Details

sample982.0ms

Algorithm

intervals

Results

490.0ms	49×	body	640	valid
360.0ms	92×	body	1280	valid
41.0ms	79×	body	80	valid
29.0ms	18×	body	320	valid
19.0ms	18×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2752
3	622
2	177
1	74
0	32

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize123.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `associate-r` `associate-l` `associate-*r/`
5×	`sqrt-prod` `difference-of-squares`
4×	`sub-neg` `times-frac` `associate-/r/` `insert-posit16`
3×	`flip3-+` `flip3--` `flip-+` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `diff-log` `div-exp` `associate-*l/` `frac-add` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `diff-cos`

Counts

4 → 92

Calls

4 calls:

79.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
37.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(- (cos x) (cos y))
5.0ms	(- 3.0 (sqrt 5.0))

series2.5s

Counts

4 → 10

Calls

4 calls:

2.3s	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
151.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
90.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify3.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	3445
1	920
0	328

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize131.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 64

Calls

4 calls:

6.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))
6.0ms	(- (cos x) (cos y))
5.0ms	(- 3.0 (sqrt 5.0))

series294.0ms

Counts

4 → 10

Calls

4 calls:

105.0ms	(- (cos x) (cos y))
82.0ms	(- (cos x) (cos y))
107.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify2.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
5	3847
4	1537
3	690
2	319
1	159
0	81

prune875.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize136.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))
0.9b	(- (cos x) (cos y))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`sub-neg` `difference-of-squares`
4×	`flip3--` `sqrt-prod` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`diff-log` `diff-cos`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `unswap-sqr`
1×	`times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

43.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms	(- (cos x) (cos y))
13.0ms	(- (cos x) (cos y))
13.0ms	(- (cos x) (cos y))

series427.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
86.0ms	(- (cos x) (cos y))
79.0ms	(- (cos x) (cos y))
97.0ms	(- (cos x) (cos y))

simplify2.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5005
3	2599
2	757
1	283
0	125

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize142.0ms

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)))
0.9b	(- (cos x) (cos y))
1.0b	(- 3.0 (sqrt 5.0))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

133.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
63.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms	(- (cos x) (cos y))
10.0ms	(- 3.0 (sqrt 5.0))

series443.0ms

Counts

4 → 10

Calls

4 calls:

196.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
162.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
84.0ms	(- (cos x) (cos y))
0.0ms	(- 3.0 (sqrt 5.0))

simplify2.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	2094
1	651
0	243

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes593.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	49
1	49
0	38

end0.0ms

sample20.5s

Algorithm

intervals

Results

11.5s	2739×	body	1280	valid
5.9s	1840×	body	640	valid
1.4s	768×	body	320	valid
1.1s	2302×	body	80	valid
479.0ms	351×	body	160	valid