Details

Time bar (total: 1.3m)

sample151.0ms

Algorithm
intervals
Results
48.0ms46×body1280valid
31.0ms40×body640valid
30.0ms139×body80valid
12.0ms21×body320valid
5.0ms10×body160valid

simplify252.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
252.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize43.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (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)))

rewrite137.0ms

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
Counts
4 → 92
Calls
4 calls:
Slowest
75.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
27.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
18.0ms
(* (cos (/ K 2)) (* -2 J))
14.0ms
(* J (* (cos (/ K 2)) 2))

series611.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
355.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
127.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
69.0ms
(* (cos (/ K 2)) (* -2 J))
60.0ms
(* J (* (cos (/ K 2)) 2))

simplify12.5s

Counts
105 → 104
Calls
105 calls:
Slowest
617.0ms
(* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2)))
564.0ms
(* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J)))
444.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
405.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
404.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize59.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.6b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
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))))
0.1b
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite211.0ms

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
Counts
4 → 89
Calls
4 calls:
Slowest
131.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
74.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
3.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
319.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
268.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
253.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify16.6s

Counts
101 → 101
Calls
101 calls:
Slowest
776.0ms
(+ (log (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (+ (log (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (+ (log (cos (/ K 2))) (log (* -2 J)))))
445.0ms
(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
431.0ms
(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
416.0ms
(* (* (* (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)))))
410.0ms
(* (cbrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

localize62.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (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)))

rewrite180.0ms

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
Counts
4 → 78
Calls
4 calls:
Slowest
176.0ms
(* (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)))

series800.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
351.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
164.0ms
(cbrt (cos (/ K 2)))
145.0ms
(cbrt (cos (/ K 2)))
140.0ms
(cbrt (cos (/ K 2)))

simplify14.9s

Counts
95 → 90
Calls
95 calls:
Slowest
776.0ms
(* (* (* (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)))))
725.0ms
(* (* (* (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)))))
595.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
554.0ms
(+ (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)))))
535.0ms
(* (* (* (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)))))

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.9b

localize54.0ms

Local error

Found 4 expressions with local error:

8.5b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
0.3b
(log1p (cbrt (cos (/ K 2))))
0.3b
(cbrt (cos (/ K 2)))
0.3b
(cbrt (cos (/ K 2)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log
26×add-cbrt-cube
22×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×pow1/3
1×log1p-udef associate-*r* log1p-expm1 *-commutative
Counts
4 → 76
Calls
4 calls:
Slowest
187.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
2.0ms
(cbrt (cos (/ K 2)))
2.0ms
(cbrt (cos (/ K 2)))
1.0ms
(log1p (cbrt (cos (/ K 2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
553.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
245.0ms
(log1p (cbrt (cos (/ K 2))))
161.0ms
(cbrt (cos (/ K 2)))
146.0ms
(cbrt (cos (/ K 2)))

simplify15.1s

Counts
90 → 88
Calls
90 calls:
Slowest
769.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2))))) (* (expm1 (log1p (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)))))
704.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
633.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
630.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (expm1 (log1p (cbrt (cos (/ K 2)))))) (expm1 (log1p (cbrt (cos (/ K 2)))))) (cos (/ K 2))) (* (* (* (cbrt (cos (/ K 2))) (* -2 J)) (* (cbrt (cos (/ K 2))) (* -2 J))) (* (cbrt (cos (/ K 2))) (* -2 J)))))
615.0ms
(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (expm1 (log1p (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J)))))

prune1.3s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 4.9b

regimes357.0ms

Accuracy

-11.9% (4.5b remaining)

Error of 7.8b against oracle of 3.4b and baseline of 7.3b

bsearch343.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s1466×body1280valid
1.7s1212×body640valid
1.2s4366×body80valid
465.0ms646×body320valid
193.0ms311×body160valid