Details

Time bar (total: 1.9m)

sample159.0ms

Algorithm
intervals
Results
65.0ms40×body1280valid
36.0ms44×body640valid
26.0ms142×body80valid
11.0ms20×body320valid
4.0ms10×body160valid

simplify626.0ms

Calls
1 calls:
Slowest
626.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize43.0ms

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)

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
98×add-cbrt-cube add-exp-log
49×prod-exp cbrt-unprod
26×pow1
24×cbrt-undiv div-exp
20×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
12×times-frac
11×associate-*r* associate-*l*
10×pow-prod-down
7×swap-sqr
5×associate-*l/
4×sqrt-div insert-posit16 div-inv add-log-exp
3×*-commutative sqrt-prod
2×flip3-+ flip-+ unswap-sqr
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up
Calls
4 calls:
Slowest
338.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
129.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
118.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
7.0ms
(* (cos (/ K 2)) J)

series530.0ms

Calls
4 calls:
Slowest
210.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
127.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
124.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
68.0ms
(* (cos (/ K 2)) J)

simplify45.2s

Calls
113 calls:
Slowest
2.4s
(* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.3s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.2s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))
1.8s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))))
1.8s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.0b

localize58.0ms

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)) (* (cbrt J) (cbrt J))) (cbrt J)))
0.6b
(cbrt J)
0.6b
(cbrt J)

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
37×pow1
36×add-exp-log
26×add-cbrt-cube
24×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
4×sqrt-div associate-*l/ insert-posit16 add-log-exp
3×sqrt-prod
2×flip3-+ pow1/3 flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative
Calls
4 calls:
Slowest
600.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
122.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)
1.0ms
(cbrt J)

series963.0ms

Calls
4 calls:
Slowest
287.0ms
(cbrt J)
277.0ms
(cbrt J)
273.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
126.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify11.3s

Calls
53 calls:
Slowest
738.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))
707.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J)))) J))
657.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (* (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))
641.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) J))
601.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (* (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) J))

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.0b

localize49.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
5.3b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
3.7b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
0.6b
(cbrt J)

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
55×pow1
54×add-exp-log
39×add-cbrt-cube
37×pow-prod-down prod-exp cbrt-unprod
10×associate-*l/
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×associate-*r*
6×cbrt-prod sqrt-div
4×insert-posit16 add-log-exp
3×flip3-+ sqrt-prod flip-+
2×associate-*l* *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Calls
4 calls:
Slowest
1.6s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
356.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
162.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)

series1.1s

Calls
4 calls:
Slowest
383.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
294.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
279.0ms
(cbrt J)
115.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify20.9s

Calls
74 calls:
Slowest
993.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))))
762.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J))))) J)
760.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))) J)
689.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))) (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))) J)
679.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J))))) J)

prune1.7s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 9.0b

localize44.0ms

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)))

rewrite588.0ms

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
Calls
4 calls:
Slowest
161.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
160.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
133.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
133.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

series764.0ms

Calls
4 calls:
Slowest
255.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
249.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
137.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
124.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify14.9s

Calls
52 calls:
Slowest
771.0ms
(exp (* 1/4 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ 1 J)))) (* 2 (log (/ 1 U))))))
518.0ms
(exp (* 1/4 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))
484.0ms
(sqrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
483.0ms
(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)))))
462.0ms
(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)))))

prune1.6s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 8.9b

regimes624.0ms

Accuracy

18% (7.3b remaining)

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

bsearch413.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.5s1526×body1280valid
1.4s1294×body640valid
1.1s4261×body80valid
484.0ms619×body320valid
137.0ms302×body160valid