Details

sample199.0ms

Algorithm

intervals

Results

74.0ms	42×	body	640	valid
61.0ms	52×	body	1280	valid
29.0ms	133×	body	80	valid
15.0ms	20×	body	320	valid
4.0ms	9×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.3b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
7.6b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
10.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite618.0ms

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:

20.0ms	(* (* J 2) (cos (/ K 2)))
112.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
345.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
138.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series641.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* J 2) (cos (/ K 2)))
135.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
273.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
170.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.2s

Counts

145 → 145

Iterations

Iter	Nodes
2	3067
1	664
0	231

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.3b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
7.6b	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
10.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite586.0ms

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:

16.0ms	(* (* J 2) (cos (/ K 2)))
94.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
342.0ms	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
130.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series530.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* J 2) (cos (/ K 2)))
125.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
209.0ms	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
127.0ms	(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

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.7b

localize67.0ms

Local error

Found 4 expressions with local error:

7.6b	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
10.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
10.1b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite787.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1`
16×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`flip3-+` `associate-*l/` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 73

Calls

4 calls:

362.0ms	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
119.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
145.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
160.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series710.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (cos (/ K 2))) (* -2 J))
150.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
144.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
170.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	4443
2	847
1	247
0	102

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.7b

localize130.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (+ 1 (* (* (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))))))
6.3b	(sqrt (+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
15.0b	(+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
22.5b	(/ (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))))) (* (cos (/ K 2)) (* -2 J))) (sqrt (+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))))

rewrite8.1s

Algorithm

rewrite-expression-head

Rules

102×	`frac-times`
90×	`frac-add`
68×	`sqrt-div` `associate-*l/`
66×	`associate-*r/`
45×	`flip3--` `flip--`
32×	`associate-/r/`
18×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-log-exp`
6×	`pow1` `associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `insert-posit16`
2×	`rem-sqrt-square` `associate-+r+` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`+-commutative` `clear-num` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 174

Calls

4 calls:

7.0ms	(sqrt (+ 1 (* (* (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))))))
3.1s	(sqrt (+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
1.6s	(+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
3.5s	(/ (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))))) (* (cos (/ K 2)) (* -2 J))) (sqrt (+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

183.0ms	(sqrt (+ 1 (* (* (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))))))
257.0ms	(sqrt (+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))))
162.0ms	(+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
482.0ms	(/ (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2)))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))) (* (/ (/ U (* 2 J)) (cos (/ K 2))) (/ (/ U (* 2 J)) (cos (/ K 2))))))) (* (cos (/ K 2)) (* -2 J))) (sqrt (+ (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))) (- (* 1 1) (* (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))))

simplify3.5s

Counts

186 → 186

Iterations

Iter	Nodes
2	5312
1	1195
0	379

prune3.3s

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 9.7b

regimes554.0ms

Accuracy

13.2% (7.9b remaining)

Error of 16.3b against oracle of 8.4b and baseline of 17.5b

bsearch827.0ms

Steps

Iters	Range		Point
10	1.3173576097355062e-157	1.2582464300175928e-144	5.249148278725304e-150
10	-1.669117216904853e-227	-9.249987226201111e-244	-3.6033028488377203e-230

simplify5.0ms

Iterations

Iter	Nodes
2	33
1	33
0	24

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.2s	1468×	body	1280	valid
1.6s	4306×	body	80	valid
1.5s	1283×	body	640	valid
542.0ms	630×	body	320	valid
146.0ms	316×	body	160	valid