Details

Time bar (total: 18.9s)

sample73.0ms

Algorithm
intervals
Results
22.0ms48×body1280valid
17.0ms50×body640valid
11.0ms127×body80valid
6.0ms21×body320valid
2.0ms10×body160valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
13424
27224
313324
419424
531524
675424
7253924
done500124

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize39.0ms

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)
7.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.4b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite423.0ms

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:
31.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
24.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
262.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
98.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series735.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
206.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
255.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
190.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts
108 → 108
Iterations

Useful iterations: 2 (437.0ms)

IterNodesCost
02012139
14521925
214791736
done50011736

prune592.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize28.0ms

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)))
7.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite206.0ms

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:
20.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
30.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
42.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
108.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
63.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
68.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
799.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 2 (471.0ms)

IterNodesCost
01931843
14781816
218991415
done50001415

prune547.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.1b

localize43.0ms

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)))
7.9b
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite104.0ms

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:
10.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
19.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
26.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
44.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
673.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
116.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
69.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
750.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify1.6s

Counts
101 → 101
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02062273
15092248
219491753
done50001752

prune568.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
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)))
7.9b
(* (* -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
33×times-frac
27×add-exp-log add-cbrt-cube
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
18×pow1
10×prod-exp cbrt-unprod
9×pow-prod-down
7×associate-/l*
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u add-log-exp
3×associate-/r*
2×*-commutative
1×hypot-udef frac-2neg clear-num associate-/l/ unswap-sqr
Counts
4 → 104
Calls
4 calls:
0.0ms
(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
20.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
31.0ms
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
59.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
629.0ms
(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
686.0ms
(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
165.0ms
(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
771.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify1.4s

Counts
116 → 116
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02502841
15912768
219872298
done50002297

prune702.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.1b

regimes5.0ms