Details

sample290.0ms

Algorithm

intervals

Results

84.0ms	69×	body	10240	exit
59.0ms	54×	body	1280	valid
56.0ms	345×	body	80	valid
30.0ms	14×	body	160	valid
24.0ms	35×	body	640	valid
10.0ms	21×	body	320	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
5	3061
4	844
3	296
2	120
1	46
0	19

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- x) (* x eps))
0.0b	(/ (exp (+ (- x) (* x eps))) eps)
0.0b	(/ (exp (- (- x) (* x eps))) eps)
3.6b	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

rewrite705.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
27×	`times-frac`
25×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
20×	`add-log-exp`
12×	`exp-sum` `frac-sub`
9×	`associate-/l*`
8×	`add-cbrt-cube` `exp-diff` `diff-log`
7×	`sub-neg`
6×	`associate-/r*` `add-exp-log` `distribute-lft-out--`
5×	`neg-sub0` `flip3--` `flip--`
4×	`pow1` `associate-+l-` `insert-posit16`
3×	`flip3-+` `frac-add` `flip-+`
2×	`cbrt-undiv` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv` `distribute-lft-out` `associate--r+` `associate-/l/`
1×	`associate--l-` `neg-log` `associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

8.0ms	(- (- x) (* x eps))
29.0ms	(/ (exp (+ (- x) (* x eps))) eps)
36.0ms	(/ (exp (- (- x) (* x eps))) eps)
629.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

series268.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (- x) (* x eps))
43.0ms	(/ (exp (+ (- x) (* x eps))) eps)
42.0ms	(/ (exp (- (- x) (* x eps))) eps)
123.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

simplify1.3s

Counts

131 → 131

Iterations

Iter	Nodes
2	2777
1	668
0	253

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2 (* x x))
0.1b	(* x (* (* x x) 2/3))
0.1b	(* (* x x) 2/3)
5.6b	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-log-exp`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l` `insert-posit16`
2×	`associate-+l+` `sum-log` `sub-neg` `diff-log` `*-commutative`
1×	`+-commutative` `flip3-+` `flip3--` `associate-+l-` `flip-+` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

8.0ms	(- 2 (* x x))
54.0ms	(* x (* (* x x) 2/3))
34.0ms	(* (* x x) 2/3)
28.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- 2 (* x x))
80.0ms	(* x (* (* x x) 2/3))
48.0ms	(* (* x x) 2/3)
63.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
3	4261
2	1006
1	313
0	110

prune505.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (posit16->real (real->posit16 (* (* x x) 2/3))))
0.1b	(* (* x x) 2/3)
5.6b	(+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))
27.4b	(posit16->real (real->posit16 (* (* x x) 2/3)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`associate-+l+` `sum-log` `*-commutative` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `associate-+l-` `flip-+` `remove-posit16`

Counts

4 → 64

Calls

4 calls:

9.0ms	(* x (posit16->real (real->posit16 (* (* x x) 2/3))))
36.0ms	(* (* x x) 2/3)
31.0ms	(+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))
1.0ms	(posit16->real (real->posit16 (* (* x x) 2/3)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* x (posit16->real (real->posit16 (* (* x x) 2/3))))
50.0ms	(* (* x x) 2/3)
47.0ms	(+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))
30.0ms	(posit16->real (real->posit16 (* (* x x) 2/3)))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
3	3074
2	781
1	256
0	99

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) 2/3)
4.8b	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))))
5.6b	(+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))
27.4b	(posit16->real (real->posit16 (* (* x x) 2/3)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-+l+` `sum-log` `remove-posit16`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `associate-l` `*-commutative` `associate-+l-` `flip-+` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

34.0ms	(* (* x x) 2/3)
0.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))))
17.0ms	(+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))
0.0ms	(posit16->real (real->posit16 (* (* x x) 2/3)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* x x) 2/3)
48.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))))
55.0ms	(+ (- 2 (* x x)) (* x (posit16->real (real->posit16 (* (* x x) 2/3)))))
29.0ms	(posit16->real (real->posit16 (* (* x x) 2/3)))

simplify1.5s

Counts

66 → 66

Iterations

Iter	Nodes
3	2822
2	691
1	232
0	92

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes129.0ms

Accuracy

96.8% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch324.0ms

Steps

Iters	Range		Point
10	0.007550379505761139	462865523371709.2	245.97670246303022

simplify8.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample11.7s

Algorithm

intervals

Results

3.2s	1880×	body	10240	exit
3.2s	1744×	body	1280	valid
3.0s	10040×	body	80	valid
1.2s	1251×	body	640	valid
445.0ms	594×	body	320	valid
141.0ms	318×	body	160	valid