Details

Time bar (total: 54.3s)

sample212.0ms

Algorithm
intervals
Results
68.0ms44×body640valid
60.0ms40×body1280valid
38.0ms142×body80valid
16.0ms20×body320valid
6.0ms10×body160valid

simplify648.0ms

Calls
1 calls:
Slowest
648.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize45.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.7b
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.1b
(* (cos (/ K 2)) J)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
13×associate-*l*
11×add-sqr-sqrt pow1
10×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×sqrt-prod
5×associate-*r*
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l/ *-commutative
2×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ div-inv
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*r/ pow-prod-up
Calls
4 calls:
Slowest
36.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
18.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
14.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
4.0ms
(* (cos (/ K 2)) J)

series554.0ms

Calls
4 calls:
Slowest
217.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
144.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
120.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
73.0ms
(* (cos (/ K 2)) J)

simplify8.4s

Calls
47 calls:
Slowest
646.0ms
(+ (log (/ U (* 2 (* (cos (/ K 2)) J)))) (log (/ U (* 2 (* (cos (/ K 2)) J)))))
454.0ms
(* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))
425.0ms
(+ (log (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (log (* -2 (* (cos (/ K 2)) J))))
384.0ms
(sqrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
382.0ms
(* (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.0b

localize29.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.7b
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (* 1/2 K)) J)))
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.1b
(* (cos (* 1/2 K)) J)

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
13×associate-*l*
11×add-sqr-sqrt pow1
10×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×sqrt-prod
5×associate-*r*
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l/ *-commutative
2×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ div-inv
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*r/ pow-prod-up
Calls
4 calls:
Slowest
51.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (* 1/2 K)) J)))
27.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
24.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
5.0ms
(* (cos (* 1/2 K)) J)

series478.0ms

Calls
4 calls:
Slowest
182.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (* 1/2 K)) J)))
118.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
103.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
74.0ms
(* (cos (* 1/2 K)) J)

simplify8.6s

Calls
47 calls:
Slowest
785.0ms
(+ (log (/ U (* 2 (* (cos (/ K 2)) J)))) (log (/ U (* 2 (* (cos (/ K 2)) J)))))
456.0ms
(* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))
434.0ms
(+ (log (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (log (* -2 (* (cos (* 1/2 K)) J))))
407.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
407.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (* 1/2 K)) J)))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 9.0b

localize12.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.8b
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
8.8b
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×*-un-lft-identity add-cube-cbrt
6×rem-sqrt-square
4×pow1 flip3-+ add-cbrt-cube pow1/2 add-exp-log flip-+ insert-posit16 add-log-exp
Calls
4 calls:
Slowest
23.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
16.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
15.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
14.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series765.0ms

Calls
4 calls:
Slowest
286.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
253.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
119.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
106.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify11.2s

Calls
44 calls:
Slowest
770.0ms
(sqrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
468.0ms
(sqrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
461.0ms
(sqrt (* (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))
437.0ms
(sqrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
422.0ms
(sqrt (* (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 9.0b

localize22.0ms

Local error

Found 4 expressions with local error:

14.6b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
14.6b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
14.6b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
10.2b
(sqrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
9×cbrt-prod flip3-+ flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×associate-*l/ associate-*r/
1×rem-sqrt-square pow1/2 sqrt-prod
Calls
4 calls:
Slowest
8.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
7.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
5.0ms
(sqrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))

series994.0ms

Calls
4 calls:
Slowest
275.0ms
(sqrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
267.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
238.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
214.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify9.8s

Calls
37 calls:
Slowest
488.0ms
(cbrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
442.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
420.0ms
(exp (* 1/3 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))
416.0ms
(sqrt (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
415.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.0b

regimes605.0ms

Accuracy

18% (7.3b remaining)

Error of 15.9b against oracle of 8.6b and baseline of 17.5b

bsearch393.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.4s1526×body1280valid
1.9s1294×body640valid
1.0s4261×body80valid
495.0ms619×body320valid
132.0ms302×body160valid