Details

Time bar (total: 25.8s)

sample88.0ms

Algorithm
intervals
Results
25.0ms48×body1280valid
14.0ms37×body640valid
14.0ms139×body80valid
5.0ms16×body320valid
3.0ms16×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27124
313224
418924
530024
673124
7246224
done500024

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize22.0ms

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

rewrite324.0ms

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:
32.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
23.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
83.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
181.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series745.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
210.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
191.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
276.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.6s

Counts
97 → 97
Iterations

Useful iterations: 2 (352.0ms)

IterNodesCost
01932013
14411800
214641613
done50001613

prune372.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.4b

localize32.0ms

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

rewrite359.0ms

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/ associate-*r* pow-exp sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ 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:
20.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
42.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
82.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
212.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
204.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
193.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
267.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify1.4s

Counts
94 → 94
Iterations

Useful iterations: 2 (453.0ms)

IterNodesCost
02001983
14731775
215611557
done50011557

prune391.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.4b

localize44.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (* -2.0 J) (* (cos (/ K 2.0)) (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)))))))
30.4b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
30.4b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
30.4b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
21×unpow-prod-down
16×pow1 add-exp-log add-cbrt-cube
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×pow-prod-down prod-exp cbrt-unprod
4×associate-*r/ add-log-exp
3×pow1/3 div-inv sqr-pow
2×sqrt-div
1×flip3-+ associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 81
Calls
4 calls:
58.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (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)))))))
18.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
10.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
10.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

series8.0s

Counts
4 → 12
Calls
4 calls:
437.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (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)))))))
2.5s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
2.3s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
2.7s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

simplify1.3s

Counts
93 → 93
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03374863
19124613
223743530
done50013519

prune804.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 14.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.5b
(* (* (* (* -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))))

rewrite777.0ms

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)))
64.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
708.0ms
(* (* (* (* -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))))

series829.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(cbrt (cos (/ K 2.0)))
188.0ms
(cbrt (cos (/ K 2.0)))
162.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
264.0ms
(* (* (* (* -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))))

simplify1.6s

Counts
86 → 86
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01512457
13802210
215611603
done50011441

prune330.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 14.4b

regimes473.0ms

Accuracy

89.2% (0.6b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 18.6b

bsearch3.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
033118
14799
done4799

end0.0ms

sample2.1s

Algorithm
intervals
Results
741.0ms1545×body1280valid
411.0ms1221×body640valid
381.0ms4300×body80valid
158.0ms626×body320valid
58.0ms312×body160valid