Details

sample892.0ms

Algorithm

intervals

Results

581.0ms	85×	body	1280	valid
160.0ms	70×	body	640	valid
43.0ms	69×	body	80	valid
39.0ms	25×	body	320	valid
6.0ms	7×	body	160	valid

simplify9.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3020
3	659
2	188
1	74
0	32

prune140.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize181.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

25.0ms	(/ (/ (fma (* (* (- (cos x) (cos y)) (sqrt 2.0)) (- (sin y) (/ (sin x) 16.0))) (- (sin x) (/ (sin y) 16.0)) 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)))
64.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
18.0ms	(- 3.0 (sqrt 5.0))
18.0ms	(- (cos x) (cos y))

series3.1s

Counts

4 → 10

Calls

4 calls:

2.8s	(/ (/ (fma (* (* (- (cos x) (cos y)) (sqrt 2.0)) (- (sin y) (/ (sin x) 16.0))) (- (sin x) (/ (sin y) 16.0)) 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)))
226.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
113.0ms	(- (cos x) (cos y))

simplify8.2s

Counts

178 → 178

Iterations

Iter	Nodes
done	5002
2	2815
1	988
0	418

prune4.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize319.0ms

Local error

Found 4 expressions with local error:

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

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 243

Calls

4 calls:

195.0ms	(* (* (- (cos x) (cos y)) (sqrt 2.0)) (- (sin y) (/ (sin x) 16.0)))
25.0ms	(/ (/ (fma (* (* (- (cos x) (cos y)) (sqrt 2.0)) (- (sin y) (/ (sin x) 16.0))) (- (sin x) (/ (sin y) 16.0)) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
81.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
25.0ms	(- (cos x) (cos y))

series4.6s

Counts

4 → 12

Calls

4 calls:

439.0ms	(* (* (- (cos x) (cos y)) (sqrt 2.0)) (- (sin y) (/ (sin x) 16.0)))
3.9s	(/ (/ (fma (* (* (- (cos x) (cos y)) (sqrt 2.0)) (- (sin y) (/ (sin x) 16.0))) (- (sin x) (/ (sin y) 16.0)) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
185.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
109.0ms	(- (cos x) (cos y))

simplify5.5s

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
1	1799
0	642

prune9.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize269.0ms

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))

rewrite656.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
105×	`prod-diff`
102×	`*-un-lft-identity`
96×	`add-cube-cbrt`
55×	`times-frac`
41×	`distribute-rgt-in` `distribute-lft-in`
14×	`sqrt-prod`
13×	`add-log-exp`
6×	`pow1` `add-exp-log` `fma-neg` `associate-r` `associate-l` `add-cbrt-cube` `div-inv`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `fma-def` `sum-log` `flip--` `distribute-lft-out--`
2×	`flip3-+` `diff-log` `associate-r/` `associate-l/` `frac-add` `flip-+` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `diff-cos`

Counts

4 → 198

Calls

4 calls:

85.0ms	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
330.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
22.0ms	(- 3.0 (sqrt 5.0))
54.0ms	(- (cos x) (cos y))

series2.1s

Counts

4 → 10

Calls

4 calls:

1.3s	(+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))
487.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
355.0ms	(- (cos x) (cos y))

simplify9.9s

Counts

208 → 208

Iterations

Iter	Nodes
done	5001
2	3844
1	1280
0	526

prune3.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize468.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (- (cos x) (cos y)) (sqrt 2.0)))
1.9b	(- (cos x) (cos y))
1.9b	(- (cos x) (cos y))
1.9b	(- (cos x) (cos y))

rewrite94.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `diff-cos` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-div` `associate-*l/`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 100

Calls

4 calls:

22.0ms	(cbrt (* (- (cos x) (cos y)) (sqrt 2.0)))
22.0ms	(- (cos x) (cos y))
18.0ms	(- (cos x) (cos y))
25.0ms	(- (cos x) (cos y))

series732.0ms

Counts

4 → 12

Calls

4 calls:

363.0ms	(cbrt (* (- (cos x) (cos y)) (sqrt 2.0)))
142.0ms	(- (cos x) (cos y))
110.0ms	(- (cos x) (cos y))
117.0ms	(- (cos x) (cos y))

simplify3.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
3	1886
2	595
1	258
0	121

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify19.0ms

Iterations

Iter	Nodes
done	41
1	41
0	32

end6.0ms

sample35.0s

Algorithm

intervals

Results

18.0s	2697×	body	1280	valid
11.9s	1879×	body	640	valid
2.4s	720×	body	320	valid
1.6s	2353×	body	80	valid
432.0ms	351×	body	160	valid