Details

Time bar (total: 44.3s)

sample192.0ms

Algorithm
intervals
Results
66.0ms44×body640valid
53.0ms40×body1280valid
32.0ms142×body80valid
14.0ms20×body320valid
5.0ms10×body160valid

simplify218.0ms

Calls
1 calls:
Slowest
218.0ms
(* (* (* -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: 8.8b

localize417.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-*r* *-commutative associate-/l*
1×clear-num associate-/r* frac-2neg div-inv
Calls
4 calls:
Slowest
49.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
30.0ms
(* (cos (/ K 2)) (* -2 J))
26.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
14.0ms
(* J (* (cos (/ K 2)) 2))

series604.0ms

Calls
4 calls:
Slowest
332.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
143.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
81.0ms
(* (cos (/ K 2)) (* -2 J))
48.0ms
(* J (* (cos (/ K 2)) 2))

simplify6.5s

Calls
55 calls:
Slowest
476.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
453.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
400.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
377.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))
355.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
27×add-cbrt-cube add-exp-log
16×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*l* sqrt-prod
10×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative
Calls
4 calls:
Slowest
106.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
70.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Calls
4 calls:
Slowest
341.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
302.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
269.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
252.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify7.2s

Calls
55 calls:
Slowest
522.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J)))))
476.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))))
380.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))))
358.0ms
(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))))
292.0ms
(+ (log (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (log (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

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

series1.5s

Calls
4 calls:
Slowest
453.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
393.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
379.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
230.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.8s

Calls
26 calls:
Slowest
431.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
415.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
396.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
266.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))
258.0ms
(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))

prune1.4s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.2b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log
23×add-cbrt-cube
22×pow-prod-down prod-exp cbrt-unprod
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l*
1×associate-*r* *-commutative
Calls
4 calls:
Slowest
205.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))
1.0ms
(cbrt (cos (/ K 2)))

series795.0ms

Calls
4 calls:
Slowest
337.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
168.0ms
(cbrt (cos (/ K 2)))
147.0ms
(cbrt (cos (/ K 2)))
141.0ms
(cbrt (cos (/ K 2)))

simplify10.0s

Calls
45 calls:
Slowest
784.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
690.0ms
(+ (log (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (+ (log (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (+ (log (cbrt (cos (/ K 2)))) (log (* -2 J)))))
667.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
529.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
442.0ms
(+ (log (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (+ (+ (log (cbrt (cos (/ K 2)))) (log (cbrt (cos (/ K 2))))) (+ (log (cbrt (cos (/ K 2)))) (+ (log -2) (log J)))))

prune1.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.2b

regimes570.0ms

Accuracy

0% (4.0b remaining)

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

bsearch2.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.2s1526×body1280valid
1.8s4261×body80valid
1.4s1294×body640valid
455.0ms619×body320valid
191.0ms302×body160valid