Details

Time bar (total: 2.5m)

sample216.0ms

Algorithm
intervals
Results
75.0ms50×body1280valid
47.0ms139×body80valid
46.0ms40×body640valid
18.0ms21×body320valid
3.0ms6×body160valid

simplify329.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
328.0ms
(* (* (* -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: 15.6b

localize60.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
6.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.2b
(* (cos (/ K 2)) J)

rewrite651.0ms

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
391.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
147.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
103.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
6.0ms
(* (cos (/ K 2)) J)

series550.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
134.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
126.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
53.0ms
(* (cos (/ K 2)) J)

simplify44.2s

Counts
113 → 143
Calls
113 calls:
Slowest
2.3s
(* (/ (* (* 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)))))
2.2s
(* (/ (* (* 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)))))
2.1s
(* (/ (* (* 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 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))
1.5s
(* (/ (* (* 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)))))

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.1b

localize38.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
6.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.2b
(* (cos (/ K 2)) J)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
95×add-cbrt-cube add-exp-log
47×prod-exp cbrt-unprod
24×cbrt-undiv div-exp
23×pow1
21×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
13×associate-*r*
12×times-frac
11×associate-*l*
8×pow-prod-down
7×swap-sqr 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 → 130
Calls
4 calls:
Slowest
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
147.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
94.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
14.0ms
(* (cos (/ K 2)) J)

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
169.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
126.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
52.0ms
(* (cos (/ K 2)) J)

simplify44.3s

Counts
112 → 142
Calls
112 calls:
Slowest
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 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) 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 (* (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)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))

prune2.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 8.1b

localize106.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
8.6b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
8.6b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
6.9b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

rewrite4.0s

Algorithm
rewrite-expression-head
Rules
32×pow1
31×add-cbrt-cube add-exp-log
18×pow-prod-down associate-*l/ prod-exp cbrt-unprod
9×add-sqr-sqrt associate-*r*
8×*-un-lft-identity sqrt-div add-cube-cbrt
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×associate-*l* *-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 88
Calls
4 calls:
Slowest
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
133.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series848.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
228.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
223.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
123.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify19.1s

Counts
61 → 100
Calls
61 calls:
Slowest
876.0ms
(* (* (* (* (* (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)))) (* (* J J) J))
585.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
539.0ms
(+ (+ (log (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (log (cos (/ K 2)))) (log J))
530.0ms
(+ (log (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2)))) (log J))
526.0ms
(* (* (* (* (* (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)))) (* (* J J) J))

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.0b

localize119.0ms

Local error

Found 4 expressions with local error:

8.8b
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
8.8b
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
8.8b
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
8.6b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
13×pow1 add-cbrt-cube add-exp-log
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×sqrt-prod
8×sqrt-div
6×cbrt-div pow-prod-down associate-*l/ prod-exp cbrt-unprod
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×pow1/3 associate-*r*
1×associate-*l* *-commutative
Counts
4 → 75
Calls
4 calls:
Slowest
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
98.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
78.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
64.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

series957.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
259.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
243.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
235.0ms
(cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
220.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)

simplify14.6s

Counts
50 → 87
Calls
50 calls:
Slowest
733.0ms
(* (* (* (sqrt (+ (pow (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 3) (pow 1 3))) -2) (cos (/ K 2))) J)
527.0ms
(cbrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
475.0ms
(cbrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
459.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
459.0ms
(+ (+ (log (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (log (cos (/ K 2)))) (log J))

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 8.0b

regimes652.0ms

Accuracy

-1.8% (8.7b remaining)

Error of 17.3b against oracle of 8.6b and baseline of 17.1b

bsearch451.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.0s1490×body1280valid
1.7s1231×body640valid
1.6s4372×body80valid
516.0ms622×body320valid
167.0ms288×body160valid