Details

Time bar (total: 25.7s)

sample70.0ms

Algorithm
intervals
Results
18.0ms40×body1280valid
14.0ms147×body80valid
13.0ms40×body640valid
5.0ms22×body320valid
1.0ms7×body160valid

simplify2.4s

Counts
1 → 1

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize41.0ms

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)
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite432.0ms

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:
38.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
44.0ms
(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)))
222.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series812.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
234.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
262.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
250.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify922.0ms

Counts
97 → 97

prune480.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.0b

localize29.0ms

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)
8.5b
(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)))))

rewrite357.0ms

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:
27.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
24.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
126.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
178.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
227.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
207.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
320.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify1.0s

Counts
94 → 94

prune489.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.4b
(* (* (* (* -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))))

rewrite809.0ms

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)))
70.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
734.0ms
(* (* (* (* -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))))

series941.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt (cos (/ K 2.0)))
260.0ms
(cbrt (cos (/ K 2.0)))
217.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
275.0ms
(* (* (* (* -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))))

simplify1.1s

Counts
86 → 86

prune457.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.9b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cbrt (cos (/ K 2.0))))
0.3b
(cbrt (cbrt (cos (/ K 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.4b
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0))))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite5.1s

Algorithm
rewrite-expression-head
Rules
58×pow1
57×add-exp-log
43×pow-prod-down prod-exp cbrt-unprod
34×add-cbrt-cube
18×cbrt-prod
15×*-un-lft-identity
12×add-sqr-sqrt
11×add-cube-cbrt
8×sqrt-prod
7×associate-*r*
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 → 92
Calls
4 calls:
3.0ms
(cbrt (cbrt (cos (/ K 2.0))))
3.0ms
(cbrt (cbrt (cos (/ K 2.0))))
109.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
5.0s
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0))))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series862.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(cbrt (cbrt (cos (/ K 2.0))))
189.0ms
(cbrt (cbrt (cos (/ K 2.0))))
167.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
290.0ms
(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0))))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify1.4s

Counts
104 → 104

prune496.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.9b

regimes396.0ms

Accuracy

0% (5.7b remaining)

Error of 18.7b against oracle of 13.0b and baseline of 18.7b

bsearch0.0ms

simplify2.1s

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.4s4298×body80valid
1.2s1484×body1280valid
662.0ms1246×body640valid
251.0ms637×body320valid
74.0ms336×body160valid