Details

Time bar (total: 11.9s)

sample70.0ms

Algorithm
intervals
Results
28.0ms56×body1280valid
10.0ms33×body640valid
10.0ms131×body80valid
5.0ms22×body320valid
2.0ms14×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17513
213913
320713
437513
5136413
6500213

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

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)
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)))

rewrite19.0ms

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)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
128.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
180.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
139.0ms
(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
0202238
1520236
21556236
35002232

prune116.0ms

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

localize15.0ms

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)))

rewrite22.0ms

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)))))
6.0ms
(* (* -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)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
205.0ms
(* (cos (/ K 2.0)) (* (* -2.0 J) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
163.0ms
(* (* -2.0 J) (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)))

simplify42.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 3 (38.0ms)

IterNodesCost
0207256
1517253
21561253
35001249

prune123.0ms

Filtered
30 candidates to 26 candidates (86.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New27330
Fresh044
Picked011
Done011
Total27936

Merged error: 9.0b

Counts
36 → 9

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)))))
6.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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
(/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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))))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
41×sqr-pow
36×prod-diff
35×associate-*r*
33×div-inv
31×unpow-prod-down
21×*-commutative
16×associate-*l*
10×swap-sqr
9×fma-neg
6×sqrt-div
5×unswap-sqr
4×distribute-rgt-out-- associate-/r/
3×flip3-+ associate-*r/ clear-num flip-+
2×frac-2neg distribute-lft-out--
1×sub-neg sqrt-undiv hypot-udef flip3-- pow1/2 un-div-inv flip--
Counts
4 → 76
Calls
4 calls:
21.0ms
(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)))))
24.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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)))))))
17.0ms
(- (* (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)))
17.0ms
(/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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))))))

series3.4s

Counts
4 → 12
Calls
4 calls:
510.0ms
(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))) (/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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)))))))
473.0ms
(- (* (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)))
1.2s
(/ (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)) (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))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08313065
133982357
250012318

prune375.0ms

Filtered
88 candidates to 51 candidates (58.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New87188
Fresh156
Picked011
Done022
Total88997

Merged error: 9.0b

Counts
97 → 9

localize35.0ms

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))))) (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2))))
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))))) (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
41×sqr-pow
38×div-inv
36×prod-diff
32×associate-*r*
31×unpow-prod-down
22×*-commutative
14×associate-*l*
10×swap-sqr
9×fma-neg
6×sqrt-div
5×associate-/r/ unswap-sqr
4×distribute-rgt-out-- times-frac associate-/l/ associate-/l*
3×frac-2neg flip3-+ clear-num flip-+
2×distribute-lft-out--
1×sub-neg sqrt-undiv hypot-udef flip3-- pow1/2 associate-/r* flip--
Counts
4 → 81
Calls
4 calls:
20.0ms
(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)))))
21.0ms
(/ (* (* -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))))) (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2))))
17.0ms
(- (* (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)))
17.0ms
(/ (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))))) (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)))

series3.5s

Counts
4 → 12
Calls
4 calls:
486.0ms
(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))))) (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2))))
654.0ms
(- (* (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)))
1.2s
(/ (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))))) (hypot (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3/2) (pow 1.0 3/2)))

simplify91.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08153287
130832568
250012546

prune402.0ms

Filtered
93 candidates to 56 candidates (60.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New91293
Fresh055
Picked011
Done213
Total939102

Merged error: 8.9b

Counts
102 → 9

regimes281.0ms

Accuracy

62.2% (2.9b 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
707.0ms1495×body1280valid
433.0ms1266×body640valid
344.0ms4264×body80valid
159.0ms656×body320valid
53.0ms322×body160valid