Details

Time bar (total: 6.6s)

sample63.0ms

Algorithm
intervals
Results
22.0ms60×body1280valid
9.0ms36×body640valid
9.0ms132×body80valid
7.0ms18×body320valid
1.0ms10×body160valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
7.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
55.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
25.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
126.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
184.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
140.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04531006
11965898
25001898

prune279.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
7.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r/ associate-*r* pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
46.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
25.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
128.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
182.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
140.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0488987
12021866
25002866

prune262.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize19.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.7b
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
7.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
29×pow1
25×add-exp-log add-cbrt-cube
20×sqrt-prod
18×associate-*r/
15×pow-prod-down prod-exp cbrt-unprod
14×*-un-lft-identity
12×add-sqr-sqrt
9×flip3-+ flip-+
8×add-cube-cbrt
6×sqrt-pow1
4×frac-times rem-sqrt-square pow1/2 add-log-exp
3×distribute-lft-out
2×associate-*l/
1×associate-*r* associate-*l* *-commutative
Counts
4 → 90
Calls
4 calls:
23.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
276.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
24.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series676.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
185.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
137.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
142.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify54.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
04371680
114731360
250011360

prune360.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
6.7b
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
29×add-exp-log
20×add-cbrt-cube
19×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 74
Calls
4 calls:
0.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
218.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
22.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series609.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(cbrt (cos (/ K 2.0)))
145.0ms
(cbrt (cos (/ K 2.0)))
186.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
135.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify63.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04011337
118281008
25002913

prune249.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 10.8b

regimes382.0ms

Accuracy

90.5% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample1.6s

Algorithm
intervals
Results
567.0ms1531×body1280valid
333.0ms1249×body640valid
309.0ms4316×body80valid
112.0ms598×body320valid
41.0ms310×body160valid