Details

Time bar (total: 9.3s)

sample83.0ms

Algorithm
intervals
Results
29.0ms47×body1280valid
18.0ms41×body640valid
12.0ms137×body80valid
6.0ms20×body320valid
3.0ms12×body160valid

simplify47.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.2b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (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)))

rewrite35.0ms

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)))
7.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
13.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
135.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
206.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
146.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04641076
11988966
25001965

prune300.0ms

Filtered
108 candidates to 73 candidates (67.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New999108
Fresh000
Picked101
Done000
Total1009109

Merged error: 7.7b

Counts
109 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
7.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite25.0ms

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)))
7.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
45.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
53.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
511.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify63.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0489993
12344770
25001770

prune289.0ms

Filtered
100 candidates to 66 candidates (66.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New955100
Fresh448
Picked011
Done000
Total9910109

Merged error: 7.6b

Counts
109 → 10

localize18.0ms

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))))
0.2b
(* (* 2.0 J) (cos (/ K 2.0)))
7.4b
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite23.0ms

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:
3.0ms
(* (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)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
619.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
94.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
47.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
522.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05241240
12426964
25002963

prune289.0ms

Filtered
101 candidates to 66 candidates (65.3%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New992101
Fresh088
Picked011
Done011
Total9912111

Merged error: 7.6b

Counts
111 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

2.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
7.6b
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
7.6b
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
7.6b
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1 add-exp-log
19×add-cbrt-cube
15×pow-prod-down prod-exp cbrt-unprod
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3
1×associate-*r* associate-*l* *-commutative
Counts
4 → 69
Calls
4 calls:
11.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
1.0ms
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.3s

Counts
4 → 12
Calls
4 calls:
635.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
552.0ms
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
561.0ms
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
565.0ms
(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify48.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03431759
112801423
250011367

prune309.0ms

Filtered
81 candidates to 60 candidates (74.1%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New79281
Fresh099
Picked101
Done022
Total801393

Merged error: 7.6b

Counts
93 → 13

regimes315.0ms

Accuracy

0% (0.3b remaining)

Error of 7.9b against oracle of 7.7b and baseline of 7.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02414
12414

end0.0ms

sample2.4s

Algorithm
intervals
Results
939.0ms1514×body1280valid
561.0ms1269×body640valid
395.0ms4275×body80valid
205.0ms626×body320valid
66.0ms318×body160valid

Profiling

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