Details

Time bar (total: 54.8s)

sample147.0ms

Algorithm
intervals
Results
55.0ms43×body1280valid
29.0ms41×body640valid
26.0ms140×body80valid
9.0ms15×body320valid
6.0ms17×body160valid

simplify299.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
299.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize26.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (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)))

rewrite142.0ms

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
78.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
29.0ms
(* J (* (cos (/ K 2)) 2))
19.0ms
(* (cos (/ K 2)) (* -2 J))
14.0ms
(/ U (* J (* (cos (/ K 2)) 2)))

series599.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
143.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
79.0ms
(* J (* (cos (/ K 2)) 2))
66.0ms
(* (cos (/ K 2)) (* -2 J))

simplify7.2s

Counts
55 → 104
Calls
55 calls:
Slowest
724.0ms
(- (log U) (+ (log J) (+ (log (cos (/ K 2))) (log 2))))
469.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
453.0ms
(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
389.0ms
(* (* (* (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))))
389.0ms
(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize59.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.7b
(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))))

rewrite173.0ms

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
108.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
59.0ms
(* (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)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
332.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
300.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
254.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
219.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify7.1s

Counts
55 → 101
Calls
55 calls:
Slowest
441.0ms
(* (* (* (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)))))
399.0ms
(* (* (* (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)))))
388.0ms
(* (* (* (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)))))
361.0ms
(* (* (* (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)))))
332.0ms
(* (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

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize62.0ms

Local error

Found 4 expressions with local error:

6.9b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.9b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.9b
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.5b
(* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
36×pow1 add-exp-log
24×pow-prod-down prod-exp cbrt-unprod
22×add-cbrt-cube
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×associate-*r* associate-*l* *-commutative
Counts
4 → 79
Calls
4 calls:
Slowest
128.0ms
(* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
1.0ms
(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

Counts
4 → 12
Calls
4 calls:
Slowest
387.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
386.0ms
(* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
363.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
328.0ms
(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify12.2s

Counts
47 → 91
Calls
47 calls:
Slowest
703.0ms
(* (* (* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))))
629.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))))
483.0ms
(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
482.0ms
(* (* (* (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (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)))))
481.0ms
(+ (+ (log (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (log (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))) (+ (log (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (+ (log (cos (/ K 2))) (+ (log -2) (log J)))))

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

localize81.0ms

Local error

Found 4 expressions with local error:

6.6b
(* (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)))

rewrite201.0ms

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
197.0ms
(* (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)))

series810.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
189.0ms
(cbrt (cos (/ K 2)))
160.0ms
(cbrt (cos (/ K 2)))
152.0ms
(cbrt (cos (/ K 2)))

simplify10.5s

Counts
45 → 90
Calls
45 calls:
Slowest
806.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))
752.0ms
(* (* (* (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)))))
731.0ms
(* (* (* (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)))))
508.0ms
(* (* (* (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)))))
472.0ms
(+ (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

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

regimes522.0ms

Accuracy

0% (3.7b remaining)

Error of 7.0b against oracle of 3.3b and baseline of 7.0b

bsearch3.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.6s1550×body1280valid
1.6s1293×body640valid
1.1s4252×body80valid
506.0ms606×body320valid
185.0ms303×body160valid