Details

Time bar (total: 2.3m)

sample251.0ms

Algorithm
intervals
Results
75.0ms130×body80valid
72.0ms47×body1280valid
52.0ms45×body640valid
18.0ms22×body320valid
7.0ms12×body160valid

simplify270.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
270.0ms
(* (* (* -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: 17.2b

localize64.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.5b
(* (* (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)

rewrite588.0ms

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
319.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
138.0ms
(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))))
10.0ms
(* (cos (/ K 2)) J)

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
142.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
121.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
69.0ms
(* (cos (/ K 2)) J)

simplify45.8s

Counts
113 → 143
Calls
113 calls:
Slowest
2.6s
(* (/ (* (* 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)))))
2.4s
(* (/ (* (* 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)))))
2.0s
(* (/ (* (* 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)))))
1.9s
(* (/ (* (* 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)))))
1.7s
(* (/ (* (* 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)))))

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.3b

localize46.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.5b
(* (* (* (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)

rewrite1.6s

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)
157.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
136.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
7.0ms
(* (cos (/ K 2)) J)

series593.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
148.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
147.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
57.0ms
(* (cos (/ K 2)) J)

simplify43.8s

Counts
112 → 142
Calls
112 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)))))
2.0s
(* (/ (* (* 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 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 (* 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)))))

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.3b

localize81.0ms

Local error

Found 4 expressions with local error:

15.8b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
15.8b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
15.8b
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
10.1b
(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))))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
Slowest
159.0ms
(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))))
60.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
49.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
47.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
294.0ms
(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))))
274.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
240.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
231.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify13.6s

Counts
46 → 82
Calls
46 calls:
Slowest
490.0ms
(cbrt (* (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))))
472.0ms
(cbrt (* (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))))
469.0ms
(exp (* 1/3 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))
456.0ms
(cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
442.0ms
(exp (* 1/3 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))

prune2.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.3b

localize57.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1))
6.5b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2) (cos (/ K 2))) J)
0.6b
(cbrt J)
0.6b
(cbrt J)

rewrite7.5s

Algorithm
rewrite-expression-head
Rules
14×pow1
13×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow-prod-down associate-*l/ prod-exp cbrt-unprod
4×sqrt-div insert-posit16 add-log-exp
3×associate-*r* sqrt-prod
2×flip3-+ pow1/3 flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 64
Calls
4 calls:
Slowest
6.7s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2) (cos (/ K 2))) J)
822.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1))
1.0ms
(cbrt J)
1.0ms
(cbrt J)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
308.0ms
(cbrt J)
299.0ms
(cbrt J)
297.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2) (cos (/ K 2))) J)
153.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1))

simplify9.7s

Counts
39 → 76
Calls
39 calls:
Slowest
1.2s
(* (* (* (sqrt (+ (pow (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 3) (pow 1 3))) -2) (cos (/ K 2))) J)
906.0ms
(* (* (* (sqrt (- (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))))) (* 1 1))) -2) (cos (/ K 2))) J)
844.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1))) (* (* -2 -2) -2)) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))) (* (* J J) J))
781.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2)) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2)) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))) (* (* J J) J))
739.0ms
(sqrt (- (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J)))))) (* 1 1)))

prune1.2s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 8.3b

regimes681.0ms

Accuracy

7.7% (7.7b remaining)

Error of 16.0b against oracle of 8.3b and baseline of 16.7b

bsearch249.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.8s1558×body1280valid
1.4s1248×body640valid
1.0s4247×body80valid
424.0ms605×body320valid
267.0ms344×body160valid