Details

sample457.0ms

Algorithm

intervals

Results

230.0ms	90×	body	1280	valid
74.0ms	46×	body	640	valid
30.0ms	30×	body	320	valid
23.0ms	76×	body	80	valid
9.0ms	14×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize427.0ms

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))
1.9b	(- (cos x) (cos y))

rewrite462.0ms

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:

270.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
141.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
18.0ms	(- 3.0 (sqrt 5.0))
24.0ms	(- (cos x) (cos y))

series542.0ms

Counts

4 → 10

Calls

4 calls:

278.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
165.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
99.0ms	(- (cos x) (cos y))

simplify3.6s

Counts

108 → 108

Iterations

Iter	Nodes
done	5006
2	2117
1	656
0	245

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize445.0ms

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b	(- (cos x) (cos y))

rewrite648.0ms

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` `insert-posit16`
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 → 110

Calls

4 calls:

202.0ms	(/ (+ 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)))))
277.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
125.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
29.0ms	(- (cos x) (cos y))

series4.8s

Counts

4 → 12

Calls

4 calls:

4.1s	(/ (+ 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)))))
342.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
176.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
118.0ms	(- (cos x) (cos y))

simplify8.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5011
2	4712
1	1162
0	386

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize441.0ms

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)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.9b	(- (cos x) (cos y))

rewrite671.0ms

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` `insert-posit16` `unswap-sqr`
3×	`associate-l/` `-commutative`
1×	`cbrt-undiv` `diff-log` `div-exp` `div-inv` `diff-cos`

Counts

4 → 124

Calls

4 calls:

112.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
355.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
157.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
26.0ms	(- (cos x) (cos y))

series842.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
377.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
176.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
128.0ms	(- (cos x) (cos y))

simplify5.3s

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	2714
1	786
0	292

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize509.0ms

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)))
0.7b	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
1.9b	(- (cos x) (cos y))

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
32×	`associate-l`
31×	`*-un-lft-identity`
29×	`sqrt-prod`
20×	`times-frac`
19×	`add-cube-cbrt`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`associate-r`
11×	`associate-*r/` `difference-of-squares`
8×	`flip3--` `flip--`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`distribute-lft-out--` `add-log-exp`
5×	`frac-times` `sub-neg` `associate-*l/`
4×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `insert-posit16`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`diff-log` `div-inv` `diff-cos`

Counts

4 → 126

Calls

4 calls:

308.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
134.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
234.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
34.0ms	(- (cos x) (cos y))

series926.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
202.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
301.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
106.0ms	(- (cos x) (cos y))

simplify5.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	5012
2	2602
1	818
0	306

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes724.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	47
1	47
0	37

end0.0ms

sample15.8s

Algorithm

intervals

Results

9.2s	2724×	body	1280	valid
3.6s	1901×	body	640	valid
1.3s	2244×	body	80	valid
969.0ms	766×	body	320	valid
368.0ms	365×	body	160	valid