Details

sample143.0ms

Algorithm

intervals

Results

53.0ms	51×	body	1280	valid
28.0ms	36×	body	640	valid
26.0ms	138×	body	80	valid
13.0ms	21×	body	320	valid
4.0ms	10×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	2067
4	616
3	185
2	79
1	34
0	17

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
6.6b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
10.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite687.0ms

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:

26.0ms	(* (* J 2) (cos (/ K 2)))
128.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
362.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
168.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series587.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (* J 2) (cos (/ K 2)))
157.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
205.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
142.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.4s

Counts

145 → 145

Iterations

Iter	Nodes
2	3067
1	664
0	231

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
6.6b	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
10.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite702.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-cbrt-cube` `add-exp-log`
51×	`prod-exp` `cbrt-unprod`
29×	`pow1`
24×	`cbrt-undiv` `div-exp`
17×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `pow-prod-down`
11×	`associate-r`
9×	`associate-l`
7×	`swap-sqr`
5×	`associate-*l/`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
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 → 131

Calls

4 calls:

33.0ms	(* (* J 2) (cos (/ K 2)))
163.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
337.0ms	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
164.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series571.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* J 2) (cos (/ K 2)))
125.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
221.0ms	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
161.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.2s

Counts

143 → 143

Iterations

Iter	Nodes
2	3038
1	664
0	231

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.9b

localize78.0ms

Local error

Found 4 expressions with local error:

6.7b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
6.7b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
10.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite712.0ms

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:

167.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
200.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
135.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
208.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series941.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
313.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
168.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
178.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify21.3s

Counts

88 → 88

Iterations

Iter	Nodes
4	15942
3	1864
2	449
1	182
0	92

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.9b

localize64.0ms

Local error

Found 4 expressions with local error:

11.1b	(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))))
15.5b	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
15.5b	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
15.5b	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite460.0ms

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:

209.0ms	(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))))
90.0ms	(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))
68.0ms	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series1.0s

Counts

4 → 12

Calls

4 calls:

284.0ms	(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))))
252.0ms	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
256.0ms	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
238.0ms	(cbrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify15.3s

Counts

82 → 82

Iterations

Iter	Nodes
4	15585
3	1886
2	444
1	203
0	115

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.9b

regimes478.0ms

Accuracy

2% (8.3b remaining)

Error of 17.1b against oracle of 8.8b and baseline of 17.2b

bsearch260.0ms

Steps

Iters	Range		Point
7	1.9226272769553932e-226	1.5350114646212834e-224	5.1968831935464863e-225
5	-2.0312189341094116e-91	-9.677896374232993e-92	-9.781248954356997e-92

simplify24.0ms

Iterations

Iter	Nodes
2	33
1	33
0	24

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.0s	1517×	body	1280	valid
1.3s	1275×	body	640	valid
1.2s	4295×	body	80	valid
512.0ms	627×	body	320	valid
132.0ms	291×	body	160	valid