Details

sample332.0ms

Algorithm

intervals

Results

121.0ms	88×	body	1280	valid
62.0ms	61×	body	640	valid
41.0ms	12×	body	160	valid
15.0ms	23×	body	320	valid
14.0ms	72×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3399
3	699
2	192
1	74
0	32

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize139.0ms

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)))))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
105×	`prod-diff`
103×	`*-un-lft-identity`
97×	`add-cube-cbrt`
58×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`div-inv`
6×	`pow1` `fma-neg` `associate-r` `associate-l` `associate-*r/`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `associate-/r/` `log1p-expm1-u`
3×	`flip3-+` `flip3--` `flip-+` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `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` `diff-cos`

Counts

4 → 207

Calls

4 calls:

85.0ms	(/ (+ 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)))))
63.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms	(- 3.0 (sqrt 5.0))
7.0ms	(- (cos x) (cos y))

series2.4s

Counts

4 → 10

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 (sqrt 5.0)) 2.0) (cos y)))))
137.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
66.0ms	(- (cos x) (cos y))

simplify738.0ms

Counts

217 → 217

Iterations

Iter	Nodes
done	5000
1	1610
0	615

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize204.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
45×	`prod-diff`
38×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
10×	`sqrt-prod`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`diff-cos`

Counts

4 → 125

Calls

4 calls:

13.0ms	(- 3.0 (sqrt 5.0))
14.0ms	(- (cos x) (cos y))
13.0ms	(- (cos x) (cos y))
10.0ms	(- (cos x) (cos y))

series233.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
80.0ms	(- (cos x) (cos y))
73.0ms	(- (cos x) (cos y))
80.0ms	(- (cos x) (cos y))

simplify1.2s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1532
1	395
0	176

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize257.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma (fabs (cbrt 5.0)) (- (sqrt (cbrt 5.0))) 3.0)
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma (fabs (cbrt 5.0)) (- (sqrt (cbrt 5.0))) 3.0)
7.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))

series228.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(fma (fabs (cbrt 5.0)) (- (sqrt (cbrt 5.0))) 3.0)
75.0ms	(- (cos x) (cos y))
64.0ms	(- (cos x) (cos y))
89.0ms	(- (cos x) (cos y))

simplify973.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1150
1	275
0	125

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize127.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(cbrt 5.0)
1.0b	(fma (fabs (cbrt 5.0)) (- (sqrt (cbrt 5.0))) 3.0)
1.7b	(- (cos x) (cos y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`cbrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

1.0ms	(cbrt 5.0)
1.0ms	(cbrt 5.0)
0.0ms	(fma (fabs (cbrt 5.0)) (- (sqrt (cbrt 5.0))) 3.0)
13.0ms	(- (cos x) (cos y))

series109.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(cbrt 5.0)
0.0ms	(fma (fabs (cbrt 5.0)) (- (sqrt (cbrt 5.0))) 3.0)
108.0ms	(- (cos x) (cos y))

simplify865.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	801
1	249
0	129

prune848.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes287.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	39
1	39
0	35

end0.0ms

sample14.8s

Algorithm

intervals

Results

7.5s	2697×	body	1280	valid
4.6s	1941×	body	640	valid
1.2s	732×	body	320	valid
860.0ms	2244×	body	80	valid
302.0ms	386×	body	160	valid