Details

Time bar (total: 19.0s)

sample102.0ms

Algorithm
intervals
Results
48.0ms83×body1280valid
16.0ms46×body640valid
11.0ms26×body2560valid
6.0ms26×body320valid
3.0ms61×body80valid
2.0ms14×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
3.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.0b
(sqrt (+ (* x x) 1.0))

rewrite37.0ms

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:
14.0ms
(+ x (sqrt (+ (* x x) 1.0)))
14.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series377.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(+ x (sqrt (+ (* x x) 1.0)))
250.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
53.0ms
(sqrt (+ (* x x) 1.0))

simplify2.2s

Counts
51 → 51
Iterations
IterNodes
done5015
33474
2937
1312
0134

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b
(* x (* x x))
0.1b
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))
0.6b
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
191×add-sqr-sqrt
190×*-un-lft-identity add-cube-cbrt
108×sqrt-prod
54×associate-/r*
42×add-cbrt-cube add-exp-log
37×div-inv
19×cbrt-undiv div-exp
17×pow1
9×prod-exp cbrt-unprod associate-/l*
6×associate-/r/
5×pow-prod-up
3×associate-*l* pow-prod-down add-log-exp
2×clear-num frac-2neg
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative unswap-sqr
Counts
3 → 310
Calls
3 calls:
13.0ms
(* x (* x x))
38.0ms
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))
16.0ms
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))

series255.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* x (* x x))
118.0ms
(/ 1/6 (/ (sqrt 1.0) (/ (* x (* x x)) 1.0)))
91.0ms
(/ (sqrt 1.0) (/ (* x (* x x)) 1.0))

simplify3.1s

Counts
319 → 319
Iterations
IterNodes
done5000
24791
11286
0447

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 0.125 x) (* x x))
0.4b
(/ 0.0625 (pow x 5))
15.3b
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.6b
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite295.0ms

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:
11.0ms
(/ (/ 0.125 x) (* x x))
6.0ms
(/ 0.0625 (pow x 5))
116.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
154.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (/ 0.125 x) (* x x))
77.0ms
(/ 0.0625 (pow x 5))
292.0ms
(log (- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
102.0ms
(- (/ (/ 0.125 x) (* x x)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify2.1s

Counts
147 → 147
Iterations
IterNodes
done5097
22797
1774
0318

prune798.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x)))
0.0b
(+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))
0.1b
(/ (/ 0.125 x) (* x x))
12.9b
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

rewrite684.0ms

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:
281.0ms
(+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x)))
143.0ms
(+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))
21.0ms
(/ (/ 0.125 x) (* x x))
234.0ms
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x)))
53.0ms
(+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))
43.0ms
(/ (/ 0.125 x) (* x x))
245.0ms
(log (+ x (+ (- x (/ (/ 0.125 x) (* x x))) (/ 0.5 x))))

simplify2.0s

Counts
112 → 112
Iterations
IterNodes
done5000
22027
1569
0227

prune412.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes47.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.6b

bsearch165.0ms

Steps
ItersRangePoint
11
3.4817375791661903e-26
573579.0075499975
0.8840407169458702
10
-84463.33967257517
-3.2432757514909933e-09
-0.9983730585657322

simplify14.0ms

Iterations
IterNodes
done40
140
035

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.8s2331×body1280valid
586.0ms1609×body640valid
377.0ms807×body2560valid
245.0ms784×body320valid
105.0ms2084×body80valid
47.0ms385×body160valid