Details

sample133.0ms

Algorithm

intervals

Results

55.0ms	59×	body	2560	valid
19.0ms	33×	body	1280	valid
18.0ms	49×	body	640	valid
11.0ms	36×	body	320	valid
6.0ms	66×	body	80	valid
3.0ms	13×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
4	28
3	26
2	21
1	13
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize50.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1.0 (cos x))
15.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 44

Calls

2 calls:

12.0ms	(- 1.0 (cos x))
59.0ms	(/ (- 1.0 (cos x)) (* x x))

series148.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- 1.0 (cos x))
121.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify4.4s

Counts

50 → 50

Iterations

Iter	Nodes
done	5000
3	2322
2	625
1	219
0	90

prune539.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* (* x x) 1/720) 1/24)
0.1b	(* (* x x) (- (* (* x x) 1/720) 1/24))
0.8b	(* (* x x) 1/720)

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`sub-neg` `insert-posit16`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-l` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 59

Calls

3 calls:

79.0ms	(- (* (* x x) 1/720) 1/24)
239.0ms	(* (* x x) (- (* (* x x) 1/720) 1/24))
55.0ms	(* (* x x) 1/720)

series271.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(- (* (* x x) 1/720) 1/24)
140.0ms	(* (* x x) (- (* (* x x) 1/720) 1/24))
31.0ms	(* (* x x) 1/720)

simplify7.7s

Counts

68 → 68

Iterations

Iter	Nodes
done	5015
3	3296
2	816
1	254
0	90

prune603.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.8b	(- 1.0 (cos x))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `insert-posit16` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 117

Calls

3 calls:

96.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
57.0ms	(/ (- 1.0 (cos x)) x)
23.0ms	(- 1.0 (cos x))

series193.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
71.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(- 1.0 (cos x))

simplify4.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1538
1	525
0	192

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize173.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (cos x))
0.2b	(* (cos x) (cos x))
0.4b	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.7b	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`sqr-cos`
4×	`insert-posit16`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`distribute-rgt-in` `difference-cubes` `+-commutative` `associate-+l+` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `distribute-rgt-out` `flip3--` `diff-log` `cube-unmult` `pow3` `flip-+` `flip--`

Counts

4 → 86

Calls

4 calls:

48.0ms	(* (cos x) (cos x))
50.0ms	(* (cos x) (cos x))
58.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
77.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos x) (cos x))
33.0ms	(* (cos x) (cos x))
109.0ms	(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
131.0ms	(- (* (* 1.0 1.0) 1.0) (* (cos x) (* (cos x) (cos x))))

simplify9.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	4775
2	1383
1	335
0	124

prune975.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes220.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.3b

bsearch157.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	1.874259372897972	0.031731941663915054
8	-0.28008678268591264	-0.00018185218373056224	-0.027773708198225854

simplify46.0ms

Iterations

Iter	Nodes
done	54
1	54
0	39

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	1535×	body	2560	valid
1.1s	1557×	body	640	valid
728.0ms	1240×	body	1280	valid
313.0ms	909×	body	320	valid
217.0ms	2260×	body	80	valid
87.0ms	499×	body	160	valid