Details

Time bar (total: 26.9s)

sample198.0ms

Algorithm
intervals
Results
70.0ms38×body1280valid
41.0ms39×body640valid
35.0ms145×body80valid
21.0ms24×body320valid
5.0ms10×body160valid

simplify971.0ms

Counts
1 → 1

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize34.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
8.0b
(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
0.2b
(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
0.1b
(* (cos (/ K 2)) (* -2 J))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
54×add-cbrt-cube add-exp-log
26×pow1
24×prod-exp cbrt-unprod
19×add-sqr-sqrt
18×associate-*l*
16×*-un-lft-identity add-cube-cbrt
12×cbrt-undiv times-frac div-exp
11×associate-*r* associate-*l/
10×pow-prod-down
9×swap-sqr
8×associate-/r/
6×flip3-+ sqrt-prod flip-+
4×sqrt-div insert-posit16 div-inv add-log-exp
3×*-commutative
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 125
Calls
4 calls:
Slowest
255.0ms
(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
134.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
48.0ms
(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
14.0ms
(* (cos (/ K 2)) (* -2 J))

series606.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
161.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
148.0ms
(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
75.0ms
(* (cos (/ K 2)) (* -2 J))

simplify1.3s

Counts
137 → 137

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.7b

localize49.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
8.1b
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
8.1b
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 76
Calls
4 calls:
Slowest
102.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
89.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
87.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
78.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

series870.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
303.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
279.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
147.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
142.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify781.0ms

Counts
88 → 88

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.7b

localize116.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
8.1b
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
14×add-sqr-sqrt
10×sqrt-div
9×pow1 *-un-lft-identity add-cube-cbrt
7×sqrt-pow1
5×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 70
Calls
4 calls:
Slowest
88.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
78.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
78.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
72.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
157.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
140.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
125.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify775.0ms

Counts
82 → 82

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.7b

localize83.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
10.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
8.4b
(cbrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

rewrite314.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
7×pow1
6×cbrt-prod
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 65
Calls
4 calls:
Slowest
119.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
83.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
73.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
36.0ms
(cbrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

series745.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(cbrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
178.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
162.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
137.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify5.0s

Counts
77 → 77

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 10.7b

regimes485.0ms

Accuracy

6.1% (8.2b remaining)

Error of 16.5b against oracle of 8.4b and baseline of 17.1b

bsearch422.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.0s1549×body1280valid
1.6s1239×body640valid
1.3s4264×body80valid
447.0ms651×body320valid
151.0ms302×body160valid