Details

sample368.0ms

Algorithm

intervals

Results

168.0ms	80×	body	1280	valid
128.0ms	58×	body	640	valid
23.0ms	28×	body	320	valid
18.0ms	80×	body	80	valid
4.0ms	10×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	181	50
3	653	50
4	2664	50
done	5000	50

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.4b	(- (cos x) (cos y))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`associate-l`
20×	`times-frac`
18×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`associate-r`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`distribute-lft-out--`
4×	`sub-neg` `unswap-sqr`
3×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `associate-r/` `pow-prod-down` `-commutative`
1×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv` `diff-cos`

Counts

4 → 102

Calls

4 calls:

44.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
57.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms	(- 3.0 (sqrt 5.0))
24.0ms	(- (cos x) (cos y))

series311.0ms

Counts

4 → 10

Calls

4 calls:

110.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
137.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
64.0ms	(- (cos x) (cos y))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	247	1369
1	584	1330
2	1689	1232
done	5000	1221

prune838.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize63.0ms

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 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b	(- (cos x) (cos y))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

96.0ms	(/ (+ 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)))))
74.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
59.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms	(- (cos x) (cos y))

series2.5s

Counts

4 → 12

Calls

4 calls:

2.2s	(/ (+ 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)))))
117.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
131.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
84.0ms	(- (cos x) (cos y))

simplify2.1s

Counts

126 → 126

Iterations

Useful iterations: 2 (800.0ms)

Iter	Nodes	Cost
0	372	3617
1	1027	3530
2	3732	3107
done	5001	3107

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

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)))
0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b	(- (cos x) (cos y))

rewrite345.0ms

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-exp-log` `add-cbrt-cube`
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:

177.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
64.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
84.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms	(- (cos x) (cos y))

series533.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
133.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
132.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
87.0ms	(- (cos x) (cos y))

simplify1.4s

Counts

132 → 132

Iterations

Useful iterations: 2 (458.0ms)

Iter	Nodes	Cost
0	284	2218
1	750	2147
2	2674	1958
done	5002	1958

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

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)))
0.6b	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
2.4b	(- (cos x) (cos y))

rewrite354.0ms

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-exp-log` `add-cbrt-cube`
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`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`diff-log` `div-inv` `diff-cos`

Counts

4 → 122

Calls

4 calls:

151.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
68.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
120.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
8.0ms	(- (cos x) (cos y))

series584.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
114.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
216.0ms	(* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (* (sqrt (/ (- (sqrt 5.0) 1.0) 2.0)) (cos x)))
77.0ms	(- (cos x) (cos y))

simplify1.6s

Counts

134 → 134

Iterations

Useful iterations: 2 (589.0ms)

Iter	Nodes	Cost
0	299	2676
1	787	2400
2	2709	2160
done	5000	2160

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	67
1	53	67
done	53	67

end0.0ms

sample15.9s

Algorithm

intervals

Results

8.8s	2636×	body	1280	valid
4.4s	1918×	body	640	valid
1.1s	2375×	body	80	valid
879.0ms	780×	body	320	valid
344.0ms	291×	body	160	valid