Details

Time bar (total: 7.3s)

sample77.0ms

Algorithm
intervals
Results
18.0ms35×body1280valid
14.0ms250×body80valid
13.0ms43×body640valid
7.0ms99×body80overflowed
5.0ms31×body320valid
1.0ms8×body160valid

simplify369.0ms

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: 15.7b

localize13.0ms

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)))
4.2b
(- (exp l) (exp (- l)))

rewrite56.0ms

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:
24.0ms
(* J (- (exp l) (exp (- l))))
25.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.0ms
(- (exp l) (exp (- l)))

series181.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* J (- (exp l) (exp (- l))))
89.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
35.0ms
(- (exp l) (exp (- l)))

simplify37.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0264566
11116481
25002475

prune200.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×associate-*r*
19×add-exp-log
13×add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity
9×pow1 prod-exp
8×unpow-prod-down
7×associate-*l* unswap-sqr
6×add-log-exp
5×cbrt-unprod
4×cube-prod sqr-pow
3×pow-prod-down *-commutative
2×pow-to-exp flip3-+ associate-*r/ associate-*l/ pow-exp flip-+
1×+-commutative cube-mult unpow3 sum-log
Counts
4 → 87
Calls
4 calls:
36.0ms
(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
5.0ms
(* 1/60 (pow l 5))
39.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
7.0ms
(* 1/3 (pow l 3))

series573.0ms

Counts
4 → 12
Calls
4 calls:
326.0ms
(+ (* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0))) U)
51.0ms
(* 1/60 (pow l 5))
158.0ms
(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
39.0ms
(* 1/3 (pow l 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0465795
12231707
25001707

prune325.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×associate-*r*
21×add-exp-log
15×add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×associate-*l*
11×pow1
10×prod-exp
8×unpow-prod-down unswap-sqr
6×cbrt-unprod
4×cube-prod pow-prod-down associate-*l/ *-commutative add-log-exp sqr-pow
2×pow-to-exp flip3-+ associate-*r/ pow-exp flip-+
1×cube-mult unpow3
Counts
4 → 96
Calls
4 calls:
5.0ms
(* 1/60 (pow l 5))
31.0ms
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
32.0ms
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
7.0ms
(* 1/3 (pow l 3))

series336.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* 1/60 (pow l 5))
87.0ms
(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
158.0ms
(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
40.0ms
(* 1/3 (pow l 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0444856
12079731
25001731

prune362.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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))))))
13.7b
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
13.7b
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
13.7b
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))

rewrite113.0ms

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:
27.0ms
(* (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))))))
27.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
30.0ms
(cbrt (* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))))
27.0ms
(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:
329.0ms
(* (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)))))
293.0ms
(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)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04122067
115001890
250021781

prune449.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes237.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03012
13012

end0.0ms

sample2.4s

Algorithm
intervals
Results
654.0ms1229×body1280valid
463.0ms8353×body80valid
404.0ms1404×body640valid
183.0ms3579×body80overflowed
147.0ms825×body320valid
59.0ms465×body160valid