Details

sample1.3s

Algorithm

intervals

Results

932.0ms	85×	body	1280	valid
183.0ms	70×	body	640	valid
45.0ms	69×	body	80	valid
37.0ms	25×	body	320	valid
6.0ms	7×	body	160	valid

simplify8.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2793
3	620
2	177
1	74
0	32

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize363.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

2.0s	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
120.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
140.0ms	(- 3.0 (sqrt 5.0))
16.0ms	(- (cos x) (cos y))

series1.5s

Counts

4 → 10

Calls

4 calls:

668.0ms	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
318.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
477.0ms	(- (cos x) (cos y))

simplify5.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5002
2	1860
1	601
0	235

prune2.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize260.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.3b	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-log-exp`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
9×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`add-cube-cbrt`
6×	`sub-neg`
4×	`associate-*r/`
3×	`flip3--` `pow-prod-down` `prod-exp` `sum-log` `flip--` `cbrt-unprod` `difference-of-squares`
2×	`flip3-+` `diff-log` `associate-*l/` `frac-add` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `associate-+l+` `associate-r` `*-commutative` `diff-cos`

Counts

4 → 79

Calls

4 calls:

151.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
60.0ms	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
14.0ms	(- 3.0 (sqrt 5.0))
15.0ms	(- (cos x) (cos y))

series703.0ms

Counts

4 → 10

Calls

4 calls:

177.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
413.0ms	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
0.0ms	(- 3.0 (sqrt 5.0))
113.0ms	(- (cos x) (cos y))

simplify3.4s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1882
1	589
0	234

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize206.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt 5.0) 1.0) (/ 2.0 (cos x)))
0.5b	(+ (/ (* (cos y) (- 3.0 (sqrt 5.0))) 2.0) (/ (- (sqrt 5.0) 1.0) (/ 2.0 (cos x))))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
129×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
67×	`add-cube-cbrt`
31×	`difference-of-squares`
16×	`distribute-lft-out--`
15×	`sqrt-prod`
13×	`associate-/r*`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
6×	`associate-/l*`
4×	`pow1`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `frac-add` `clear-num` `sum-log` `associate-/r/` `flip-+` `diff-cos` `distribute-lft-out`

Counts

4 → 159

Calls

4 calls:

53.0ms	(/ (- (sqrt 5.0) 1.0) (/ 2.0 (cos x)))
141.0ms	(+ (/ (* (cos y) (- 3.0 (sqrt 5.0))) 2.0) (/ (- (sqrt 5.0) 1.0) (/ 2.0 (cos x))))
14.0ms	(- 3.0 (sqrt 5.0))
10.0ms	(- (cos x) (cos y))

series672.0ms

Counts

4 → 10

Calls

4 calls:

167.0ms	(/ (- (sqrt 5.0) 1.0) (/ 2.0 (cos x)))
393.0ms	(+ (/ (* (cos y) (- 3.0 (sqrt 5.0))) 2.0) (/ (- (sqrt 5.0) 1.0) (/ 2.0 (cos x))))
0.0ms	(- 3.0 (sqrt 5.0))
112.0ms	(- (cos x) (cos y))

simplify4.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5009
2	2768
1	955
0	342

prune4.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize210.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (/ (* (cos y) (- 3.0 (sqrt 5.0))) 2.0) (/ (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (/ (sqrt 2.0) (cos x))))
0.6b	(/ (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (/ (sqrt 2.0) (cos x)))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

2446×	`times-frac`
1532×	`add-sqr-sqrt`
1256×	`*-un-lft-identity`
974×	`add-cube-cbrt`
922×	`sqrt-prod`
279×	`difference-of-squares`
140×	`distribute-lft-out--`
65×	`div-inv`
40×	`associate-/l*`
22×	`associate-/r*`
16×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `div-sub`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `frac-add` `clear-num` `sum-log` `associate-/r/` `flip-+` `diff-cos` `associate-/l/` `distribute-lft-out`

Counts

4 → 1007

Calls

4 calls:

1.6s	(+ (/ (* (cos y) (- 3.0 (sqrt 5.0))) 2.0) (/ (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (/ (sqrt 2.0) (cos x))))
201.0ms	(/ (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (/ (sqrt 2.0) (cos x)))
14.0ms	(- 3.0 (sqrt 5.0))
15.0ms	(- (cos x) (cos y))

series2.4s

Counts

4 → 10

Calls

4 calls:

1.6s	(+ (/ (* (cos y) (- 3.0 (sqrt 5.0))) 2.0) (/ (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (/ (sqrt 2.0) (cos x))))
624.0ms	(/ (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (/ (sqrt 2.0) (cos x)))
0.0ms	(- 3.0 (sqrt 5.0))
128.0ms	(- (cos x) (cos y))

simplify13.2s

Counts

1017 → 1017

Iterations

Iter	Nodes
done	5002
1	3672
0	1069

prune17.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes879.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample34.8s

Algorithm

intervals

Results

19.4s	2697×	body	1280	valid
9.3s	1879×	body	640	valid
2.9s	720×	body	320	valid
1.8s	2353×	body	80	valid
717.0ms	351×	body	160	valid