Details

Time bar (total: 16.6s)

sample88.0ms

Algorithm
intervals
Results
38.0ms69×body1280valid
21.0ms69×body640valid
10.0ms24×body2560valid
4.0ms21×body320valid
3.0ms61×body80valid
1.0ms12×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ x (sqrt (+ (* x x) 1.0)))
2.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.0b
(sqrt (+ (* x x) 1.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 42
Calls
3 calls:
24.0ms
(+ x (sqrt (+ (* x x) 1.0)))
40.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
12.0ms
(sqrt (+ (* x x) 1.0))

series381.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(+ x (sqrt (+ (* x x) 1.0)))
250.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
55.0ms
(sqrt (+ (* x x) 1.0))

simplify2.2s

Counts
51 → 51
Iterations
IterNodes
done5015
33474
2937
1312
0134

prune316.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ x (sqrt 1.0)) (- (log (sqrt 1.0)) (/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))))
0.1b
(* x (* x x))
0.3b
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))
0.4b
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))

rewrite466.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
200×*-un-lft-identity
194×add-sqr-sqrt
193×add-cube-cbrt
111×sqrt-prod
54×associate-/r*
43×add-cbrt-cube add-exp-log
37×div-inv
19×pow1 cbrt-undiv div-exp
9×prod-exp cbrt-unprod associate-/l*
8×associate-+r+ add-log-exp
6×log-prod associate--l+ associate-/r/
5×pow-prod-up
3×associate-*l* pow-prod-down distribute-lft-out
2×clear-num sum-log frac-2neg frac-add distribute-lft-out--
1×pow2 +-commutative associate-+r- sub-neg flip3-+ pow-plus flip3-- diff-log cube-unmult associate-*r* pow-sqr log-pow *-commutative flip-+ flip-- unswap-sqr
Counts
4 → 336
Calls
4 calls:
343.0ms
(+ (/ x (sqrt 1.0)) (- (log (sqrt 1.0)) (/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))))
20.0ms
(* x (* x x))
28.0ms
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))
43.0ms
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(+ (/ x (sqrt 1.0)) (- (log (sqrt 1.0)) (/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))))
52.0ms
(* x (* x x))
96.0ms
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))
121.0ms
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))

simplify1.5s

Counts
348 → 348
Iterations
IterNodes
done5000
11458
0500

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.1b
(/ (/ 0.125 x) (* x x))
11.4b
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
21.5b
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
58×times-frac
49×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
22×add-exp-log
18×add-cbrt-cube
16×associate-/l*
12×unpow-prod-down
9×div-exp add-log-exp
8×log-prod associate-/r*
7×cbrt-undiv
6×frac-sub difference-of-squares
5×pow1 log-div
4×div-inv distribute-lft-out-- sqr-pow
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add prod-exp cbrt-unprod flip-+ flip-- distribute-lft-out
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+ associate-/l/
Counts
4 → 135
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
11.0ms
(/ (/ 0.125 x) (* x x))
122.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
139.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 0.0625 (pow x 5))
55.0ms
(/ (/ 0.125 x) (* x x))
251.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
83.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.8s

Counts
147 → 147
Iterations
IterNodes
done5000
22854
1785
0318

prune782.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))
0.0b
(+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x)))
0.1b
(/ (/ 0.125 x) (* x x))
9.0b
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

rewrite668.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×times-frac
19×add-sqr-sqrt add-cube-cbrt
18×add-log-exp
17×add-exp-log
16×add-cbrt-cube
13×associate-/l*
12×distribute-lft-out
7×sum-log
6×cbrt-undiv log-prod div-exp
5×pow1
3×flip3-+ flip-+ div-inv distribute-lft-out--
2×+-commutative log-div associate-+l+ diff-log frac-add prod-exp associate-+l- cbrt-unprod
1×associate-+r+ clear-num associate-+r- associate-/r* sub-neg frac-2neg flip3-- rem-log-exp log-pow flip-- associate-/l/
Counts
4 → 100
Calls
4 calls:
137.0ms
(+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))
267.0ms
(+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x)))
15.0ms
(/ (/ 0.125 x) (* x x))
244.0ms
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))
56.0ms
(+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x)))
47.0ms
(/ (/ 0.125 x) (* x x))
232.0ms
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

simplify1.6s

Counts
112 → 112
Iterations
IterNodes
done5010
22034
1569
0227

prune392.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.2b

bsearch122.0ms

Steps
ItersRangePoint
8
0.02586244036059231
44.35744796693956
0.8950674725377756
10
-733100.9210806559
-4.034181863829644e-08
-1.0212215988225002

simplify7.0ms

Iterations
IterNodes
done40
140
035

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s2298×body1280valid
462.0ms1550×body640valid
306.0ms819×body2560valid
167.0ms806×body320valid
147.0ms2136×body80valid
83.0ms391×body160valid