Details

sample440.0ms

Algorithm

intervals

Results

220.0ms	90×	body	1280	valid
117.0ms	46×	body	640	valid
30.0ms	30×	body	320	valid
23.0ms	76×	body	80	valid
11.0ms	14×	body	160	valid

simplify5.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
4	3022
3	657
2	188
1	74
0	32

prune54.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize334.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`prod-diff`
14×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`times-frac` `flip3--` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `diff-cos` `unswap-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 123

Calls

4 calls:

34.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
117.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
17.0ms	(- 3.0 (sqrt 5.0))
23.0ms	(- (cos x) (cos y))

series2.8s

Counts

4 → 10

Calls

4 calls:

2.5s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
168.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
120.0ms	(- (cos x) (cos y))

simplify5.8s

Counts

133 → 133

Iterations

Iter	Nodes
done	5002
2	2466
1	802
0	332

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize323.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
35×	`add-cube-cbrt`
27×	`prod-diff`
14×	`sqrt-prod`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `fma-neg` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `flip3--` `flip--` `associate-/l` `distribute-lft-out--`
2×	`sub-neg` `diff-log` `associate-*l/` `diff-cos` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 129

Calls

4 calls:

11.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
91.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
18.0ms	(- 3.0 (sqrt 5.0))
35.0ms	(- (cos x) (cos y))

series2.6s

Counts

4 → 10

Calls

4 calls:

2.2s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
227.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
118.0ms	(- (cos x) (cos y))

simplify5.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5004
2	2179
1	760
0	328

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize476.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.2b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.9b	(- (cos x) (cos y))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
23×	`add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-l`
11×	`pow1`
10×	`times-frac` `associate-*l/`
9×	`prod-diff`
8×	`flip3--` `flip--`
7×	`associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r` `fma-neg` `associate-/l` `distribute-lft-out--`
2×	`associate-r/` `-commutative` `diff-cos` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

260.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
19.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
86.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
44.0ms	(- (cos x) (cos y))

series3.4s

Counts

4 → 12

Calls

4 calls:

338.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
2.7s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
209.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
107.0ms	(- (cos x) (cos y))

simplify6.6s

Counts

134 → 134

Iterations

Iter	Nodes
done	5002
2	2848
1	829
0	325

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize365.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))) (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) 3.0))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
41×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`prod-diff`
25×	`times-frac`
19×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
14×	`sqrt-prod`
9×	`prod-exp`
8×	`pow1` `div-exp` `add-log-exp` `unswap-sqr`
6×	`fma-neg`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `associate-*l/` `flip--` `distribute-lft-out--`
2×	`rec-exp` `sub-neg` `diff-log` `1-exp` `pow-prod-down` `*-commutative` `div-inv` `diff-cos`
1×	`frac-times` `associate-*r/`

Counts

4 → 158

Calls

4 calls:

58.0ms	(* (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))) (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) 3.0))
65.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
17.0ms	(- 3.0 (sqrt 5.0))
36.0ms	(- (cos x) (cos y))

series2.9s

Counts

4 → 10

Calls

4 calls:

2.6s	(* (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))) (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) 3.0))
192.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
146.0ms	(- (cos x) (cos y))

simplify7.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	3306
1	1026
0	396

prune2.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes647.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify31.0ms

Iterations

Iter	Nodes
done	35
1	35
0	32

end0.0ms

sample16.9s

Algorithm

intervals

Results

8.9s	2724×	body	1280	valid
4.6s	1901×	body	640	valid
1.5s	766×	body	320	valid
1.3s	2244×	body	80	valid
352.0ms	365×	body	160	valid