Details

Time bar (total: 1.6m)

sample157.0ms

Algorithm
intervals
Results
61.0ms51×body640valid
40.0ms42×body1280valid
25.0ms136×body80valid
10.0ms18×body320valid
3.0ms9×body160valid

simplify243.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
243.0ms
(* (* (* -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: 18.3b

localize58.0ms

Local error

Found 4 expressions with local error:

9.2b
(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)) -2) (* (cos (/ K 2)) J))
0.3b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.1b
(* (cos (/ K 2)) J)

rewrite667.0ms

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
Counts
4 → 131
Calls
4 calls:
Slowest
372.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
171.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
114.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
7.0ms
(* (cos (/ K 2)) J)

series507.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
143.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
108.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
53.0ms
(* (cos (/ K 2)) J)

simplify44.8s

Counts
113 → 143
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)))))
2.0s
(* (/ (* (* 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)))))
2.0s
(* (/ (* (* 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)))))
1.9s
(* (/ (* (* 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)))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

localize57.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
9.2b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
9.2b
(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)) -2) (* (cos (/ K 2)) J))

rewrite859.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
16×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×sqrt-prod
8×sqrt-div pow-prod-down prod-exp cbrt-unprod
7×*-un-lft-identity add-cube-cbrt
4×flip3-+ associate-*l/ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*r* associate-*l* *-commutative
Counts
4 → 73
Calls
4 calls:
Slowest
401.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
172.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
146.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
138.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series655.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
157.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
154.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
139.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify13.6s

Counts
48 → 85
Calls
48 calls:
Slowest
756.0ms
(* (* (sqrt (+ (pow (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 3) (pow 1 3))) -2) (* (cos (/ K 2)) J))
504.0ms
(+ (log (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (+ (log (cos (/ K 2))) (log J)))
499.0ms
(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))))
483.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
469.0ms
(+ (log (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (log (* (cos (/ K 2)) J)))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

localize103.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
9.2b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
9.2b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
9.2b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

rewrite568.0ms

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
165.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
143.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
130.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
128.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series483.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
122.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
120.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
117.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify8.7s

Counts
40 → 76
Calls
40 calls:
Slowest
451.0ms
(+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)
428.0ms
(+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)
427.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
421.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
390.0ms
(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))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.9b

localize58.0ms

Local error

Found 4 expressions with local error:

9.2b
(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)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
0.6b
(cbrt J)
0.6b
(cbrt J)

rewrite640.0ms

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
Counts
4 → 77
Calls
4 calls:
Slowest
468.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
169.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)
1.0ms
(cbrt J)

series951.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(cbrt J)
291.0ms
(cbrt J)
250.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))
102.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify11.6s

Counts
53 → 89
Calls
53 calls:
Slowest
713.0ms
(* (* (* (* (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))
648.0ms
(* (* (* (* (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))))
620.0ms
(* (* (* (* (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))
620.0ms
(* (* (* (* (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))))
596.0ms
(* (* (* (* (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

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.8b

regimes496.0ms

Accuracy

7.9% (7.5b remaining)

Error of 15.9b against oracle of 8.4b and baseline of 16.6b

bsearch560.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.0s1434×body1280valid
1.5s1210×body640valid
1.2s4413×body80valid
510.0ms635×body320valid
127.0ms312×body160valid