Details

Time bar (total: 29.2s)

sample137.0ms

Algorithm
intervals
Results
65.0ms56×body1280valid
24.0ms37×body640valid
23.0ms140×body80valid
7.0ms15×body320valid
2.0ms8×body160valid

simplify728.0ms

Counts
1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize39.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (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)))

rewrite119.0ms

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
61.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
27.0ms
(* J (* (cos (/ K 2)) 2))
17.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
14.0ms
(* (cos (/ K 2)) (* -2 J))

series534.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
108.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
73.0ms
(* (cos (/ K 2)) (* -2 J))
50.0ms
(* J (* (cos (/ K 2)) 2))

simplify3.4s

Counts
104 → 104

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize33.0ms

Local error

Found 4 expressions with local error:

5.2b
(* (* (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)))

rewrite62.0ms

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
27.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
14.0ms
(* J (* (cos (/ K 2)) 2))
13.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
7.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

series779.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
356.0ms
(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
237.0ms
(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
115.0ms
(/ U (* J (* (cos (/ K 2)) 2)))
70.0ms
(* J (* (cos (/ K 2)) 2))

simplify3.3s

Counts
105 → 105

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

localize33.0ms

Local error

Found 4 expressions with local error:

5.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
5.3b
(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))))
0.2b
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite180.0ms

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
110.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
65.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
370.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
337.0ms
(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
230.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
211.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify3.2s

Counts
101 → 101

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.3b

localize43.0ms

Local error

Found 4 expressions with local error:

5.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
5.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
5.3b
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b
(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
16×pow1
13×add-sqr-sqrt add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
9×associate-*l*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*r* *-commutative
Counts
4 → 78
Calls
4 calls:
Slowest
79.0ms
(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
463.0ms
(* (sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (cos (/ K 2)) (* -2 J)))
246.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
246.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
217.0ms
(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify1.9s

Counts
90 → 90

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.3b

regimes378.0ms

Accuracy

0% (3.7b remaining)

Error of 7.4b against oracle of 3.7b and baseline of 7.4b

bsearch2.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.6s1490×body1280valid
1.5s4309×body80valid
1.4s1255×body640valid
584.0ms672×body320valid
147.0ms276×body160valid