Details

Time bar (total: 14.3s)

sample54.0ms

Algorithm
intervals
Results
14.0ms41×body1280valid
10.0ms151×body80valid
10.0ms39×body640valid
3.0ms16×body320valid
1.0ms9×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
13424
27224
313324
419424
531524
675424
7253924
done500124

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

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)
7.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite266.0ms

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:
19.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
21.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
71.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
151.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
144.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
157.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
201.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.0s

Counts
108 → 108
Iterations

Useful iterations: 2 (226.0ms)

IterNodesCost
02012139
14521925
214961736
done50001736

prune369.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.4b

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)))
8.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite115.0ms

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:
17.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
19.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
18.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
58.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series726.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
49.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
55.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
525.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.0s

Counts
100 → 100
Iterations

Useful iterations: 2 (278.0ms)

IterNodesCost
01931843
14781816
218991415
done50001415

prune568.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.4b
(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
8.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
57×add-exp-log
37×add-cbrt-cube
33×times-frac
24×pow1
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×prod-exp
17×div-exp
15×cbrt-unprod
12×pow-prod-down
9×associate-*r*
7×cbrt-undiv associate-/r*
5×div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×associate-*l* *-commutative associate-/l*
1×pow-flip frac-2neg clear-num associate-/r/ inv-pow
Counts
4 → 125
Calls
4 calls:
18.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
20.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
28.0ms
(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
57.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2))))

series715.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
52.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
96.0ms
(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
519.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2))))

simplify926.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (339.0ms)

IterNodesCost
02602663
16192506
222031966
done50001966

prune391.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.4b

localize27.0ms

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))))) (sqrt (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2)))))
0.4b
(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
8.1b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.1b
(sqrt (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2))))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
33×times-frac
32×add-cbrt-cube
26×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
21×pow1
19×prod-exp
17×div-exp
13×cbrt-unprod
10×pow-prod-down
9×sqrt-prod
7×cbrt-undiv associate-/r*
6×associate-*r*
5×div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-flip frac-2neg associate-*l* clear-num associate-/r/ *-commutative inv-pow
Counts
4 → 121
Calls
4 calls:
195.0ms
(* (* (* (* -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 (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2)))))
30.0ms
(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
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 (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2))))

series1.7s

Counts
4 → 12
Calls
4 calls:
531.0ms
(* (* (* (* -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 (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2)))))
97.0ms
(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
499.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
568.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2))))

simplify1.2s

Counts
133 → 133
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02884101
16943623
224522574
done50002546

prune488.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 8.4b

regimes364.0ms

Accuracy

0% (0.3b remaining)

Error of 7.9b against oracle of 7.6b and baseline of 7.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01926
12426
done2426

end0.0ms

sample1.6s

Algorithm
intervals
Results
529.0ms1499×body1280valid
323.0ms1238×body640valid
286.0ms4301×body80valid
117.0ms645×body320valid
40.0ms320×body160valid