Details

sample612.0ms

Algorithm

intervals

Results

293.0ms	81×	body	1280	valid
211.0ms	74×	body	640	valid
32.0ms	73×	body	80	valid
26.0ms	17×	body	320	valid
13.0ms	11×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.3b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
2.1b	(- (cos x) (cos y))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

63.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
37.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
9.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))

series328.0ms

Counts

4 → 10

Calls

4 calls:

154.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
98.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
76.0ms	(- (cos x) (cos y))

simplify2.2s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	1967
1	654
0	273

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

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 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)) 3.0))
0.3b	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.3b	(* (- (cos x) (cos y)) (sqrt 2.0))
2.1b	(- (cos x) (cos y))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

12.0ms	(/ (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)) 3.0))
62.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
35.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
26.0ms	(- (cos x) (cos y))

series2.4s

Counts

4 → 12

Calls

4 calls:

2.0s	(/ (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)) 3.0))
156.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
130.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
85.0ms	(- (cos x) (cos y))

simplify2.8s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	3057
1	875
0	331

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize127.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.3b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (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)) 3.0))
0.3b	(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
2.1b	(- (cos x) (cos y))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

64.0ms	(* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
7.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (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)) 3.0))
217.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
12.0ms	(- (cos x) (cos y))

series2.5s

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
2.1s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (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)) 3.0))
193.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (* (- (cos x) (cos y)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
62.0ms	(- (cos x) (cos y))

simplify3.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5019
2	3664
1	948
0	346

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (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))
2.1b	(- (cos x) (cos y))

rewrite185.0ms

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` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 295

Calls

4 calls:

106.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
42.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms	(- 3.0 (sqrt 5.0))
14.0ms	(- (cos x) (cos y))

series391.0ms

Counts

4 → 10

Calls

4 calls:

177.0ms	(* (* (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))
81.0ms	(- (cos x) (cos y))

simplify2.3s

Counts

305 → 305

Iterations

Iter	Nodes
done	5001
1	2007
0	742

prune2.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes375.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	39
1	39
0	34

end0.0ms

sample17.1s

Algorithm

intervals

Results

9.5s	2667×	body	1280	valid
4.5s	1777×	body	640	valid
1.5s	758×	body	320	valid
1.1s	2433×	body	80	valid
335.0ms	365×	body	160	valid