Details

Time bar (total: 13.8s)

sample59.0ms

Algorithm
intervals
Results
19.0ms53×body1280valid
13.0ms49×body640valid
9.0ms129×body80valid
3.0ms14×body320valid
2.0ms11×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
312724
416924
527124
665424
7206724
done500124

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

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)
8.3b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
7.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
9.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
60.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
23.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
136.0ms
(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))))
155.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.1s

Counts
97 → 97
Iterations

Useful iterations: 2 (223.0ms)

IterNodesCost
01932013
14551800
215251613
done50001613

prune506.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.4b

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)
8.3b
(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r* pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*r/ associate-*l* associate-*l/ *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
7.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
9.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
49.0ms
(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
26.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
138.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
206.0ms
(* (* -2.0 J) (* (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cos (/ K 2.0))))
148.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.0s

Counts
94 → 94
Iterations

Useful iterations: 2 (213.0ms)

IterNodesCost
02001999
14971791
215481573
done50001573

prune303.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.5b

localize22.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.6b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.6b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.6b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
19×*-un-lft-identity
16×sqrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt
8×sqrt-div
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 67
Calls
4 calls:
23.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
13.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
12.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series844.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
238.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
228.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
227.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.3s

Counts
79 → 79
Iterations

Useful iterations: 4 (642.0ms)

IterNodesCost
0942099
11861897
24031776
39801758
432731749
done50001749

prune377.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (cos (/ K 2.0)))
0.4b
(cbrt (cos (/ K 2.0)))
8.3b
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
29×add-exp-log
20×add-cbrt-cube
19×pow-prod-down prod-exp cbrt-unprod
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
6×cbrt-prod
4×sqrt-div add-log-exp
2×flip3-+ pow1/3 associate-*r/ flip-+ distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 74
Calls
4 calls:
1.0ms
(cbrt (cos (/ K 2.0)))
1.0ms
(cbrt (cos (/ K 2.0)))
227.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
24.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (cos (/ K 2.0)))
148.0ms
(cbrt (cos (/ K 2.0)))
205.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
148.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify873.0ms

Counts
86 → 86
Iterations

Useful iterations: 2 (166.0ms)

IterNodesCost
01512457
14042210
215241603
done50001603

prune301.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.5b

regimes368.0ms

Accuracy

2.9% (8.9b remaining)

Error of 17.9b against oracle of 9.0b and baseline of 18.2b

bsearch364.0ms

Steps
ItersRangePoint
9
9.246150242615916e-90
3.252989322604537e-82
2.1734863457091326e-87
7
5.56679059598137e-197
4.9068444523282e-195
1.726751503988064e-196
8
9.939134482145974e-277
4.166653144369135e-274
9.304555376088434e-275
10
-5.3362097854891745e-199
-1.3813405654223604e-211
-1.838279836993495e-208

simplify15.0ms

Iterations

Useful iterations: 4 (7.0ms)

IterNodesCost
033100
14477
24772
35349
45648
55948
66248
76348
done6348

end0.0ms

sample1.6s

Algorithm
intervals
Results
567.0ms1502×body1280valid
344.0ms1292×body640valid
302.0ms4285×body80valid
116.0ms606×body320valid
42.0ms318×body160valid