Details

Time bar (total: 11.4s)

sample66.0ms

Algorithm
intervals
Results
25.0ms56×body1280valid
10.0ms33×body640valid
9.0ms131×body80valid
5.0ms22×body320valid
2.0ms14×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5135213
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: 15.7b

Counts
2 → 1

localize17.0ms

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)
6.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-*l*
5×*-commutative
4×sqrt-div
2×flip3-+ associate-*r/ flip-+
1×pow-to-exp unpow-prod-down pow1/2 div-inv sqr-pow
Counts
4 → 16
Calls
4 calls:
4.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
3.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
4.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
135.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
187.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
144.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0199238
1507238
21486238
35002234

prune123.0ms

Filtered
28 candidates to 25 candidates (89.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New23528
Fresh000
Picked011
Done000
Total23629

Merged error: 11.3b

Counts
29 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
0.3b
(* (cos (/ K 2.0)) (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
6.2b
(* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×sqrt-div associate-*r/
5×*-commutative
4×associate-*r* associate-*l*
3×flip3-+ flip-+
1×pow-to-exp unpow-prod-down pow1/2 div-inv sqr-pow
Counts
4 → 18
Calls
4 calls:
3.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms
(* (cos (/ K 2.0)) (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
7.0ms
(* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
4.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series670.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
216.0ms
(* (cos (/ K 2.0)) (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
174.0ms
(* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0204256
1504256
21491256
35002252

prune130.0ms

Filtered
30 candidates to 26 candidates (86.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New26430
Fresh134
Picked011
Done011
Total27936

Merged error: 9.0b

Counts
36 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

5.8b
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
6.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (/ (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
12.4b
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
19.4b
(/ (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
10×sqrt-div
7×associate-*r* *-commutative
6×associate-*r/ associate-*l*
5×flip3-+ flip-+
4×distribute-rgt-out-- associate-/r/ div-inv associate-/l/
3×clear-num
2×unpow-prod-down frac-2neg sqrt-prod sum-cubes associate-/l* distribute-lft-out-- sqr-pow
1×sub-neg sqrt-undiv flip3-- pow1/2 un-div-inv flip--
Counts
4 → 37
Calls
4 calls:
16.0ms
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
30.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (/ (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
16.0ms
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
26.0ms
(/ (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

series3.2s

Counts
4 → 12
Calls
4 calls:
506.0ms
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
1.2s
(* (* (* -2.0 J) (cos (/ K 2.0))) (/ (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
679.0ms
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
811.0ms
(/ (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05241230
121411198
250021196

prune311.0ms

Filtered
49 candidates to 42 candidates (85.7%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New47249
Fresh156
Picked011
Done022
Total481058

Merged error: 9.0b

Counts
58 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

5.8b
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
6.3b
(/ (* (* -2.0 J) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))))
12.4b
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
21.1b
(/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div associate-/r/
12×times-frac *-commutative
9×flip3-+ flip-+ div-inv
8×associate-*l*
5×associate-/r*
4×distribute-rgt-out-- associate-*r* associate-/l/ associate-/l*
3×frac-2neg clear-num
2×unpow-prod-down sqrt-prod sum-cubes distribute-lft-out-- sqr-pow
1×sub-neg sqrt-undiv flip3-- pow1/2 flip--
Counts
4 → 50
Calls
4 calls:
16.0ms
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
34.0ms
(/ (* (* -2.0 J) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))))
16.0ms
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
25.0ms
(/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))))

series3.1s

Counts
4 → 12
Calls
4 calls:
525.0ms
(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
1.2s
(/ (* (* -2.0 J) (cos (/ K 2.0))) (/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))))
492.0ms
(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
865.0ms
(/ (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))) (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))))

simplify82.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06632099
126802057
250022057

prune396.0ms

Filtered
62 candidates to 55 candidates (88.7%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New60262
Fresh066
Picked011
Done123
Total611172

Merged error: 8.9b

Counts
72 → 11

regimes370.0ms

Accuracy

62.2% (3.0b remaining)

Error of 13.2b against oracle of 10.3b and baseline of 18.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04656
14656

end0.0ms

sample1.9s

Algorithm
intervals
Results
702.0ms1495×body1280valid
421.0ms1266×body640valid
328.0ms4264×body80valid
164.0ms656×body320valid
51.0ms322×body160valid