Details

sample473.0ms

Algorithm

intervals

Results

276.0ms	88×	body	1280	valid
90.0ms	62×	body	640	valid
28.0ms	26×	body	320	valid
21.0ms	67×	body	80	valid
9.0ms	13×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

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

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize107.0ms

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.1b	(- (cos x) (cos y))

rewrite296.0ms

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-cbrt-cube` `add-exp-log`
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:

151.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
100.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms	(- 3.0 (sqrt 5.0))
8.0ms	(- (cos x) (cos y))

series455.0ms

Counts

4 → 10

Calls

4 calls:

246.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
133.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
76.0ms	(- (cos x) (cos y))

simplify2.3s

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	2008
0	738

prune3.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize111.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.5b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.1b	(- (cos x) (cos y))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

14.0ms	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
68.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
11.0ms	(- 3.0 (sqrt 5.0))
11.0ms	(- (cos x) (cos y))

series1.7s

Counts

4 → 10

Calls

4 calls:

1.5s	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
115.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
68.0ms	(- (cos x) (cos y))

simplify2.6s

Counts

178 → 178

Iterations

Iter	Nodes
done	5002
2	2981
1	1036
0	438

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.3b	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.5b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
1.1b	(- (cos x) (cos y))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
77×	`times-frac`
70×	`add-cube-cbrt`
27×	`prod-diff`
13×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
12×	`associate-r` `associate-l`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`pow1` `flip3--` `flip--`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `sqrt-prod` `log1p-expm1-u` `distribute-lft-out--`
3×	`cbrt-undiv` `associate-/r*` `sub-neg` `fma-neg` `div-exp` `unswap-sqr`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `diff-cos`
1×	`clear-num` `frac-2neg` `diff-log` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

65.0ms	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
14.0ms	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
70.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
18.0ms	(- (cos x) (cos y))

series2.2s

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
1.9s	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
100.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
69.0ms	(- (cos x) (cos y))

simplify3.2s

Counts

198 → 198

Iterations

Iter	Nodes
done	5002
2	3632
1	1152
0	468

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (cos x) (cos y)) (- (sin y) (* 0.0625 (sin x))))
0.3b	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (cos x) (cos y)) (- (sin y) (* 0.0625 (sin x)))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.5b	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
1.1b	(- (cos x) (cos y))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
75×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
15×	`prod-diff`
13×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
12×	`associate-l`
9×	`associate-r`
8×	`pow1` `flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `sqrt-prod` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `sub-neg` `fma-neg` `div-exp` `distribute-lft-out--` `unswap-sqr`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `diff-cos`
1×	`clear-num` `frac-2neg` `diff-log` `associate-/l/`

Counts

4 → 171

Calls

4 calls:

35.0ms	(* (- (cos x) (cos y)) (- (sin y) (* 0.0625 (sin x))))
9.0ms	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (cos x) (cos y)) (- (sin y) (* 0.0625 (sin x)))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
46.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
7.0ms	(- (cos x) (cos y))

series2.9s

Counts

4 → 12

Calls

4 calls:

581.0ms	(* (- (cos x) (cos y)) (- (sin y) (* 0.0625 (sin x))))
2.1s	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0)) (* (- (cos x) (cos y)) (- (sin y) (* 0.0625 (sin x)))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
147.0ms	(* (- (sin x) (/ (sin y) 16.0)) (sqrt 2.0))
66.0ms	(- (cos x) (cos y))

simplify3.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5002
2	3693
1	1120
0	453

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes375.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	33

end0.0ms

sample14.3s

Algorithm

intervals

Results

7.7s	2737×	body	1280	valid
3.2s	1819×	body	640	valid
1.7s	784×	body	320	valid
1.0s	2308×	body	80	valid
241.0ms	352×	body	160	valid