Details

Time bar (total: 2.4m)

sample174.0ms

Algorithm
intervals
Results
64.0ms42×body1280valid
38.0ms41×body640valid
35.0ms142×body80valid
12.0ms18×body320valid
6.0ms13×body160valid

simplify246.0ms

Calls
1 calls:
Slowest
246.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize59.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.4b
(* (* (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)

rewrite689.0ms

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
362.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
183.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
133.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
8.0ms
(* (cos (/ K 2)) J)

series584.0ms

Calls
4 calls:
Slowest
235.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
145.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
137.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
67.0ms
(* (cos (/ K 2)) J)

simplify45.1s

Calls
113 calls:
Slowest
2.2s
(* (/ (* (* 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)))))
2.2s
(* (/ (* (* 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)))))
2.2s
(* (/ (* (* 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)))))
2.0s
(* (/ (* (* 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)))))
1.8s
(* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize70.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.4b
(* (* (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)

rewrite678.0ms

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
327.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (* 1/2 K)) J))
180.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
153.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
15.0ms
(* (cos (* 1/2 K)) J)

series533.0ms

Calls
4 calls:
Slowest
191.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (* 1/2 K)) J))
155.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
122.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
64.0ms
(* (cos (* 1/2 K)) J)

simplify46.2s

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)) 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)))))
2.1s
(* (/ (* (* 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)))))
2.0s
(* (/ (* (* 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)))))
1.9s
(* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize40.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.4b
(* (* (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)

rewrite740.0ms

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
575.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
163.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)
1.0ms
(cbrt J)

series961.0ms

Calls
4 calls:
Slowest
304.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
270.0ms
(cbrt J)
267.0ms
(cbrt J)
121.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify11.5s

Calls
53 calls:
Slowest
758.0ms
(* (* (* (* (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))
756.0ms
(* (* (* (* (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))))
730.0ms
(* (* (* (* (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))))
708.0ms
(* (* (* (* (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))
649.0ms
(* (* (* (* (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))

prune1.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.4b

localize83.0ms

Local error

Found 4 expressions with local error:

8.4b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.4b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J)))
0.6b
(cbrt J)
0.6b
(cbrt J)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
50×pow1
49×add-exp-log
35×pow-prod-down prod-exp cbrt-unprod
33×add-cbrt-cube
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
1.1s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J)))
214.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)
1.0ms
(cbrt J)

series951.0ms

Calls
4 calls:
Slowest
296.0ms
(cbrt J)
283.0ms
(cbrt J)
240.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J)))
133.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify18.7s

Calls
59 calls:
Slowest
1.3s
(* (* (* (* (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 (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J)))))) (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J)))))) J))
1.2s
(* (* (* (* (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 (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J)) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J))) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J))))
1.1s
(* (* (* (* (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 (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J)))))) (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J)))))) J))
1.1s
(* (* (* (* (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 (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J)) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J))) (* (* (cos (/ K 2)) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (cbrt J))))
1.1s
(* (* (* (* (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 (* (cbrt J) (cbrt J))) (cbrt (cbrt J)))) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J))))) (* (cbrt J) (* (cbrt (* (cbrt J) (cbrt J))) (cbrt (cbrt J)))))) J))

prune1.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.4b

regimes838.0ms

Accuracy

5.9% (8.1b remaining)

Error of 16.6b against oracle of 8.5b and baseline of 17.1b

bsearch699.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.8s1479×body1280valid
1.5s1292×body640valid
1.1s4304×body80valid
457.0ms602×body320valid
151.0ms324×body160valid