Details

Time bar (total: 2.4m)

sample177.0ms

Algorithm
intervals
Results
74.0ms48×body1280valid
39.0ms45×body640valid
27.0ms127×body80valid
17.0ms27×body320valid
4.0ms9×body160valid

simplify208.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
208.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize59.0ms

Local error

Found 4 expressions with local error:

9.1b
(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)

rewrite621.0ms

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
309.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
163.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
131.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
13.0ms
(* (cos (/ K 2)) J)

series630.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
241.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
164.0ms
(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))))
72.0ms
(* (cos (/ K 2)) J)

simplify46.9s

Counts
113 → 143
Calls
113 calls:
Slowest
2.4s
(* (/ (* (* 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)))))
2.3s
(* (/ (* (* 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)))))
2.1s
(* (/ (* (* 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)))))
1.8s
(* (* (* (/ 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)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.8b

localize46.0ms

Local error

Found 4 expressions with local error:

9.1b
(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)

rewrite647.0ms

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
379.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (* 1/2 K)) J))
142.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
101.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
21.0ms
(* (cos (* 1/2 K)) J)

series581.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (* 1/2 K)) J))
148.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
116.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
57.0ms
(* (cos (* 1/2 K)) J)

simplify46.8s

Counts
113 → 143
Calls
113 calls:
Slowest
2.4s
(* (/ (* (* 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)))))
2.3s
(* (/ (* (* 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)))))
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)))))
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)))))

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.8b

localize43.0ms

Local error

Found 4 expressions with local error:

9.1b
(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) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))
0.6b
(cbrt (* (cos (/ K 2)) J))
0.6b
(cbrt (* (cos (/ K 2)) J))

rewrite558.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1
25×add-exp-log
17×add-cbrt-cube
15×pow-prod-down prod-exp cbrt-unprod
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×sqrt-div associate-*l/ insert-posit16 add-log-exp
3×sqrt-prod
2×cbrt-prod flip3-+ pow1/3 flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 67
Calls
4 calls:
Slowest
432.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))
118.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
3.0ms
(cbrt (* (cos (/ K 2)) J))
3.0ms
(cbrt (* (cos (/ K 2)) J))

series667.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))
150.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
143.0ms
(cbrt (* (cos (/ K 2)) J))
120.0ms
(cbrt (* (cos (/ K 2)) J))

simplify14.9s

Counts
43 → 79
Calls
43 calls:
Slowest
648.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))
646.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))
633.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))
619.0ms
(+ (+ (log (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (log -2)) (log (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J)))))
589.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (cbrt (* (cos (/ K 2)) J))))

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.7b

localize69.0ms

Local error

Found 4 expressions with local error:

9.1b
(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) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J))))
0.6b
(cbrt J)
0.6b
(cbrt (* (cos (/ K 2)) J))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
46×pow1
45×add-exp-log
31×pow-prod-down prod-exp cbrt-unprod
29×add-cbrt-cube
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×cbrt-prod 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 → 81
Calls
4 calls:
Slowest
461.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J))))
154.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
7.0ms
(cbrt (* (cos (/ K 2)) J))
1.0ms
(cbrt J)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
535.0ms
(cbrt (* (cos (/ K 2)) J))
282.0ms
(cbrt J)
255.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J))))
146.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify16.0s

Counts
57 → 93
Calls
57 calls:
Slowest
1.0s
(* (* (* (* (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)) (* (* (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J)))) (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J)))) (* (* (* (cbrt (cos (/ K 2))) (cbrt J)) (* (cbrt (cos (/ K 2))) (cbrt J))) (* (cbrt (cos (/ K 2))) (cbrt J)))))
984.0ms
(* (* (* (* (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)) (* (* (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J))) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J)))) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J)))))
972.0ms
(* (* (* (* (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)) (* (* (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J))) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J)))) (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (cos (/ K 2))) (cbrt J)))))
972.0ms
(* (* (* (* (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)) J) (* (cos (/ K 2)) J)) (* (* (* (cbrt (cos (/ K 2))) (cbrt J)) (* (cbrt (cos (/ K 2))) (cbrt J))) (* (cbrt (cos (/ K 2))) (cbrt J)))))
965.0ms
(* (* (* (* (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)) (* (* (* (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J))) (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J)))) (* (cbrt (* (cos (/ K 2)) J)) (cbrt (* (cos (/ K 2)) J)))) (* (* (* (cbrt (cos (/ K 2))) (cbrt J)) (* (cbrt (cos (/ K 2))) (cbrt J))) (* (cbrt (cos (/ K 2))) (cbrt J)))))

prune1.5s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 9.7b

regimes767.0ms

Accuracy

6.5% (8.2b remaining)

Error of 16.7b against oracle of 8.5b and baseline of 17.2b

bsearch693.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.4s1516×body1280valid
1.4s4297×body80valid
1.4s1233×body640valid
518.0ms619×body320valid
166.0ms335×body160valid