqrt
218×add-cube-cbrt
200×prod-diff
84×distribute-lft-out
80×unpow-prod-down
68×cube-prod
40×fma-neg
28×sqr-pow
22×cube-mult unpow3
19×associate-/r*
15×add-exp-log
11×log-prod
10×difference-of-squares
9×add-log-exp
8×add-cbrt-cube div-inv
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 408
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
160.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
183.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 0.0625 (pow x 5))
41.0ms
(/ 0.125 (pow x 3))
179.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
58.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.3s

Counts
420 → 420
Iterations

Useful iterations: done (1.3s)

IterNodesCost
046617338
1101711893
228049355
done50008895

prune581.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

10.7b
(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))))
10.7b
(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))))
19.2b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
19.2b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite651.0ms

Algorithm
rewrite-expression-head
Rules
876×*-un-lft-identity
620×times-frac
404×add-sqr-sqrt
400×prod-diff
352×add-cube-cbrt
168×distribute-lft-out
112×unpow-prod-down cube-prod
80×fma-neg
40×sqr-pow
36×cube-mult unpow3
28×log-prod
22×sqrt-prod
20×difference-of-squares
14×add-log-exp
12×frac-sub div-inv distribute-lft-out--
10×log-div sqrt-div
8×pow1
6×add-exp-log log-pow
4×expm1-log1p-u flip3-- flip3-+ diff-log frac-add add-cbrt-cube flip-- flip-+ log1p-expm1-u
2×sub-neg sqrt-pow1 pow1/2 rem-log-exp sum-log associate--r+
Counts
4 → 598
Calls
4 calls:
117.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))))
118.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))))
180.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
185.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))))
92.0ms
(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))))
55.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
60.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.5s

Counts
610 → 610
Iterations

Useful iterations: done (1.4s)

IterNodesCost
037532452
182721942
2217316966
done500011586

prune896.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.4b

bsearch81.0ms

Steps
ItersRangePoint
10
0.0001820196720056695
1126179.5725289274
0.8946210124348296
9
-76786.820650899
-0.0002772006047103471
-0.9952950592534084

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03575
13975
done3975

end0.0ms

sample1.9s

Algorithm
intervals
Results
994.0ms2472×body1280valid
357.0ms1549×body640valid
202.0ms786×body2560valid
105.0ms786×body320valid
59.0ms2034×body80valid
28.0ms373×body160valid