Details

Time bar (total: 9.2s)

sample95.0ms

Algorithm
intervals
Results
29.0ms69×body1280valid
21.0ms82×body640valid
14.0ms260×body80valid
9.0ms51×body320valid
3.0ms26×body160valid

simplify371.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0239
1419
2839
31739
42719
55339
610239
713959
843699
950029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* J (- (exp l) (exp (- l))))
0.0b
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
8.0b
(- (exp l) (exp (- l)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
8×associate-*r*
6×add-cube-cbrt
5×add-log-exp
4×associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod
3×sub-neg flip3-- flip--
2×distribute-rgt-in distribute-lft-in associate-*l/ *-commutative distribute-lft-out-- difference-of-squares
1×diff-log unswap-sqr
Counts
3 → 60
Calls
3 calls:
22.0ms
(* J (- (exp l) (exp (- l))))
32.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
7.0ms
(- (exp l) (exp (- l)))

series186.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(* J (- (exp l) (exp (- l))))
92.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
36.0ms
(- (exp l) (exp (- l)))

simplify38.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0264566
11116481
25002475

prune218.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.1b
(* 1/60 (pow l 5))
0.1b
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
0.1b
(* 1/3 (pow l 3))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×associate-*r*
21×add-exp-log
15×add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
11×pow1
10×associate-*l* prod-exp
8×unpow-prod-down unswap-sqr
6×cbrt-unprod
4×cube-prod associate-*r/ pow-prod-down *-commutative add-log-exp sqr-pow
2×pow-to-exp flip3-+ associate-*l/ pow-exp flip-+
1×distribute-rgt-in cube-mult distribute-lft-in unpow3
Counts
4 → 98
Calls
4 calls:
34.0ms
(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
6.0ms
(* 1/60 (pow l 5))
45.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
7.0ms
(* 1/3 (pow l 3))

series383.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
46.0ms
(* 1/60 (pow l 5))
163.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
40.0ms
(* 1/3 (pow l 3))

simplify71.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0464817
12375697
25001697

prune376.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))))
16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/ associate-*l/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
30.0ms
(* (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))))
38.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
40.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
38.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
338.0ms
(* (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))) (cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))))
293.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
297.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
300.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

simplify57.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04242067
115571890
250011781

prune493.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
16.6b
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-div associate-*r/ associate-*l/
4×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 44
Calls
4 calls:
38.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
37.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
40.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
38.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
307.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
307.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
301.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))
304.0ms
(cbrt (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))))

simplify159.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02571188
18561088
242571048
350011048

prune428.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes296.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03012
13012

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s2732×body1280valid
650.0ms2515×body640valid
454.0ms8281×body80valid
253.0ms1471×body320valid
92.0ms825×body160valid