Details

sample367.0ms

Algorithm

intervals

Results

211.0ms	93×	body	1280	valid
68.0ms	60×	body	640	valid
25.0ms	28×	body	320	valid
15.0ms	66×	body	80	valid
5.0ms	9×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3141
3	655
2	181
1	74
0	32

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize127.0ms

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))
1.5b	(- (cos x) (cos y))

rewrite238.0ms

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` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

136.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
77.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms	(- 3.0 (sqrt 5.0))
11.0ms	(- (cos x) (cos y))

series395.0ms

Counts

4 → 10

Calls

4 calls:

205.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
118.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
72.0ms	(- (cos x) (cos y))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2910
1	652
0	241

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize136.0ms

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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
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)))
1.5b	(- (cos x) (cos y))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

106.0ms	(/ (+ 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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
145.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
56.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms	(- (cos x) (cos y))

series3.5s

Counts

4 → 12

Calls

4 calls:

3.1s	(/ (+ 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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
224.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
131.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
111.0ms	(- (cos x) (cos y))

simplify2.3s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
1	1158
0	382

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
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)))
1.5b	(- (cos x) (cos y))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
15×	`associate-r`
13×	`pow1`
11×	`difference-of-squares`
10×	`associate-*r/`
8×	`flip3--` `flip--`
7×	`sqrt-prod`
6×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `pow-prod-down`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `unswap-sqr`
3×	`associate-l/` `-commutative`
1×	`cbrt-undiv` `diff-log` `div-exp` `div-inv` `diff-cos`

Counts

4 → 120

Calls

4 calls:

59.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
121.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
71.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms	(- (cos x) (cos y))

series637.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
239.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
178.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
72.0ms	(- (cos x) (cos y))

simplify2.1s

Counts

132 → 132

Iterations

Iter	Nodes
done	5002
2	3737
1	781
0	288

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize130.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
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)))
1.5b	(- (cos x) (cos y))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
15×	`associate-r`
13×	`pow1`
11×	`difference-of-squares`
10×	`associate-*r/`
8×	`flip3--` `flip--`
7×	`sqrt-prod`
6×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `pow-prod-down`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `unswap-sqr`
3×	`associate-l/` `-commutative`
1×	`cbrt-undiv` `diff-log` `div-exp` `div-inv` `diff-cos`

Counts

4 → 120

Calls

4 calls:

50.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
117.0ms	(* (* (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)))
6.0ms	(- (cos x) (cos y))

series689.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
265.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
187.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
99.0ms	(- (cos x) (cos y))

simplify2.6s

Counts

132 → 132

Iterations

Iter	Nodes
done	5002
2	3737
1	781
0	288

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes445.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	50
1	50
0	37

end0.0ms

sample14.3s

Algorithm

intervals

Results

8.0s	2700×	body	1280	valid
3.6s	1843×	body	640	valid
1.2s	791×	body	320	valid
645.0ms	2325×	body	80	valid
351.0ms	341×	body	160	valid