Details

sample287.0ms

Algorithm

intervals

Results

75.0ms	48×	body	640	valid
60.0ms	64×	body	1280	valid
56.0ms	316×	body	80	valid
53.0ms	56×	body	10240	exit
7.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1521
3	381
2	122
1	48
0	19

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- -1 eps))
0.0b	(/ (exp (* x (- -1 eps))) eps)
0.0b	(/ (exp (* (+ eps -1) x)) eps)
2.9b	(+ (/ (exp (* (+ eps -1) x)) eps) (+ (- (exp (* (+ eps -1) x)) (/ (exp (* x (- -1 eps))) eps)) (exp (* x (- -1 eps)))))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `times-frac`
26×	`add-cube-cbrt`
16×	`exp-sum`
13×	`add-log-exp`
10×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*`
5×	`sum-log` `associate-r` `distribute-lft-out`
4×	`insert-posit16`
3×	`associate-l`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-add` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out--`
1×	`+-commutative` `associate-+r+` `associate-+r-` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

28.0ms	(* x (- -1 eps))
12.0ms	(/ (exp (* x (- -1 eps))) eps)
11.0ms	(/ (exp (* (+ eps -1) x)) eps)
293.0ms	(+ (/ (exp (* (+ eps -1) x)) eps) (+ (- (exp (* (+ eps -1) x)) (/ (exp (* x (- -1 eps))) eps)) (exp (* x (- -1 eps)))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* x (- -1 eps))
31.0ms	(/ (exp (* x (- -1 eps))) eps)
27.0ms	(/ (exp (* (+ eps -1) x)) eps)
147.0ms	(+ (/ (exp (* (+ eps -1) x)) eps) (+ (- (exp (* (+ eps -1) x)) (/ (exp (* x (- -1 eps))) eps)) (exp (* x (- -1 eps)))))

simplify2.3s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	1680
1	569
0	237

prune895.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* 2/3 x) (* x x))
0.3b	(* 2/3 x)
5.6b	(- (+ 2 (* (* 2/3 x) (* x x))) (* x x))

rewrite80.0ms

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))
9.0ms	(* 2/3 x)
47.0ms	(- (+ 2 (* (* 2/3 x) (* x x))) (* x x))

series139.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* 2/3 x) (* x x))
29.0ms	(* 2/3 x)
57.0ms	(- (+ 2 (* (* 2/3 x) (* x x))) (* x x))

simplify3.7s

Counts

67 → 67

Iterations

Iter	Nodes
done	5004
3	4555
2	814
1	251
0	92

prune288.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (posit16->real (real->posit16 (* 2/3 x))) (* x x))
0.3b	(* 2/3 x)
5.6b	(- (+ 2 (* (posit16->real (real->posit16 (* 2/3 x))) (* x x))) (* x x))
60.2b	(posit16->real (real->posit16 (* 2/3 x)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

14.0ms	(* (posit16->real (real->posit16 (* 2/3 x))) (* x x))
9.0ms	(* 2/3 x)
41.0ms	(- (+ 2 (* (posit16->real (real->posit16 (* 2/3 x))) (* x x))) (* x x))
1.0ms	(posit16->real (real->posit16 (* 2/3 x)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (posit16->real (real->posit16 (* 2/3 x))) (* x x))
28.0ms	(* 2/3 x)
62.0ms	(- (+ 2 (* (posit16->real (real->posit16 (* 2/3 x))) (* x x))) (* x x))
32.0ms	(posit16->real (real->posit16 (* 2/3 x)))

simplify3.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	4042
2	797
1	243
0	99

prune544.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

8.5b	(cbrt (- (+ 2 (* (posit16->real (real->posit16 (* 2/3 x))) (* x x))) (* x x)))
60.2b	(posit16->real (real->posit16 (* 2/3 x)))
60.2b	(posit16->real (real->posit16 (* 2/3 x)))
60.2b	(posit16->real (real->posit16 (* 2/3 x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`remove-posit16`
2×	`cbrt-div`
1×	`flip3--` `pow1/3` `flip--` `difference-of-squares`

Counts

4 → 42

Calls

4 calls:

11.0ms	(cbrt (- (+ 2 (* (posit16->real (real->posit16 (* 2/3 x))) (* x x))) (* x x)))
0.0ms	(posit16->real (real->posit16 (* 2/3 x)))
0.0ms	(posit16->real (real->posit16 (* 2/3 x)))
0.0ms	(posit16->real (real->posit16 (* 2/3 x)))

series158.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (- (+ 2 (* (posit16->real (real->posit16 (* 2/3 x))) (* x x))) (* x x)))
17.0ms	(posit16->real (real->posit16 (* 2/3 x)))
17.0ms	(posit16->real (real->posit16 (* 2/3 x)))
17.0ms	(posit16->real (real->posit16 (* 2/3 x)))

simplify1.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	2440
2	615
1	207
0	94

prune559.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes86.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.5b

bsearch182.0ms

Steps

Iters	Range		Point
6	0.9820002734449668	5.220773054910798	1.9334006562055708

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.6s	10104×	body	80	valid
2.4s	1680×	body	1280	valid
2.1s	1901×	body	10240	exit
812.0ms	1287×	body	640	valid
297.0ms	644×	body	320	valid
69.0ms	320×	body	160	valid