Details

Time bar (total: 25.1s)

sample173.0ms

Algorithm
intervals
Results
56.0ms46×body1280valid
45.0ms40×body640valid
33.0ms141×body80valid
14.0ms19×body320valid
5.0ms10×body160valid

simplify936.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize40.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
7.6b
(* (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))

rewrite398.0ms

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
197.0ms
(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
89.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
81.0ms
(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
27.0ms
(* (cos (/ K 2)) (* -2 J))

series534.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(* (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
157.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
131.0ms
(* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2)))))
55.0ms
(* (cos (/ K 2)) (* -2 J))

simplify1.1s

Counts
137 → 137

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize46.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
7.6b
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
7.6b
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

rewrite353.0ms

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
92.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
88.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
87.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
84.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

series805.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
242.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
236.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
182.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
145.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify731.0ms

Counts
88 → 88

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize66.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
7.6b
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))

rewrite324.0ms

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
96.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
80.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
74.0ms
(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)))

series709.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(sqrt (sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1)))
167.0ms
(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))
140.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify814.0ms

Counts
82 → 82

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.8b

localize90.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

rewrite368.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×rem-sqrt-square sqrt-pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 64
Calls
4 calls:
Slowest
118.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
94.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
81.0ms
(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))

series643.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
163.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
161.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))
153.0ms
(sqrt (+ (* (/ U (* (+ J J) (cos (/ K 2)))) (/ U (* (+ J J) (cos (/ K 2))))) 1))

simplify3.6s

Counts
76 → 76

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.8b

regimes540.0ms

Accuracy

7.1% (7.6b remaining)

Error of 16.3b against oracle of 8.7b and baseline of 16.9b

bsearch748.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.1s1526×body1280valid
1.3s1206×body640valid
1.2s4301×body80valid
553.0ms330×body160valid
470.0ms641×body320valid