Details

Time bar (total: 25.2s)

sample143.0ms

Algorithm
intervals
Results
39.0ms40×body1280valid
36.0ms44×body640valid
34.0ms142×body80valid
11.0ms20×body320valid
5.0ms10×body160valid

simplify185.0ms

Calls
1 calls:
Slowest
185.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize24.0ms

Local error

Found 4 expressions with local error:

8.7b
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (cos (/ K 2)) J)))
0.1b
(* (cos (/ K 2)) J)
0.1b
(* (cos (/ K 2)) J)
0.1b
(/ U (* 2 (* (cos (/ K 2)) J)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
9×associate-*l*
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
1×clear-num associate-/r* frac-2neg associate-*r* pow-prod-down prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
17.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (cos (/ K 2)) J)))
8.0ms
(* (cos (/ K 2)) J)
8.0ms
(* (cos (/ K 2)) J)
5.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

series589.0ms

Calls
4 calls:
Slowest
380.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (cos (/ K 2)) J)))
84.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))
77.0ms
(* (cos (/ K 2)) J)
47.0ms
(* (cos (/ K 2)) J)

simplify1.7s

Calls
23 calls:
Slowest
282.0ms
(* (* (* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (* (* -2 (* (cos (/ K 2)) J)) (* -2 (* (cos (/ K 2)) J))) (* -2 (* (cos (/ K 2)) J))))
234.0ms
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
203.0ms
(- J (* 1/8 (* (pow K 2) J)))
193.0ms
(- (+ (* 2 J) (* 1/4 (/ (pow U 2) J))))
164.0ms
(- J (* 1/8 (* (pow K 2) J)))

prune846.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 4 expressions with local error:

8.8b
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
8.8b
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
0.2b
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))
0.2b
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l* sqrt-prod
11×pow1 add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2 associate-*r* *-commutative
Calls
4 calls:
Slowest
28.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))))
12.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))
1.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
1.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

series1.1s

Calls
4 calls:
Slowest
310.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))))
286.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))
268.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
238.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

simplify3.5s

Calls
41 calls:
Slowest
354.0ms
(* (* (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (* (* (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))))
335.0ms
(* (* (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (* (* (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (* (* (* -2 (* (cos (/ K 2)) J)) (* -2 (* (cos (/ K 2)) J))) (* -2 (* (cos (/ K 2)) J)))))
290.0ms
(+ (log (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (+ (log (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (log (* -2 (* (cos (/ K 2)) J)))))
272.0ms
(+ (log (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (log (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))))
253.0ms
(* (* (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))) (* (* (* -2 (* (cos (/ K 2)) J)) (* -2 (* (cos (/ K 2)) J))) (* -2 (* (cos (/ K 2)) J))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.2b

localize46.0ms

Local error

Found 4 expressions with local error:

9.1b
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
9.1b
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
9.1b
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
8.8b
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
2.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
1.0ms
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
1.0ms
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
1.0ms
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

series1.3s

Calls
4 calls:
Slowest
343.0ms
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
343.0ms
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
327.0ms
(cbrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
263.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

simplify2.4s

Calls
25 calls:
Slowest
378.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
377.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
334.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
242.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))
226.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.2b

localize30.0ms

Local error

Found 4 expressions with local error:

8.7b
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
87.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series841.0ms

Calls
4 calls:
Slowest
361.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
188.0ms
(cbrt (cos (/ K 2)))
158.0ms
(cbrt (cos (/ K 2)))
133.0ms
(cbrt (cos (/ K 2)))

simplify2.2s

Calls
27 calls:
Slowest
545.0ms
(* (* (* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (* (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))))
397.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
317.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))))
193.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
164.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune945.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.2b

regimes942.0ms

Accuracy

0% (4.0b remaining)

Error of 7.8b against oracle of 3.8b and baseline of 7.8b

bsearch2.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.1s1526×body1280valid
1.5s4261×body80valid
1.3s1294×body640valid
461.0ms619×body320valid
126.0ms302×body160valid