Details

Time bar (total: 4.3s)

sample35.0ms

Algorithm
intervals
Results
15.0ms362×body80valid
5.0ms125×body80nan

simplify117.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-sqr-sqrt
11×add-cbrt-cube add-log-exp
9×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×prod-exp
4×pow1 unpow-prod-down div-exp sum-log
3×flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 74
Calls
4 calls:
2.0ms
(+ 1.0 (* 10.0 k))
6.0ms
(* a (pow k m))
9.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ 1.0 (* 10.0 k))
55.0ms
(* a (pow k m))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
113.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify64.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0457599
12146533
25001526

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.0b
(* a (pow k (/ m 2)))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
45×prod-exp
20×add-cbrt-cube
16×add-sqr-sqrt
15×pow-to-exp pow-exp
14×associate-*r*
13×div-exp
11×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×unpow-prod-down cbrt-unprod
4×pow1 associate-*l*
3×cbrt-undiv times-frac associate-/r* sum-log unswap-sqr sqr-pow
2×flip3-+ associate-/r/ *-commutative flip-+
1×+-commutative associate-+l+ frac-2neg clear-num div-inv associate-/l*
Counts
4 → 103
Calls
4 calls:
11.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
6.0ms
(* a (pow k (/ m 2)))
12.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
21.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
61.0ms
(* a (pow k (/ m 2)))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
132.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify84.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
05371089
12875900
25002870

prune254.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.0b
(* a (pow k m))
0.1b
(/ 1 (+ 1.0 (* k (+ 10.0 k))))
1.7b
(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
32×prod-exp
31×add-sqr-sqrt
26×*-un-lft-identity associate-*r*
24×add-cube-cbrt
22×add-cbrt-cube
18×times-frac
10×div-exp
9×pow1
8×cbrt-unprod
7×associate-*l*
5×pow-to-exp rec-exp 1-exp pow-exp
4×unpow-prod-down associate-/r/ add-log-exp unswap-sqr
3×cbrt-undiv flip3-+ associate-*r/ associate-/r* *-commutative flip-+ associate-/l*
2×pow-prod-down div-inv sqr-pow
1×distribute-rgt-in pow-flip frac-2neg distribute-lft-in clear-num un-div-inv distribute-lft-out inv-pow
Counts
4 → 128
Calls
4 calls:
10.0ms
(* k (+ 10.0 k))
6.0ms
(* a (pow k m))
5.0ms
(/ 1 (+ 1.0 (* k (+ 10.0 k))))
21.0ms
(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* k (+ 10.0 k))
56.0ms
(* a (pow k m))
40.0ms
(/ 1 (+ 1.0 (* k (+ 10.0 k))))
116.0ms
(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0634958
13411839
25001812

prune279.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.0b
(* (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (sqrt 1) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
14.5b
(sqrt (+ 1.0 (* k (+ 10.0 k))))
14.5b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt sqrt-prod
54×times-frac
51×add-exp-log
42×associate-*r*
40×*-un-lft-identity
38×add-cube-cbrt
30×add-cbrt-cube
19×prod-exp
17×div-exp
12×associate-*l*
10×sqrt-div
9×cbrt-undiv cbrt-unprod
8×pow1
7×unswap-sqr
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×add-log-exp
3×pow-to-exp pow-exp div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 150
Calls
4 calls:
7.0ms
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
43.0ms
(* (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (sqrt 1) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
3.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
117.0ms
(* (/ (* a (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (sqrt 1) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
53.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))
47.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify137.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (117.0ms)

IterNodesCost
08322276
145822063
250021961

prune495.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.7b

regimes57.0ms

Accuracy

0% (0.1b remaining)

Error of 2.2b against oracle of 2.1b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02011
12011

end0.0ms

sample1.0s

Algorithm
intervals
Results
506.0ms11935×body80valid
151.0ms4285×body80nan