Details

Time bar (total: 24.9s)

sample183.0ms

Algorithm
intervals
Results
66.0ms55×body1280valid
44.0ms132×body80valid
39.0ms42×body640valid
11.0ms16×body320valid
6.0ms12×body160valid

simplify200.0ms

Calls
1 calls:
Slowest
200.0ms
(* (* (* -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: 7.2b

localize27.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (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)))

rewrite40.0ms

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
18.0ms
(* (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)))

series587.0ms

Calls
4 calls:
Slowest
352.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (cos (/ K 2)) J)))
119.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))
62.0ms
(* (cos (/ K 2)) J)
53.0ms
(* (cos (/ K 2)) J)

simplify1.7s

Calls
23 calls:
Slowest
312.0ms
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
215.0ms
(* (* (* (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))))
192.0ms
(- J (* 1/8 (* (pow K 2) J)))
165.0ms
(- (+ (* 2 J) (* 1/4 (/ (pow U 2) J))))
164.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (cos (/ K 2)) J))))

prune944.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize22.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
7.2b
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
0.1b
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))
0.1b
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))))

rewrite85.0ms

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
55.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))))
25.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))
2.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
2.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

series1.3s

Calls
4 calls:
Slowest
369.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J)))
365.0ms
(* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* (sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (* -2 (* (cos (/ K 2)) J))))
310.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))
246.0ms
(sqrt (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))))

simplify3.6s

Calls
41 calls:
Slowest
332.0ms
(* (* (* (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)))))
307.0ms
(* (* (* (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)))))
305.0ms
(+ (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)))))
249.0ms
(* (* (* (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))))
223.0ms
(- (+ (* 2 J) (* 1/8 (/ (pow U 2) J))))

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.9b

localize31.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))

rewrite99.0ms

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
96.0ms
(* (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)))

series772.0ms

Calls
4 calls:
Slowest
317.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
170.0ms
(cbrt (cos (/ K 2)))
147.0ms
(cbrt (cos (/ K 2)))
138.0ms
(cbrt (cos (/ K 2)))

simplify2.4s

Calls
27 calls:
Slowest
577.0ms
(* (* (* (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)))))
430.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
363.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))))
213.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
184.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize24.0ms

Local error

Found 4 expressions with local error:

7.1b
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
0.5b
(expm1 (cbrt (cos (/ K 2))))
0.4b
(cbrt (cos (/ K 2)))
0.4b
(cbrt (cos (/ K 2)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 add-cbrt-cube add-exp-log
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*l*
2×pow1/3
1×expm1-log1p associate-*r* pow-prod-down prod-exp *-commutative cbrt-unprod expm1-udef
Calls
4 calls:
Slowest
69.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (log1p (expm1 (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)))
0.0ms
(expm1 (cbrt (cos (/ K 2))))

series1.2s

Calls
4 calls:
Slowest
570.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
317.0ms
(expm1 (cbrt (cos (/ K 2))))
182.0ms
(cbrt (cos (/ K 2)))
168.0ms
(cbrt (cos (/ K 2)))

simplify1.9s

Calls
25 calls:
Slowest
483.0ms
(* (* (* (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 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))) (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))) (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))))
241.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
219.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (* (log1p (expm1 (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))))
192.0ms
(- E (+ (* 1/24 (* (pow K 2) E)) (+ (* 13/414720 (* (pow K 6) E)) 1)))
183.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

regimes471.0ms

Accuracy

0% (3.8b remaining)

Error of 7.5b against oracle of 3.7b and baseline of 7.5b

bsearch3.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.0s1513×body1280valid
2.0s1258×body640valid
981.0ms4289×body80valid
403.0ms636×body320valid
118.0ms307×body160valid