Details

sample41.0ms

Algorithm

intervals

Results

22.0ms	260×	body	80	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	640	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (63.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	94	29
3	205	29
4	460	28
5	1278	28
6	4692	28
done	5000	28

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(- (/ (* K (+ m n)) 2.0) M)
34.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
90×	`prod-diff`
82×	`add-cube-cbrt`
71×	`times-frac`
23×	`cos-sum` `fma-neg`
12×	`distribute-lft-out`
11×	`div-inv`
8×	`add-log-exp`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `distribute-lft-out--`
2×	`flip3--` `diff-log` `flip--`
1×	`cos-diff` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 180

Calls

4 calls:

36.0ms	(- (/ (+ m n) 2.0) M)
36.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(- (/ (* K (+ m n)) 2.0) M)
21.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series617.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (/ (+ m n) 2.0) M)
472.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
61.0ms	(- (/ (* K (+ m n)) 2.0) M)
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.7s

Counts

192 → 192

Iterations

Useful iterations: 3 (814.0ms)

Iter	Nodes	Cost
0	343	4791
1	650	3695
2	1288	3147
3	3807	2698
done	5001	2698

prune544.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (+ m n) 2.0) M)
0.0b	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
60×	`prod-diff`
50×	`times-frac`
19×	`fma-neg`
16×	`distribute-lft-out`
10×	`add-log-exp`
6×	`unpow-prod-down`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `div-inv` `distribute-lft-out--`
3×	`expm1-log1p-u` `pow-unpow` `diff-log` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sum-log` `associate--r+` `sqr-pow`

Counts

3 → 137

Calls

3 calls:

37.0ms	(- (/ (+ m n) 2.0) M)
481.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
34.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series478.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(- (/ (+ m n) 2.0) M)
184.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.1s

Counts

146 → 146

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	239	3661
1	515	2789
2	1279	2345
3	4799	1936
done	5000	1936

prune361.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize35.0ms

Local error

Found 4 expressions with local error:

14.0b	(cbrt (/ (* K (+ m n)) 2.0))
14.0b	(cbrt (/ (* K (+ m n)) 2.0))
33.9b	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
34.5b	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

156×	`prod-diff`
102×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
98×	`cbrt-prod`
80×	`cos-sum` `sin-sum`
60×	`unpow-prod-down` `cube-prod`
42×	`times-frac`
14×	`div-inv`
6×	`cube-mult` `unpow3` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`cos-diff` `sin-diff`

Counts

4 → 216

Calls

4 calls:

3.0ms	(cbrt (/ (* K (+ m n)) 2.0))
3.0ms	(cbrt (/ (* K (+ m n)) 2.0))
67.0ms	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
68.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series546.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (/ (* K (+ m n)) 2.0))
156.0ms	(cbrt (/ (* K (+ m n)) 2.0))
114.0ms	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
118.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify1.8s

Counts

228 → 228

Iterations

Useful iterations: 3 (673.0ms)

Iter	Nodes	Cost
0	493	14384
1	880	8056
2	1307	6156
3	2707	5792
done	5001	5792

prune672.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize46.0ms

Local error

Found 4 expressions with local error:

14.0b	(cbrt (/ (* K (+ m n)) 2.0))
14.1b	(cbrt (* K (+ m n)))
34.2b	(cos (- (pow (/ (cbrt (* K (+ m n))) (cbrt 2.0)) 3) M))
34.5b	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

264×	`prod-diff`
208×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
188×	`cos-sum`
165×	`times-frac`
158×	`cbrt-prod`
114×	`unpow-prod-down` `cube-prod`
80×	`sin-sum`
13×	`div-inv`
6×	`cube-mult` `unpow3` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div`
2×	`sub-neg` `pow1/3` `associate-*r/`
1×	`cos-diff` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 319

Calls

4 calls:

3.0ms	(cbrt (/ (* K (+ m n)) 2.0))
4.0ms	(cbrt (* K (+ m n)))
152.0ms	(cos (- (pow (/ (cbrt (* K (+ m n))) (cbrt 2.0)) 3) M))
69.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series517.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (/ (* K (+ m n)) 2.0))
108.0ms	(cbrt (* K (+ m n)))
123.0ms	(cos (- (pow (/ (cbrt (* K (+ m n))) (cbrt 2.0)) 3) M))
119.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify1.3s

Counts

331 → 331

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	1031	24897
1	1900	16967
2	3622	11676
done	5001	10488

prune727.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.8b

regimes251.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	21	17
done	21	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

647.0ms	8115×	body	80	valid
54.0ms	112×	body	1280	valid
49.0ms	143×	body	640	valid
26.0ms	105×	body	320	valid
11.0ms	68×	body	160	valid
2.0ms	3×	body	2560	valid