Details

Time bar (total: 1.9m)

sample418.0ms

Algorithm
intervals
Results
249.0ms46×body1280valid
40.0ms146×body80valid
35.0ms32×body640valid
19.0ms23×body320valid
5.0ms9×body160valid

simplify324.0ms

Calls
1 calls:
Slowest
324.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize165.0ms

Local error

Found 4 expressions with local error:

12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.2b
(* (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
(/ U (* 2 (* (cos (/ K 2)) J)))

rewrite985.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt associate-*l*
9×*-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/ div-inv
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
1×pow2 frac-times rem-sqrt-square clear-num associate-/r* frac-2neg pow-plus pow1/2 associate-*r/ pow-prod-up
Calls
4 calls:
Slowest
54.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
49.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
21.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
4.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

series512.0ms

Calls
4 calls:
Slowest
194.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
114.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
112.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
92.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

simplify17.7s

Calls
46 calls:
Slowest
1.8s
(+ (log (/ U (* 2 (* (cos (/ K 2)) J)))) (log (/ U (* 2 (* (cos (/ K 2)) J)))))
1.3s
(* (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))))
1.3s
(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))))
956.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
863.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.0b

localize22.0ms

Local error

Found 4 expressions with local error:

12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.2b
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
6.2b
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

rewrite117.0ms

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
31.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
29.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
28.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
27.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

series709.0ms

Calls
4 calls:
Slowest
243.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
238.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
114.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
114.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify24.7s

Calls
44 calls:
Slowest
1.5s
(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))))
1.4s
(sqrt (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)))))
1.4s
(sqrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
1.2s
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
1.1s
(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)))))

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.0b

localize51.0ms

Local error

Found 4 expressions with local error:

17.5b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
17.5b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
17.5b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
27.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
18.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
15.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
14.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series952.0ms

Calls
4 calls:
Slowest
326.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
262.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
252.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
112.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify15.5s

Calls
33 calls:
Slowest
1.6s
(sqrt (+ (pow (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 3) (pow 1 3)))
1.4s
(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))))
1.1s
(exp (* 1/3 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))
906.0ms
(exp (* 1/3 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))
752.0ms
(exp (* 1/3 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))

prune3.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.0b

localize31.0ms

Local error

Found 4 expressions with local error:

12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
12.5b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.2b
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×pow1 add-cbrt-cube associate-*l* add-exp-log
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square pow1/2
2×associate-*l/
1×associate-*r* pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
138.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
34.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
28.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
26.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series772.0ms

Calls
4 calls:
Slowest
368.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
187.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
111.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
105.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify20.2s

Calls
41 calls:
Slowest
1.7s
(+ (log (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (log (* -2 (* (cos (/ K 2)) J))))
1.6s
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
1.3s
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
1.2s
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0s
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

prune2.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.0b

regimes1.1s

Accuracy

7.8% (8.0b remaining)

Error of 16.5b against oracle of 8.5b and baseline of 17.2b

bsearch521.0ms

end0.0ms

sample21.0s

Algorithm
intervals
Results
7.5s1470×body1280valid
4.6s4321×body80valid
4.5s1249×body640valid
3.7s638×body320valid
266.0ms324×body160valid