Details

Time bar (total: 11.5s)

sample58.0ms

Algorithm
intervals
Results
17.0ms46×body1280valid
14.0ms54×body640valid
9.0ms127×body80valid
2.0ms13×body320valid
2.0ms16×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
312724
416924
527224
677424
7313724
done500024

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
16×*-un-lft-identity
15×pow1
13×add-sqr-sqrt
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×sqrt-prod
7×unpow-prod-down associate-*r*
6×times-frac div-exp pow-prod-down
4×sqrt-div pow-exp add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative sqr-pow
Counts
4 → 90
Calls
4 calls:
7.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
9.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
25.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
64.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series564.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
137.0ms
(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)))
194.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify685.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (210.0ms)

IterNodesCost
02142168
15451954
221031735
done50011735

prune312.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.7b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×add-cbrt-cube
18×pow1
14×prod-exp
12×*-un-lft-identity
11×add-sqr-sqrt cbrt-unprod
10×add-cube-cbrt
8×pow-prod-down
7×unpow-prod-down
6×times-frac div-exp
4×sqrt-div associate-*r/ pow-exp sqrt-prod add-log-exp
3×cbrt-undiv pow-unpow associate-/l*
2×flip3-+ flip-+ div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r* associate-*l* clear-num associate-/r* *-commutative distribute-lft-out sqr-pow
Counts
4 → 87
Calls
4 calls:
7.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
9.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
25.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
47.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
131.0ms
(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)))
186.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify748.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (177.0ms)

IterNodesCost
02122138
15391929
219601679
done50011679

prune290.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.7b

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×add-exp-log cbrt-prod add-cbrt-cube
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*l* *-commutative
Counts
4 → 70
Calls
4 calls:
27.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
21.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series739.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
81.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
219.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
220.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify534.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
01582281
13582142
212261856
done50011856

prune365.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 13.7b

localize27.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.8b
(cbrt (pow (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))
15.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
42×cbrt-prod
22×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt sqrt-prod
13×pow1 add-exp-log add-cbrt-cube
10×unpow-prod-down cube-prod
8×cbrt-div
6×pow-prod-down prod-exp cbrt-unprod
4×distribute-lft-out add-log-exp
3×flip3-+ pow1/3 associate-*r* flip-+
2×cube-div sqrt-div
1×cube-mult unpow3 associate-*l* *-commutative rem-cbrt-cube sqr-pow
Counts
4 → 86
Calls
4 calls:
21.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
26.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
217.0ms
(cbrt (pow (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) 3))
216.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
225.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify566.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (160.0ms)

IterNodesCost
01973133
14692672
215022348
done50002348

prune376.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 13.7b

regimes358.0ms

Accuracy

91.3% (0.5b remaining)

Error of 13.2b against oracle of 12.8b and baseline of 18.2b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample1.6s

Algorithm
intervals
Results
574.0ms1509×body1280valid
354.0ms1286×body640valid
302.0ms4297×body80valid
122.0ms603×body320valid
45.0ms307×body160valid