Details

Time bar (total: 28.1s)

sample127.0ms

Algorithm
intervals
Results
53.0ms52×body1280valid
19.0ms32×body640valid
19.0ms145×body80valid
7.0ms17×body320valid
3.0ms10×body160valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
13424
27124
313524
420624
549124
6330124
done500024

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.5b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite388.0ms

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:
19.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
22.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
220.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
123.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
197.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
308.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
208.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.7s

Counts
102 → 102
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02142168
16011954
228131741
done50021735

prune597.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
10.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite342.0ms

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:
18.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
31.0ms
(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)))))
97.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series874.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
229.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
299.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
228.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.3s

Counts
99 → 99
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02122138
15921929
223561685
done50011679

prune492.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.2b

localize60.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
32.0b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
32.0b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
32.0b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
21×unpow-prod-down
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod div-inv sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 72
Calls
4 calls:
20.0ms
(sqrt (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
20.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
20.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
20.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

series7.9s

Counts
4 → 12
Calls
4 calls:
334.0ms
(sqrt (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
2.4s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
2.6s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
2.6s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: done (996.0ms)

IterNodesCost
03114063
18173915
219353235
done50003224

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 12.2b

localize36.0ms

Local error

Found 4 expressions with local error:

1.2b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
5.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
15.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite771.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
25×add-exp-log add-cbrt-cube
15×pow-prod-down prod-exp cbrt-unprod
14×*-un-lft-identity
13×cbrt-prod
10×add-sqr-sqrt
8×add-cube-cbrt cbrt-div
7×sqrt-prod
6×associate-*r/
4×flip3-+ sqrt-div flip-+ add-log-exp
3×pow1/3 distribute-lft-out
2×rem-sqrt-square sqrt-pow1
1×pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 79
Calls
4 calls:
88.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
544.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
60.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
72.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
331.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
410.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))))
297.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
319.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.0s

Counts
91 → 91
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01813428
14473145
218952595
done50002546

prune482.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 12.2b

regimes492.0ms

Accuracy

91.4% (0.4b remaining)

Error of 12.9b against oracle of 12.4b and baseline of 17.6b

bsearch4.0ms

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s1472×body1280valid
681.0ms4308×body80valid
674.0ms1278×body640valid
348.0ms628×body320valid
69.0ms314×body160valid