Details

Time bar (total: 7.9s)

sample107.0ms

Algorithm
intervals
Results
45.0ms100×body1280valid
12.0ms37×body640valid
9.0ms164×body80valid
6.0ms25×body320valid
6.0ms161×body80nan
4.0ms75×body80overflowed
4.0ms8×body640nan
2.0ms2×body1280nan
1.0ms10×body160valid
1.0ms5×body320nan
0.0ms2×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: 24.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow x (/ 1.0 n))
0.2b
(pow (+ x 1.0) (/ 1.0 n))
1.8b
(- (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))
44.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(pow x (/ 1.0 n))
148.0ms
(pow (+ x 1.0) (/ 1.0 n))
278.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0476639
11600623
25001609

prune227.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
0.0b
(pow x (/ 1.0 n))
0.2b
(pow (+ x 1.0) (/ 1.0 n))
1.8b
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
47×unpow-prod-down
46×cbrt-prod
33×*-un-lft-identity
27×difference-of-squares
26×pow-unpow
25×add-cube-cbrt
23×sqr-pow
18×times-frac
17×cube-prod
6×pow1 add-exp-log add-log-exp
4×add-cbrt-cube
3×distribute-lft-out
2×pow-to-exp pow-pow pow-exp div-inv
1×cube-mult sub-neg flip3-- pow1/3 diff-log unpow3 flip-- rem-cbrt-cube distribute-lft-out--
Counts
4 → 126
Calls
4 calls:
9.0ms
(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
98.0ms
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series757.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
196.0ms
(pow x (/ 1.0 n))
147.0ms
(pow (+ x 1.0) (/ 1.0 n))
272.0ms
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify57.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05961222
121121179
250011176

prune336.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1.0 n) x)
1.8b
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.3b
(* x (pow n 2))
10.3b
(/ (/ 0.5 n) (pow x 2))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
155×add-sqr-sqrt
145×*-un-lft-identity
140×add-cube-cbrt
46×unpow-prod-down
27×add-exp-log
26×associate-/l*
16×add-cbrt-cube unpow2 sqr-pow
15×div-inv
12×div-exp
11×associate-/r*
9×add-log-exp
8×associate-*r*
6×cbrt-undiv
4×pow1 frac-sub unswap-sqr
3×pow-to-exp diff-log associate-*l* pow-exp prod-exp distribute-lft-out-- difference-of-squares
2×sub-neg flip3-- frac-2neg clear-num flip-- associate-/l/ associate--r+
1×*-commutative cbrt-unprod associate--r-
Counts
4 → 265
Calls
4 calls:
6.0ms
(/ (/ 1.0 n) x)
188.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms
(* x (pow n 2))
8.0ms
(/ (/ 0.5 n) (pow x 2))

series140.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (/ 1.0 n) x)
64.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
28.0ms
(* x (pow n 2))
29.0ms
(/ (/ 0.5 n) (pow x 2))

simplify51.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012432282
150022119

prune781.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(log (exp (/ 0.5 (* (pow x 2) n))))
1.8b
(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.3b
(* x (pow n 2))
10.2b
(* (pow x 2) n)

rewrite107.0ms

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:
4.0ms
(log (exp (/ 0.5 (* (pow x 2) n))))
88.0ms
(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms
(* x (pow n 2))
6.0ms
(* (pow x 2) n)

series143.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(log (exp (/ 0.5 (* (pow x 2) n))))
64.0ms
(- (/ (/ 1.0 n) x) (- (log (exp (/ 0.5 (* (pow x 2) n)))) (/ (* (log x) 1.0) (* x (pow n 2)))))
33.0ms
(* x (pow n 2))
19.0ms
(* (pow x 2) n)

simplify75.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0514973
12276880
25001868

prune345.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 18.6b

regimes255.0ms

Accuracy

81.6% (1.6b remaining)

Error of 22.2b against oracle of 20.6b and baseline of 29.3b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.4s3131×body1280valid
557.0ms1610×body640valid
258.0ms4802×body80valid
192.0ms5101×body80nan
178.0ms815×body320valid
133.0ms2313×body80overflowed
131.0ms266×body640nan
124.0ms128×body1280nan
64.0ms470×body160valid
42.0ms162×body320nan
13.0ms95×body160nan