Details

Time bar (total: 9.0s)

sample161.0ms

Algorithm
intervals
Results
55.0ms96×body1280valid
29.0ms60×body640valid
12.0ms144×body80valid
10.0ms32×body320valid
10.0ms152×body80nan
9.0ms13×body1280nan
6.0ms20×body320nan
6.0ms35×body80overflowed
5.0ms13×body640nan
3.0ms16×body160valid
1.0ms6×body160nan

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1346
2806
32366
48686
550016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(pow x (/ 1.0 n))
0.7b
(pow (+ x 1.0) (/ 1.0 n))
1.7b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
28×*-un-lft-identity
26×pow-unpow
19×add-cube-cbrt
18×times-frac
17×unpow-prod-down
9×difference-of-squares
8×sqr-pow
5×pow1 add-exp-log add-log-exp
3×add-cbrt-cube distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
3 → 79
Calls
3 calls:
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
43.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series481.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(pow x (/ 1.0 n))
148.0ms
(pow (+ x 1.0) (/ 1.0 n))
272.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0476639
11600623
25001609

prune225.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 22.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (* (log x) 1.0) (* x (pow n 2)))
2.5b
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.4b
(/ (/ 0.5 n) (pow x 2))
9.0b
(* x (pow n 2))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
189×times-frac
113×add-sqr-sqrt
103×*-un-lft-identity
98×add-cube-cbrt
46×add-exp-log unpow-prod-down
23×add-cbrt-cube
17×div-exp
16×unpow2 sqr-pow
14×associate-/l*
13×prod-exp
11×div-inv
9×associate-/r* add-log-exp
8×associate-*r*
7×cbrt-undiv
5×pow-to-exp pow-exp cbrt-unprod
4×pow1 frac-sub unswap-sqr
3×diff-log associate-*l* distribute-lft-out-- difference-of-squares
2×sub-neg flip3-- frac-2neg clear-num flip-- associate--r+
1×*-commutative associate-/l/ associate--r-
Counts
4 → 220
Calls
4 calls:
5.0ms
(/ (* (log x) 1.0) (* x (pow n 2)))
189.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.0ms
(/ (/ 0.5 n) (pow x 2))
6.0ms
(* x (pow n 2))

series207.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (* (log x) 1.0) (* x (pow n 2)))
67.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
24.0ms
(/ (/ 0.5 n) (pow x 2))
33.0ms
(* x (pow n 2))

simplify45.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011122049
150011857

prune589.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b
(log (exp (/ 0.5 (* (pow x 2) n))))
2.5b
(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.5b
(* (pow x 2) n)
9.0b
(* x (pow n 2))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
21×*-un-lft-identity
14×add-exp-log add-cube-cbrt
11×associate-*r* associate-*l*
9×log-pow
8×unpow-prod-down add-cbrt-cube add-log-exp unswap-sqr
7×exp-prod
6×pow1 log-prod times-frac prod-exp
5×associate--r+ distribute-lft-out--
4×unpow2 sqr-pow
3×diff-log associate--l+ difference-of-squares
2×pow-to-exp sub-neg flip3-- pow-exp *-commutative frac-sub flip-- cbrt-unprod
1×rem-log-exp div-inv associate--r-
Counts
4 → 100
Calls
4 calls:
5.0ms
(log (exp (/ 0.5 (* (pow x 2) n))))
92.0ms
(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
6.0ms
(* (pow x 2) n)
6.0ms
(* x (pow n 2))

series136.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(log (exp (/ 0.5 (* (pow x 2) n))))
67.0ms
(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
18.0ms
(* (pow x 2) n)
29.0ms
(* x (pow n 2))

simplify71.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0514973
12276880
25001868

prune380.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.2b

localize24.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (pow x 2) n)
8.5b
(* (pow x 2) n)
8.5b
(* (pow x 2) n)
9.0b
(* x (pow n 2))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
27×associate-*l*
24×add-exp-log
17×associate-*r*
16×add-cube-cbrt unpow-prod-down *-un-lft-identity unswap-sqr
12×prod-exp add-cbrt-cube
8×unpow2 sqr-pow
4×pow1 pow-to-exp pow-exp *-commutative cbrt-unprod add-log-exp
Counts
4 → 108
Calls
4 calls:
5.0ms
(* (pow x 2) n)
6.0ms
(* (pow x 2) n)
6.0ms
(* (pow x 2) n)
6.0ms
(* x (pow n 2))

series86.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (pow x 2) n)
17.0ms
(* (pow x 2) n)
18.0ms
(* (pow x 2) n)
33.0ms
(* x (pow n 2))

simplify35.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0189408
1829340
25001340

prune481.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.2b

regimes292.0ms

Accuracy

82.3% (1.5b remaining)

Error of 22.5b against oracle of 21.0b and baseline of 29.6b

bsearch243.0ms

Steps
ItersRangePoint
8
249936452872729.84
1.4736071778219855e+18
253373043857974.97
11
-1450154140655066.2
-7.158504719359286e-08
-20133141455.183243

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04034
14034

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.9s3115×body1280valid
737.0ms1602×body640valid
410.0ms4811×body80valid
353.0ms601×body1280nan
317.0ms5106×body80nan
281.0ms896×body320valid
261.0ms573×body640nan
102.0ms363×body320nan
99.0ms1284×body80overflowed
89.0ms440×body160valid
34.0ms207×body160nan