Details

sample116.0ms

Algorithm

intervals

Results

72.0ms	257×	body	80	valid
6.0ms	6×	body	320	valid
4.0ms	4×	body	640	valid
3.0ms	2×	body	1280	valid
1.0ms	2×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2) M)
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
35.6b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

217×	`add-sqr-sqrt`
186×	`*-un-lft-identity`
181×	`prod-diff`
96×	`add-cube-cbrt`
78×	`unpow-prod-down`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
54×	`difference-of-squares`
46×	`distribute-lft-out--`
34×	`times-frac`
33×	`fma-neg`
23×	`cos-sum`
16×	`add-log-exp`
13×	`unpow2` `sqr-pow`
11×	`associate--r+`
7×	`diff-log` `div-inv`
6×	`neg-mul-1`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

4 → 295

Calls

4 calls:

15.0ms	(- (/ (* K (+ m n)) 2) M)
923.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
66.0ms	(pow (- (/ (+ m n) 2) M) 2)
33.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series461.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (/ (* K (+ m n)) 2) M)
203.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
83.0ms	(pow (- (/ (+ m n) 2) M) 2)
92.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.3s

Counts

307 → 307

Iterations

Iter	Nodes
done	2000
3	2000
2	1952
1	991
0	460

prune5.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

342×	`add-sqr-sqrt`
289×	`*-un-lft-identity`
269×	`prod-diff`
138×	`unpow-prod-down`
133×	`exp-sum`
125×	`distribute-rgt-neg-in`
121×	`distribute-lft-neg-in`
119×	`add-cube-cbrt`
100×	`difference-of-squares`
87×	`distribute-lft-out--`
26×	`fma-neg`
24×	`add-log-exp`
23×	`times-frac` `unpow2` `sqr-pow`
12×	`diff-log`
11×	`neg-mul-1` `associate--r+`
8×	`exp-prod`
5×	`rem-exp-log`
4×	`pow1` `neg-log` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `flip3--` `exp-diff` `pow-exp` `flip--`

Counts

3 → 373

Calls

3 calls:

1.4s	(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
781.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
41.0ms	(pow (- (/ (+ m n) 2) M) 2)

series459.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
215.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
106.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.4s

Counts

382 → 382

Iterations

Iter	Nodes
done	2000
3	2000
2	1848
1	820
0	394

prune6.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2) M)
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) (- l (fabs (- m n))))
0.0b	(log1p (expm1 (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) (- l (fabs (- m n)))))))
35.6b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

42×	`prod-diff`
34×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-cube-cbrt`
23×	`cos-sum`
21×	`times-frac`
7×	`fma-neg` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg`
1×	`cos-diff` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 102

Calls

4 calls:

15.0ms	(- (/ (* K (+ m n)) 2) M)
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) (- l (fabs (- m n))))
0.0ms	(log1p (expm1 (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) (- l (fabs (- m n)))))))
49.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series682.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (/ (* K (+ m n)) 2) M)
248.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) (- l (fabs (- m n))))
242.0ms	(log1p (expm1 (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) (- l (fabs (- m n)))))))
111.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	2003
3	2003
2	892
1	453
0	247

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize99.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2) M)))
35.6b	(cos (- (/ (* K (+ m n)) 2) M))
35.6b	(cos (- (/ (* K (+ m n)) 2) M))
35.6b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite90.0ms

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:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2) M)))
23.0ms	(cos (- (/ (* K (+ m n)) 2) M))
23.0ms	(cos (- (/ (* K (+ m n)) 2) M))
40.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series428.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2) M)))
92.0ms	(cos (- (/ (* K (+ m n)) 2) M))
67.0ms	(cos (- (/ (* K (+ m n)) 2) M))
94.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	2004
4	2004
3	1071
2	519
1	323
0	192

prune4.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

regimes684.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.8s	8066×	body	80	valid
171.0ms	165×	body	640	valid
156.0ms	116×	body	1280	valid
82.0ms	105×	body	320	valid
22.0ms	46×	body	160	valid
2.0ms	1×	body	2560	valid