Details

sample303.0ms

Algorithm

intervals

Results

95.0ms	69×	body	10240	exit
54.0ms	49×	body	1280	valid
53.0ms	323×	body	80	valid
37.0ms	22×	body	320	valid
32.0ms	42×	body	640	valid
2.0ms	6×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize34.0ms

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)
1.5b	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

rewrite748.0ms

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`
6×	`associate-/r*` `sub-neg` `diff-log` `add-exp-log` `distribute-lft-out--`
5×	`neg-sub0` `associate-+l-`
4×	`pow1` `sum-log` `flip3-+` `flip3--` `flip-+` `insert-posit16` `flip--`
3×	`frac-add`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `distribute-lft-out` `associate--r+` `associate-/l/`
1×	`+-commutative` `neg-log` `associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 118

Calls

4 calls:

7.0ms	(+ (- x) (* x eps))
23.0ms	(/ (exp (+ (- x) (* x eps))) eps)
25.0ms	(/ (exp (- (- x) (* x eps))) eps)
691.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (- x) (* x eps))
40.0ms	(/ (exp (+ (- x) (* x eps))) eps)
29.0ms	(/ (exp (- (- x) (* x eps))) eps)
131.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
2	2690
1	677
0	252

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* (* x x) 2/3))
0.2b	(* (* x x) 2/3)
6.8b	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

72.0ms	(* x (* (* x x) 2/3))
24.0ms	(* (* x x) 2/3)
22.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* x (* (* x x) 2/3))
44.0ms	(* (* x x) 2/3)
46.0ms	(+ (- 2 (* x x)) (* x (* (* x x) 2/3)))

simplify1.7s

Counts

67 → 67

Iterations

Iter	Nodes
3	3301
2	764
1	242
0	91

prune610.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* 2/3 x) (* x x))
0.3b	(* 2/3 x)
6.8b	(- (+ (* (* 2/3 x) (* x x)) 2) (* x x))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

22.0ms	(* (* 2/3 x) (* x x))
10.0ms	(* 2/3 x)
227.0ms	(- (+ (* (* 2/3 x) (* x x)) 2) (* x x))

series149.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* (* 2/3 x) (* x x))
26.0ms	(* 2/3 x)
53.0ms	(- (+ (* (* 2/3 x) (* x x)) 2) (* x x))

simplify3.7s

Counts

67 → 67

Iterations

Iter	Nodes
3	6452
2	954
1	243
0	92

prune536.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2/3 x) (* x x))
0.3b	(* 2/3 x)
3.6b	(posit16->real (real->posit16 (- (+ (* (* 2/3 x) (* x x)) 2) (* x x))))
6.8b	(- (+ (* (* 2/3 x) (* x x)) 2) (* x x))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

38.0ms	(* (* 2/3 x) (* x x))
5.0ms	(* 2/3 x)
0.0ms	(posit16->real (real->posit16 (- (+ (* (* 2/3 x) (* x x)) 2) (* x x))))
142.0ms	(- (+ (* (* 2/3 x) (* x x)) 2) (* x x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 2/3 x) (* x x))
27.0ms	(* 2/3 x)
51.0ms	(posit16->real (real->posit16 (- (+ (* (* 2/3 x) (* x x)) 2) (* x x))))
39.0ms	(- (+ (* (* 2/3 x) (* x x)) 2) (* x x))

simplify3.6s

Counts

79 → 79

Iterations

Iter	Nodes
3	5709
2	941
1	256
0	101

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

regimes233.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch352.0ms

Steps

Iters	Range		Point
10	0.0042870261776910435	159184409.05021107	2.1846861365271546

simplify10.0ms

Iterations

Iter	Nodes
2	32
1	32
0	25

end0.0ms

sample12.0s

Algorithm

intervals

Results

3.5s	1767×	body	1280	valid
3.2s	1964×	body	10240	exit
2.6s	9993×	body	80	valid
1.3s	1282×	body	640	valid
876.0ms	636×	body	320	valid
141.0ms	282×	body	160	valid