Details

sample589.0ms

Algorithm

intervals

Results

336.0ms	88×	body	1280	valid
116.0ms	52×	body	640	valid
51.0ms	80×	body	80	valid
40.0ms	28×	body	320	valid
6.0ms	8×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
4	3022
3	657
2	188
1	74
0	32

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.0b	(- 3.0 (sqrt 5.0))
1.9b	(- (cos x) (cos y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`prod-diff`
14×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`times-frac` `flip3--` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `diff-cos` `unswap-sqr`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 123

Calls

4 calls:

7.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
25.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
5.0ms	(- 3.0 (sqrt 5.0))
9.0ms	(- (cos x) (cos y))

series1.7s

Counts

4 → 10

Calls

4 calls:

1.5s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
117.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
0.0ms	(- 3.0 (sqrt 5.0))
85.0ms	(- (cos x) (cos y))

simplify2.5s

Counts

133 → 133

Iterations

Iter	Nodes
done	5005
2	2442
1	802
0	332

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
0.3b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.9b	(- (cos x) (cos y))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
12×	`associate-l`
11×	`pow1`
10×	`associate-*l/`
9×	`prod-diff`
8×	`flip3--` `flip--`
7×	`associate-r`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `times-frac` `pow-prod-down` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `div-exp` `associate-r/` `-commutative` `diff-cos` `unswap-sqr`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-inv`

Counts

4 → 116

Calls

4 calls:

96.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
10.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
30.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
15.0ms	(- (cos x) (cos y))

series2.3s

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0)))
1.9s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (* (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)) 3.0))
119.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
102.0ms	(- (cos x) (cos y))

simplify3.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	3072
1	876
0	331

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize141.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (* (- (sin x) (/ (sin y) 16.0)) (* (- (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))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
8×	`cbrt-div` `associate-*l/`
4×	`expm1-log1p-u` `frac-times` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `diff-cos` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*r/`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 110

Calls

4 calls:

79.0ms	(cbrt (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))))
12.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))
7.0ms	(- (cos x) (cos y))

series2.5s

Counts

4 → 12

Calls

4 calls:

2.2s	(cbrt (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))))
71.0ms	(- (cos x) (cos y))
75.0ms	(- (cos x) (cos y))
93.0ms	(- (cos x) (cos y))

simplify3.3s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
3	4799
2	1190
1	393
0	165

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))) 3.0)
0.2b	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.4b	(* (- (cos x) (cos y)) (sqrt 2.0))
1.9b	(- (cos x) (cos y))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
64×	`add-cube-cbrt`
16×	`associate-/l*`
13×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`pow1` `associate-/r` `associate-r` `associate-l*` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*l/` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 163

Calls

4 calls:

13.0ms	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))) 3.0)
8.0ms	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
37.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
7.0ms	(- (cos x) (cos y))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.9s	(/ (/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0))) 3.0)
1.7s	(/ (fma (* (- (sin x) (/ (sin y) 16.0)) (* (- (cos x) (cos y)) (sqrt 2.0))) (- (sin y) (/ (sin x) 16.0)) 2.0) (fma (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
124.0ms	(* (- (cos x) (cos y)) (sqrt 2.0))
86.0ms	(- (cos x) (cos y))

simplify3.2s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
2	2793
1	959
0	394

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes301.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	38
1	38
0	34

end0.0ms

sample18.0s

Algorithm

intervals

Results

9.9s	2720×	body	1280	valid
5.2s	1809×	body	640	valid
1.2s	756×	body	320	valid
1.1s	2359×	body	80	valid
404.0ms	356×	body	160	valid