Details

Time bar (total: 28.5s)

sample201.0ms

Algorithm
intervals
Results
91.0ms59×body1280valid
37.0ms41×body640valid
27.0ms126×body80valid
13.0ms18×body320valid
6.0ms12×body160valid

simplify1.1s

Counts
1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize55.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
8.7b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
0.2b
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
0.1b
(* (* J 2) (cos (/ K 2)))

rewrite605.0ms

Algorithm
rewrite-expression-head
Rules
98×add-cbrt-cube add-exp-log
49×prod-exp cbrt-unprod
26×pow1
24×cbrt-undiv div-exp
19×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
14×associate-*l*
12×times-frac
11×associate-*r*
10×pow-prod-down
7×swap-sqr
6×sqrt-prod
4×sqrt-div insert-posit16 div-inv add-log-exp
3×associate-*l/ *-commutative
2×flip3-+ flip-+
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 133
Calls
4 calls:
Slowest
335.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
149.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
104.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
15.0ms
(* (* J 2) (cos (/ K 2)))

series579.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
154.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
134.0ms
(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
61.0ms
(* (* J 2) (cos (/ K 2)))

simplify1.2s

Counts
145 → 145

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize91.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
8.8b
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
8.8b
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))

rewrite751.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 76
Calls
4 calls:
Slowest
195.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
194.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
190.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
170.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))

series863.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
314.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
252.0ms
(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
159.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
137.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.1s

Counts
88 → 88

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.8b

localize69.0ms

Local error

Found 4 expressions with local error:

16.0b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
16.0b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
16.0b
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.8b
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))

rewrite410.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
Slowest
165.0ms
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
92.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
82.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
70.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(sqrt (* (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
278.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
254.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
251.0ms
(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.1s

Counts
82 → 82

prune1.9s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.8b

localize93.0ms

Local error

Found 4 expressions with local error:

9.6b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.6b
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
8.7b
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
16×pow1
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*l/
1×associate-*r* *-commutative
Counts
4 → 75
Calls
4 calls:
Slowest
520.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
346.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
159.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
154.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series701.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
261.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
154.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
152.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
133.0ms
(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.1s

Counts
87 → 87

prune1.9s

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 7.8b

regimes628.0ms

Accuracy

9.6% (7.8b remaining)

Error of 16.4b against oracle of 8.6b and baseline of 17.2b

bsearch345.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.1s1553×body1280valid
1.5s4281×body80valid
1.4s1260×body640valid
581.0ms613×body320valid
245.0ms294×body160valid