Details

sample179.0ms

Algorithm

intervals

Results

98.0ms	87×	body	1280	valid
35.0ms	52×	body	640	valid
12.0ms	25×	body	320	valid
11.0ms	82×	body	80	valid
3.0ms	10×	body	160	valid

simplify726.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	50
1	74	50
2	176	50
3	542	50
4	1700	50
done	5000	50

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

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)))))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `associate-r/` `associate-r` `associate-l*`
5×	`sqrt-prod` `difference-of-squares`
4×	`sub-neg` `times-frac` `associate-/r/`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `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` `div-inv` `diff-cos`

Counts

4 → 88

Calls

4 calls:

25.0ms	(/ (+ 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)))))
29.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series1.4s

Counts

4 → 10

Calls

4 calls:

1.3s	(/ (+ 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)))))
88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
55.0ms	(- (cos x) (cos y))

simplify814.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (254.0ms)

Iter	Nodes	Cost
0	311	2970
1	842	2897
2	3003	2544
done	5001	2544

prune560.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))
0.6b	(cbrt (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `cbrt-div` `flip3--` `associate-*r/` `add-cbrt-cube` `flip--`
3×	`difference-of-squares`
2×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `distribute-lft-out--`
1×	`sqrt-prod` `diff-cos`

Counts

4 → 52

Calls

4 calls:

8.0ms	(cbrt (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))
9.0ms	(cbrt (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))
3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series515.0ms

Counts

4 → 10

Calls

4 calls:

226.0ms	(cbrt (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))
231.0ms	(cbrt (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))))
0.0ms	(- 3.0 (sqrt 5.0))
57.0ms	(- (cos x) (cos y))

simplify1.1s

Counts

62 → 62

Iterations

Useful iterations: 4 (458.0ms)

Iter	Nodes	Cost
0	141	873
1	300	846
2	642	784
3	1335	768
4	3340	738
done	5000	738

prune650.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))
2.8b	(- (cos x) (cos y))
2.8b	(- (cos x) (cos y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 60

Calls

4 calls:

3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))
3.0ms	(- (cos x) (cos y))
3.0ms	(- (cos x) (cos y))

series164.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
56.0ms	(- (cos x) (cos y))
51.0ms	(- (cos x) (cos y))
57.0ms	(- (cos x) (cos y))

simplify494.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	102	697
1	220	676
2	517	638
3	1440	630
done	5000	630

prune479.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.0b	(- 3.0 (sqrt 5.0))
1.0b	(- 3.0 (sqrt 5.0))
2.8b	(- (cos x) (cos y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
7×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sqrt-prod`
1×	`diff-cos`

Counts

4 → 60

Calls

4 calls:

3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- 3.0 (sqrt 5.0))
3.0ms	(- (cos x) (cos y))

series56.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
0.0ms	(- 3.0 (sqrt 5.0))
0.0ms	(- 3.0 (sqrt 5.0))
56.0ms	(- (cos x) (cos y))

simplify653.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (167.0ms)

Iter	Nodes	Cost
0	104	711
1	230	680
2	556	646
3	1597	638
done	5000	638

prune443.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes436.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	75
1	45	75
done	45	75

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.9s	2675×	body	1280	valid
1.3s	1850×	body	640	valid
398.0ms	823×	body	320	valid
324.0ms	2318×	body	80	valid
104.0ms	334×	body	160	valid