Details

Time bar (total: 23.7s)

sample190.0ms

Algorithm
intervals
Results
64.0ms44×body1280valid
49.0ms146×body80valid
36.0ms37×body640valid
21.0ms25×body320valid
2.0ms4×body160valid

simplify210.0ms

Calls
1 calls:
Slowest
210.0ms
(* (* (* -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: 8.3b

localize50.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (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)))

rewrite45.0ms

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
23.0ms
(* (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)))

series416.0ms

Calls
4 calls:
Slowest
266.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (cos (/ K 2)) J)))
76.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))
41.0ms
(* (cos (/ K 2)) J)
32.0ms
(* (cos (/ K 2)) J)

simplify1.7s

Calls
23 calls:
Slowest
274.0ms
(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
246.0ms
(* (* (* (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))))
188.0ms
(- J (* 1/8 (* (pow K 2) J)))
171.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (cos (/ K 2)) J))))
170.0ms
(- J (* 1/8 (* (pow K 2) J)))

prune992.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize15.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (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)))

rewrite62.0ms

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
59.0ms
(* (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)))

series634.0ms

Calls
4 calls:
Slowest
202.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
150.0ms
(cbrt (cos (/ K 2)))
144.0ms
(cbrt (cos (/ K 2)))
138.0ms
(cbrt (cos (/ K 2)))

simplify2.2s

Calls
27 calls:
Slowest
585.0ms
(* (* (* (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)))))
343.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J))))
340.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) J)))))
194.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
168.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize38.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J))))
0.4b
(cbrt (cbrt (cos (/ K 2))))
0.3b
(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))
0.3b
(cbrt (cos (/ K 2)))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
13×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
341.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J))))
8.0ms
(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))
2.0ms
(cbrt (cbrt (cos (/ K 2))))
1.0ms
(cbrt (cos (/ K 2)))

series749.0ms

Calls
4 calls:
Slowest
253.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J))))
178.0ms
(cbrt (cos (/ K 2)))
162.0ms
(cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))))
155.0ms
(cbrt (cbrt (cos (/ K 2))))

simplify2.7s

Calls
28 calls:
Slowest
752.0ms
(* (* (* (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 (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J)))))
522.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J)))))
214.0ms
(- 1 (+ (* 5/10368 (pow K 4)) (* 1/72 (pow K 2))))
182.0ms
(- 1 (+ (* 1/1296 (pow K 4)) (* 1/36 (pow K 2))))
181.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.3b

localize27.0ms

Local error

Found 4 expressions with local error:

6.4b
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))
0.2b
(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
9×associate-*l*
8×add-exp-log
7×associate-*r*
6×add-cbrt-cube pow1/3
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down
2×prod-exp *-commutative pow-prod-up cbrt-unprod
1×pow2 pow-plus
Calls
4 calls:
Slowest
92.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J))))
8.0ms
(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series773.0ms

Calls
4 calls:
Slowest
250.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J))))
231.0ms
(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
153.0ms
(cbrt (cos (/ K 2)))
138.0ms
(cbrt (cos (/ K 2)))

simplify2.2s

Calls
44 calls:
Slowest
575.0ms
(* (* (* (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)))) (* (pow (cos (/ K 2)) 1/3) J))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J)))))
273.0ms
(+ (log (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J))))) (log (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J)))))
243.0ms
(* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (pow (cos (/ K 2)) 1/3) J))))
202.0ms
(- 1 (+ (* 1/25920 (pow K 6)) (* 1/12 (pow K 2))))
177.0ms
(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.3b

regimes374.0ms

Accuracy

-11.2% (4.1b remaining)

Error of 7.9b against oracle of 3.8b and baseline of 7.5b

bsearch154.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.3s1468×body1280valid
1.2s1305×body640valid
1.1s4297×body80valid
553.0ms313×body160valid
424.0ms617×body320valid