Details

sample443.0ms

Algorithm

intervals

Results

240.0ms	83×	body	1280	valid
76.0ms	55×	body	640	valid
56.0ms	84×	body	80	valid
29.0ms	29×	body	320	valid
4.0ms	5×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	192	47
3	699	47
4	3390	47
done	5001	47

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
3.4b	(- (cos x) (cos y))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
137×	`add-cube-cbrt`
130×	`times-frac`
105×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
13×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube` `div-inv`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `associate-r` `associate-l`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `diff-cos` `associate-/l/`

Counts

4 → 250

Calls

4 calls:

21.0ms	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
111.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms	(- 3.0 (sqrt 5.0))
13.0ms	(- (cos x) (cos y))

series1.5s

Counts

4 → 10

Calls

4 calls:

1.3s	(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
104.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
73.0ms	(- (cos x) (cos y))

simplify998.0ms

Counts

260 → 260

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	658	11736
1	1570	10876
done	5000	9459

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize97.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 5.0)
1.0b	(cbrt 5.0)
2.0b	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
3.4b	(- (cos x) (cos y))

rewrite20.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `diff-cos` `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 (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
15.0ms	(- (cos x) (cos y))

series78.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 5.0)
0.0ms	(cbrt 5.0)
0.0ms	(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
77.0ms	(- (cos x) (cos y))

simplify765.0ms

Counts

71 → 71

Iterations

Useful iterations: done (762.0ms)

Iter	Nodes	Cost
0	133	1015
1	258	902
2	812	720
done	5000	602

prune915.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize78.0ms

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))
3.4b	(- (cos x) (cos y))

rewrite203.0ms

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-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
6×	`pow1` `fma-neg` `associate-r/` `associate-r` `associate-l*`
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` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `diff-cos`

Counts

4 → 207

Calls

4 calls:

97.0ms	(/ (+ 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)))))
65.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms	(- 3.0 (sqrt 5.0))
16.0ms	(- (cos x) (cos y))

series1.8s

Counts

4 → 10

Calls

4 calls:

1.7s	(/ (+ 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)))))
101.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
62.0ms	(- (cos x) (cos y))

simplify791.0ms

Counts

217 → 217

Iterations

Useful iterations: done (780.0ms)

Iter	Nodes	Cost
0	602	8074
1	1561	7221
done	5000	5700

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.5b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
3.4b	(- (cos x) (cos y))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

152×	`add-sqr-sqrt`
143×	`*-un-lft-identity`
137×	`add-cube-cbrt`
130×	`times-frac`
105×	`prod-diff`
41×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-exp-log`
14×	`sqrt-prod`
13×	`associate-/l*`
11×	`add-cbrt-cube` `div-inv`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `div-exp` `associate-r` `associate-l`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `associate-/r*` `flip--` `distribute-lft-out--`
2×	`diff-log` `associate-*r/` `unswap-sqr`
1×	`rec-exp` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `diff-cos` `associate-/l/`

Counts

4 → 252

Calls

4 calls:

12.0ms	(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
90.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms	(- 3.0 (sqrt 5.0))
15.0ms	(- (cos x) (cos y))

series692.0ms

Counts

4 → 10

Calls

4 calls:

500.0ms	(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
129.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
63.0ms	(- (cos x) (cos y))

simplify728.0ms

Counts

262 → 262

Iterations

Useful iterations: done (712.0ms)

Iter	Nodes	Cost
0	614	8935
1	1413	8009
done	5000	6719

prune1.6s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes385.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	72
1	49	72
2	51	72
done	51	72

end0.0ms

sample16.0s

Algorithm

intervals

Results

9.5s	2797×	body	1280	valid
3.7s	1848×	body	640	valid
1.0s	721×	body	320	valid
999.0ms	2288×	body	80	valid
346.0ms	346×	body	160	valid