Details

sample185.0ms

Algorithm

intervals

Results

94.0ms	87×	body	1280	valid
39.0ms	52×	body	640	valid
16.0ms	25×	body	320	valid
12.0ms	82×	body	80	valid
3.0ms	10×	body	160	valid

simplify654.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	187	47
3	593	47
4	1971	47
done	5000	47

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

184×	`add-sqr-sqrt`
183×	`prod-diff`
172×	`*-un-lft-identity`
164×	`add-cube-cbrt`
110×	`times-frac`
82×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
12×	`associate-r` `div-inv`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg` `fma-neg`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
2×	`diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 291

Calls

4 calls:

62.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series275.0ms

Counts

4 → 10

Calls

4 calls:

134.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
89.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
51.0ms	(- (cos x) (cos y))

simplify516.0ms

Counts

301 → 301

Iterations

Useful iterations: done (501.0ms)

Iter	Nodes	Cost
0	732	12252
1	1735	10935
done	5000	10884

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- (sin y) (/ (sin x) 16.0)))
0.7b	(cbrt (- (sin y) (/ (sin x) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
12×	`cbrt-prod`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`difference-of-squares`
6×	`fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--`
2×	`sub-neg` `times-frac` `pow1/3` `diff-log`
1×	`diff-cos`

Counts

4 → 103

Calls

4 calls:

6.0ms	(cbrt (- (sin y) (/ (sin x) 16.0)))
7.0ms	(cbrt (- (sin y) (/ (sin x) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series334.0ms

Counts

4 → 10

Calls

4 calls:

138.0ms	(cbrt (- (sin y) (/ (sin x) 16.0)))
141.0ms	(cbrt (- (sin y) (/ (sin x) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
55.0ms	(- (cos x) (cos y))

simplify2.7s

Counts

113 → 113

Iterations

Useful iterations: 3 (579.0ms)

Iter	Nodes	Cost
0	227	1843
1	476	1511
2	1199	1276
3	4614	1174
done	5000	1174

prune666.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.9b	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
96×	`prod-diff`
93×	`*-un-lft-identity`
89×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-prod` `sub-neg` `fma-neg`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`pow1/3` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 172

Calls

4 calls:

1.0ms	(cbrt (cos x))
38.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- 3.0 (sqrt 5.0))
0.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series340.0ms

Counts

4 → 10

Calls

4 calls:

93.0ms	(cbrt (cos x))
87.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
159.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify1.2s

Counts

182 → 182

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	415	5603
1	795	4914
2	2803	3444
done	5000	3426

prune735.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
1.0b	(cbrt 16.0)
2.9b	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
1.0ms	(cbrt 16.0)
0.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series155.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
0.0ms	(cbrt 16.0)
155.0ms	(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify609.0ms

Counts

55 → 55

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	79	653
1	144	598
2	345	425
3	1332	370
done	5001	370

prune494.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes275.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	99
1	53	99
done	53	99

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.0s	2675×	body	1280	valid
1.4s	1850×	body	640	valid
425.0ms	823×	body	320	valid
335.0ms	2318×	body	80	valid
121.0ms	334×	body	160	valid