Details

Time bar (total: 8.4s)

sample150.0ms

Algorithm
intervals
Results
51.0ms115×body1280valid
18.0ms36×body10240exit
17.0ms53×body640valid
10.0ms23×body1280nan
8.0ms151×body80valid
7.0ms210×body80nan
7.0ms20×body640nan
5.0ms22×body320valid
2.0ms14×body320nan
1.0ms13×body160nan
1.0ms9×body160valid

simplify34.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016
done50016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.5b
(pow x (/ 1.0 n))
1.0b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b
(pow (+ x 1.0) (/ 1.0 n))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×unpow-prod-down
63×add-sqr-sqrt
56×prod-diff
51×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
5×pow1 add-exp-log add-log-exp
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 149
Calls
3 calls:
4.0ms
(pow x (/ 1.0 n))
90.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms
(pow (+ x 1.0) (/ 1.0 n))

series463.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(pow x (/ 1.0 n))
263.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
140.0ms
(pow (+ x 1.0) (/ 1.0 n))

simplify62.0ms

Counts
158 → 158
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06542164
121641642
250021637
done50021637

prune313.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 22.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (pow x (/ 1.0 n))))
0.5b
(pow x (/ 1.0 n))
1.2b
(pow (+ x 1.0) (/ 1.0 n))
35.9b
(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
41×add-sqr-sqrt
36×add-cube-cbrt
26×pow-unpow
24×unpow-prod-down prod-diff
18×times-frac
8×fma-neg
7×sqr-pow
6×pow1 add-exp-log add-log-exp
5×distribute-lft-out
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×difference-of-squares
2×pow-to-exp pow-pow pow-exp div-inv expm1-udef
1×sub-neg expm1-log1p flip3-- diff-log flip-- distribute-lft-out-- associate--r-
Counts
4 → 121
Calls
4 calls:
0.0ms
(expm1 (log1p (pow x (/ 1.0 n))))
4.0ms
(pow x (/ 1.0 n))
10.0ms
(pow (+ x 1.0) (/ 1.0 n))
87.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

series589.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(expm1 (log1p (pow x (/ 1.0 n))))
60.0ms
(pow x (/ 1.0 n))
138.0ms
(pow (+ x 1.0) (/ 1.0 n))
303.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (expm1 (log1p (pow x (/ 1.0 n)))))

simplify54.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05561604
119711009
25003997
done5003997

prune335.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 22.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* x n))
2.0b
(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
10.2b
(* (pow x 2) n)
10.9b
(* x (pow n 2))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
24×add-sqr-sqrt
13×add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
9×prod-exp
8×unpow-prod-down unswap-sqr
7×pow1
4×expm1-log1p-u div-exp log1p-expm1-u unpow2 add-log-exp sqr-pow
3×times-frac cbrt-unprod associate-/l*
2×cbrt-undiv pow-to-exp rec-exp pow-flip 1-exp pow-exp *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* fma-udef div-inv inv-pow
Counts
4 → 98
Calls
4 calls:
11.0ms
(/ 1 (* x n))
0.0ms
(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
11.0ms
(* (pow x 2) n)
15.0ms
(* x (pow n 2))

series152.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ 1 (* x n))
89.0ms
(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
22.0ms
(* (pow x 2) n)
29.0ms
(* x (pow n 2))

simplify55.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0383546
11807466
25001459
done5001459

prune341.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (log (/ 1 x)) (* x (pow n 2)))
2.0b
(+ (/ (/ 1.0 n) x) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
10.2b
(* (pow x 2) n)
10.9b
(* x (pow n 2))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
59×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
43×fma-def
24×add-exp-log
13×add-cbrt-cube
11×associate-*r* associate-*l*
9×prod-exp
8×pow1 unpow-prod-down add-log-exp unswap-sqr
6×log-pow associate-/l*
5×div-inv
4×expm1-log1p-u div-exp log1p-expm1-u unpow2 sqr-pow
3×pow-to-exp pow-exp cbrt-unprod
2×cbrt-undiv pow-flip sum-log *-commutative distribute-lft-out inv-pow
1×+-commutative neg-sub0 associate-+r- log-div associate-+r+ distribute-neg-in distribute-rgt-neg-in frac-2neg flip3-+ div-sub distribute-frac-neg unsub-neg log-rec neg-log clear-num associate-/r* flip-+ fma-udef
Counts
4 → 154
Calls
4 calls:
15.0ms
(/ (log (/ 1 x)) (* x (pow n 2)))
52.0ms
(+ (/ (/ 1.0 n) x) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
11.0ms
(* (pow x 2) n)
15.0ms
(* x (pow n 2))

series198.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (log (/ 1 x)) (* x (pow n 2)))
70.0ms
(+ (/ (/ 1.0 n) x) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
22.0ms
(* (pow x 2) n)
30.0ms
(* x (pow n 2))

simplify64.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0474844
12224739
25001738
done5001738

prune589.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.8b

regimes234.0ms

Accuracy

83% (1.4b remaining)

Error of 22.4b against oracle of 21.0b and baseline of 29.3b

bsearch201.0ms

Steps
ItersRangePoint
11
0.007160366775085844
5.482779149720861e+18
32842187320271.035
9
-66911392.43097515
-2.284674362912159
-36780699.510345064

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04638
14638
done4638

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.4s3162×body1280valid
524.0ms1550×body640valid
435.0ms1100×body10240exit
273.0ms611×body1280nan
248.0ms4773×body80valid
224.0ms696×body640nan
202.0ms5097×body80nan
185.0ms835×body320valid
70.0ms358×body320nan
61.0ms461×body160valid
22.0ms197×body160nan