Details

Time bar (total: 8.8s)

sample150.0ms

Algorithm
intervals
Results
45.0ms98×body1280valid
20.0ms23×body10240exit
19.0ms56×body640valid
14.0ms28×body1280nan
10.0ms160×body80nan
8.0ms152×body80valid
6.0ms18×body640nan
6.0ms28×body320valid
3.0ms17×body320nan
1.0ms9×body160valid
0.0ms4×body160nan

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1346
2806
32366
48686
550016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b
(pow x (/ 1.0 n))
0.5b
(pow (+ x 1.0) (/ 1.0 n))
1.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite52.0ms

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))
39.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series504.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(pow x (/ 1.0 n))
150.0ms
(pow (+ x 1.0) (/ 1.0 n))
291.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0476639
11600623
25001609

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow x (/ 1.0 n)) 3)
0.3b
(pow x (/ 1.0 n))
0.5b
(pow (+ x 1.0) (/ 1.0 n))
1.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
44×unpow-prod-down
29×pow-unpow *-un-lft-identity
27×difference-of-squares
25×add-cube-cbrt
24×cbrt-prod
23×sqr-pow
18×times-frac
16×cube-prod
8×add-exp-log
6×pow1 pow-exp add-log-exp
5×add-cbrt-cube
4×pow-to-exp
3×pow-pow
2×div-inv
1×cube-mult sub-neg flip3-- diff-log unpow3 flip-- distribute-lft-out distribute-lft-out-- rem-cube-cbrt
Counts
4 → 128
Calls
4 calls:
3.0ms
(pow (pow x (/ 1.0 n)) 3)
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
52.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(pow (pow x (/ 1.0 n)) 3)
63.0ms
(pow x (/ 1.0 n))
156.0ms
(pow (+ x 1.0) (/ 1.0 n))
288.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify66.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06801196
124971152
250021138

prune348.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow x (/ 1.0 n))
0.5b
(pow (+ x 1.0) (/ 1.0 n))
1.8b
(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (exp (log (pow (pow x (/ 1.0 n)) 3)))))
3.9b
(log (pow (pow x (/ 1.0 n)) 3))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
45×unpow-prod-down
44×log-prod
30×difference-of-squares
29×*-un-lft-identity
27×cbrt-prod
26×pow-unpow
25×add-cube-cbrt
24×exp-sum sqr-pow
18×times-frac
16×cube-prod
9×add-exp-log
6×pow1 pow-exp add-log-exp
5×rem-log-exp
4×pow-to-exp add-cbrt-cube
2×pow-pow div-inv
1×cube-mult sub-neg flip3-- diff-log unpow3 log-pow flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 131
Calls
4 calls:
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
56.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (exp (log (pow (pow x (/ 1.0 n)) 3)))))
3.0ms
(log (pow (pow x (/ 1.0 n)) 3))

series635.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow x (/ 1.0 n))
156.0ms
(pow (+ x 1.0) (/ 1.0 n))
289.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (exp (log (pow (pow x (/ 1.0 n)) 3)))))
126.0ms
(log (pow (pow x (/ 1.0 n)) 3))

simplify63.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06851516
123311411
250021391

prune397.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* (log x) 1.0) (* x (pow n 2)))
3.0b
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.2b
(/ (/ 0.5 n) (pow x 2))
7.9b
(* x (pow n 2))

rewrite213.0ms

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)))
181.0ms
(- (/ (/ 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))
9.0ms
(* x (pow n 2))

series220.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (* (log x) 1.0) (* x (pow n 2)))
71.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
26.0ms
(/ (/ 0.5 n) (pow x 2))
35.0ms
(* x (pow n 2))

simplify47.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011122049
150011857

prune591.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.1b

regimes184.0ms

Accuracy

81.7% (1.6b remaining)

Error of 22.4b against oracle of 20.8b and baseline of 29.4b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s3180×body1280valid
544.0ms1614×body640valid
457.0ms1152×body10240exit
404.0ms4669×body80valid
276.0ms627×body1280nan
209.0ms654×body640nan
190.0ms832×body320valid
184.0ms5087×body80nan
69.0ms363×body320nan
63.0ms458×body160valid
21.0ms188×body160nan