Details

Time bar (total: 8.1s)

sample66.0ms

Algorithm
intervals
Results
19.0ms46×body1280valid
17.0ms45×body640valid
10.0ms134×body80valid
4.0ms19×body320valid
2.0ms12×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17513
213913
320713
437513
5137313
6500113

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize16.0ms

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)
7.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite40.0ms

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:
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
11.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
128.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
133.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
181.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify57.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04641076
11988966
25001965

prune314.0ms

Filtered
108 candidates to 73 candidates (67.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.6b

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)))
8.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite27.0ms

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:
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
5.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
5.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
9.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series648.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
43.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
48.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
474.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify61.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0489993
12344770
25001770

prune301.0ms

Filtered
100 candidates to 66 candidates (66.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
8.4b
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×associate-*r*
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv unswap-sqr
Counts
4 → 89
Calls
4 calls:
4.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
5.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
6.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
429.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
85.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
43.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
479.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05241240
12426964
25002963

prune326.0ms

Filtered
101 candidates to 67 candidates (66.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.6b

localize19.0ms

Local error

Found 4 expressions with local error:

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)))))
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)))))
8.3b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.3b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
27×add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*r* sqrt-prod
10×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 85
Calls
4 calls:
8.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
11.0ms
(* (* (* (* -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))))

series2.0s

Counts
4 → 12
Calls
4 calls:
541.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
487.0ms
(* (* (* (* -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)))))
478.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
478.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify68.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03991872
118291509
250011503

prune349.0ms

Filtered
97 candidates to 64 candidates (66.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.6b

regimes259.0ms

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

sample1.8s

Algorithm
intervals
Results
689.0ms1558×body1280valid
399.0ms1251×body640valid
320.0ms4276×body80valid
136.0ms615×body320valid
46.0ms301×body160valid