Details

sample95.0ms

Algorithm

intervals

Results

51.0ms	260×	body	80	valid
17.0ms	4×	body	640	valid
3.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
5	2004
4	821
3	262
2	104
1	51
0	21

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2)
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
36.0b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

202×	`add-sqr-sqrt`
171×	`*-un-lft-identity`
160×	`prod-diff`
83×	`add-cube-cbrt`
78×	`unpow-prod-down`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
53×	`difference-of-squares`
45×	`distribute-lft-out--`
26×	`fma-neg`
25×	`times-frac`
23×	`cos-sum`
14×	`add-log-exp`
13×	`unpow2` `sqr-pow`
11×	`associate--r+`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`neg-mul-1` `diff-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `associate-/r*` `sub-neg`
2×	`cbrt-undiv` `div-exp` `neg-log` `associate-*r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `flip3-+` `flip3--` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `flip--` `associate-/l*` `associate--r-`

Counts

4 → 276

Calls

4 calls:

24.0ms	(/ (* K (+ m n)) 2)
928.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
36.0ms	(pow (- (/ (+ m n) 2) M) 2)
49.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series473.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* K (+ m n)) 2)
227.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
109.0ms	(pow (- (/ (+ m n) 2) M) 2)
77.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.2s

Counts

288 → 288

Iterations

Iter	Nodes
done	2000
2	2000
1	1059
0	473

prune5.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)

rewrite961.0ms

Algorithm

rewrite-expression-head

Rules

195×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
148×	`prod-diff`
78×	`unpow-prod-down`
74×	`add-cube-cbrt`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
54×	`difference-of-squares`
46×	`distribute-lft-out--`
29×	`fma-neg`
15×	`add-log-exp`
13×	`times-frac` `unpow2` `sqr-pow`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

3 → 245

Calls

3 calls:

6.0ms	(- l (fabs (- m n)))
912.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
32.0ms	(pow (- (/ (+ m n) 2) M) 2)

series309.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(- l (fabs (- m n)))
191.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
102.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.3s

Counts

254 → 254

Iterations

Iter	Nodes
done	2003
3	2003
2	1455
1	697
0	290

prune4.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.3b	(log1p (expm1 (cos (- (/ (* K (+ m n)) 2) M))))
0.3b	(expm1 (cos (- (/ (* K (+ m n)) 2) M)))
36.0b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`cos-sum`
21×	`*-un-lft-identity` `prod-diff`
19×	`add-cube-cbrt`
10×	`times-frac`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`difference-of-squares`
1×	`cos-diff` `pow-to-exp` `log1p-udef` `expm1-log1p` `sub-neg` `pow-pow` `pow-exp` `log1p-expm1` `distribute-lft-out--` `unpow2` `expm1-udef` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

64.0ms	(pow (- (/ (+ m n) 2) M) 2)
0.0ms	(log1p (expm1 (cos (- (/ (* K (+ m n)) 2) M))))
1.0ms	(expm1 (cos (- (/ (* K (+ m n)) 2) M)))
44.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series489.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow (- (/ (+ m n) 2) M) 2)
131.0ms	(log1p (expm1 (cos (- (/ (* K (+ m n)) 2) M))))
174.0ms	(expm1 (cos (- (/ (* K (+ m n)) 2) M)))
81.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify932.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	2001
3	2001
2	983
1	511
0	255

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (expm1 (cos (- (/ (* K (+ m n)) 2) M))))
36.0b	(cos (- (/ (* K (+ m n)) 2) M))
36.0b	(cos (- (/ (* K (+ m n)) 2) M))
36.0b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
9×	`div-inv`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt (expm1 (cos (- (/ (* K (+ m n)) 2) M))))
21.0ms	(cos (- (/ (* K (+ m n)) 2) M))
46.0ms	(cos (- (/ (* K (+ m n)) 2) M))
22.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series633.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(cbrt (expm1 (cos (- (/ (* K (+ m n)) 2) M))))
72.0ms	(cos (- (/ (* K (+ m n)) 2) M))
93.0ms	(cos (- (/ (* K (+ m n)) 2) M))
95.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	2003
4	2003
3	1107
2	539
1	338
0	200

prune3.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

regimes746.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.8s	8088×	body	80	valid
170.0ms	122×	body	1280	valid
155.0ms	139×	body	640	valid
120.0ms	117×	body	320	valid
26.0ms	52×	body	160	valid
2.0ms	1×	body	2560	valid