Details

Time bar (total: 8.9s)

sample52.0ms

Algorithm
intervals
Results
13.0ms36×body1280valid
11.0ms44×body640valid
10.0ms154×body80valid
2.0ms12×body320valid
1.0ms10×body160valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17513
213913
320713
437513
5137313
6500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
17×add-sqr-sqrt
15×*-un-lft-identity
12×prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×unpow-prod-down sqrt-prod
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×pow-unpow times-frac div-exp hypot-def
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out sqr-pow
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv
Counts
4 → 96
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)
58.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
26.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series513.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
131.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
188.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
145.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04641076
11988966
25001965

prune331.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
6.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-*l* *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 88
Calls
4 calls:
7.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
6.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
21.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series688.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
51.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
45.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
500.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify65.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0489993
12344770
25001770

prune331.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
6.7b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.7b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
23×add-exp-log add-cbrt-cube
13×pow-prod-down prod-exp cbrt-unprod
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity associate-*r* sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 79
Calls
4 calls:
7.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
81.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.6s

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
505.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
503.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
499.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify62.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
03771470
116661156
250021152

prune368.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
6.7b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.7b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.7b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1
19×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 122
Calls
4 calls:
12.0ms
(* (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.0s

Counts
4 → 12
Calls
4 calls:
511.0ms
(* (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
500.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
499.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
512.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify198.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02411874
18381729
245491678
350011678

prune487.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes280.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02414
12414

end0.0ms

sample1.6s

Algorithm
intervals
Results
566.0ms1512×body1280valid
321.0ms1239×body640valid
299.0ms4291×body80valid
121.0ms649×body320valid
41.0ms315×body160valid