Details

Time bar (total: 55.9s)

sample197.0ms

Algorithm
intervals
Results
74.0ms42×body1280valid
48.0ms51×body640valid
35.0ms136×body80valid
12.0ms18×body320valid
5.0ms9×body160valid

simplify256.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
255.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize45.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (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)))

rewrite146.0ms

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
73.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
30.0ms
(* J (* (cos (/ K 2)) 2))
27.0ms
(* (cos (/ K 2)) (* -2 J))
15.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series594.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
325.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
126.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
90.0ms
(* (cos (/ K 2)) (* -2 J))
52.0ms
(* J (* (cos (/ K 2)) 2))

simplify7.9s

Counts
55 → 104
Calls
55 calls:
Slowest
743.0ms
(* (* (* (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))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J))))
489.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
460.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
459.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
451.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize45.0ms

Local error

Found 4 expressions with local error:

9.0b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
0.1b
(* J (* (cos (/ K 2)) 2))
0.1b
(/ U (* J (* (cos (/ K 2)) 2)))
0.1b
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
11×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×associate-*l*
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp *-commutative associate-/l*
1×clear-num associate-/r* frac-2neg div-inv unswap-sqr
Counts
4 → 93
Calls
4 calls:
Slowest
35.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
33.0ms
(* J (* (cos (/ K 2)) 2))
28.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
12.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

series787.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
345.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
283.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
104.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
54.0ms
(* J (* (cos (/ K 2)) 2))

simplify7.1s

Counts
58 → 105
Calls
58 calls:
Slowest
455.0ms
(* (* (* (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))) (cos (/ K 2))))
422.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
415.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
381.0ms
(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
367.0ms
(* (* (* (* (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))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.9b

localize58.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.2b
(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
0.1b
(/ 1 (* J (* (cos (/ K 2)) 2)))
0.1b
(* J (* (cos (/ K 2)) 2))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
71×add-exp-log
41×add-cbrt-cube
37×prod-exp
26×pow1
19×cbrt-unprod
13×add-sqr-sqrt pow-prod-down
12×div-exp
11×*-un-lft-identity add-cube-cbrt
9×associate-*r* associate-*l*
6×cbrt-undiv rec-exp times-frac 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative pow-flip associate-/l*
2×div-inv
1×clear-num associate-/r* frac-2neg associate-*r/ un-div-inv inv-pow unswap-sqr
Counts
4 → 120
Calls
4 calls:
Slowest
89.0ms
(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
56.0ms
(* (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
49.0ms
(/ 1 (* J (* (cos (/ K 2)) 2)))
26.0ms
(* J (* (cos (/ K 2)) 2))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
341.0ms
(* (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
145.0ms
(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
87.0ms
(/ 1 (* J (* (cos (/ K 2)) 2)))
59.0ms
(* J (* (cos (/ K 2)) 2))

simplify14.3s

Counts
81 → 132
Calls
81 calls:
Slowest
786.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
504.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
499.0ms
(+ (log U) (- (log 1) (log (* J (* (cos (/ K 2)) 2)))))
476.0ms
(* (* (* U U) U) (/ (* (* 1 1) 1) (* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))))
473.0ms
(+ (log (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (+ (log (cos (/ K 2))) (+ (log -2) (log J))))

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.9b

localize59.0ms

Local error

Found 4 expressions with local error:

9.0b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
9.0b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
9.0b
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
0.5b
(cbrt (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
40×pow1 add-cbrt-cube add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* *-commutative
1×cbrt-prod pow1/3
Counts
4 → 87
Calls
4 calls:
Slowest
61.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
47.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
33.0ms
(cbrt (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J)))
28.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
497.0ms
(cbrt (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J)))
379.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
376.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
337.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))

simplify9.0s

Counts
52 → 99
Calls
52 calls:
Slowest
394.0ms
(* (* (* (* (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))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
371.0ms
(* (cbrt -2) (exp (* 1/3 (- (log 1/2) (log (/ 1 U))))))
362.0ms
(* (* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))) (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
353.0ms
(* (* (* (* (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))) (cos (/ K 2)))) (* (* (* -2 -2) -2) (* (* J J) J)))
343.0ms
(* (* (* (* (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))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.9b

regimes418.0ms

Accuracy

0% (3.8b remaining)

Error of 7.8b against oracle of 4.0b and baseline of 7.8b

bsearch3.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.4s1434×body1280valid
1.7s1210×body640valid
1.0s4413×body80valid
507.0ms635×body320valid
171.0ms312×body160valid