Details

sample347.0ms

Algorithm

intervals

Results

100.0ms	65×	body	1280	valid
91.0ms	332×	body	80	valid
85.0ms	66×	body	10240	exit
38.0ms	51×	body	640	valid
7.0ms	14×	body	320	valid
3.0ms	9×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
5	2873
4	824
3	298
2	122
1	48
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize84.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (- 1 eps) x)))
0.0b	(* (+ 1 eps) x)
0.0b	(* (- 1 eps) x)
2.1b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
73×	`exp-neg`
72×	`frac-times`
55×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
18×	`un-div-inv`
16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`exp-prod` `associate-r`
4×	`insert-posit16`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr` `rem-exp-log`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 158

Calls

4 calls:

15.0ms	(exp (- (* (- 1 eps) x)))
28.0ms	(* (+ 1 eps) x)
31.0ms	(* (- 1 eps) x)
53.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (- (* (- 1 eps) x)))
43.0ms	(* (+ 1 eps) x)
46.0ms	(* (- 1 eps) x)
177.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify2.4s

Counts

170 → 170

Iterations

Iter	Nodes
2	3233
1	1179
0	376

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* 2/3 (* (* x x) x))
6.2b	(+ (* 2/3 (* (* x x) x)) (- 2 (* x x)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`pow2` `associate-+r+` `sum-log` `pow-sqr` `*-commutative`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `pow3` `flip-+` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

29.0ms	(* (* x x) x)
70.0ms	(* 2/3 (* (* x x) x))
48.0ms	(+ (* 2/3 (* (* x x) x)) (- 2 (* x x)))

series167.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* (* x x) x)
51.0ms	(* 2/3 (* (* x x) x))
64.0ms	(+ (* 2/3 (* (* x x) x)) (- 2 (* x x)))

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
3	3140
2	727
1	246
0	88

prune631.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* 2/3 (* (* x x) x))
6.2b	(+ (* 2/3 (* (* x x) x)) (- 2 (* x x)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`pow2` `associate-+r+` `sum-log` `pow-sqr` `*-commutative`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `pow3` `flip-+` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

28.0ms	(* (* x x) x)
64.0ms	(* 2/3 (* (* x x) x))
53.0ms	(+ (* 2/3 (* (* x x) x)) (- 2 (* x x)))

series176.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(* (* x x) x)
48.0ms	(* 2/3 (* (* x x) x))
63.0ms	(+ (* 2/3 (* (* x x) x)) (- 2 (* x x)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
3	3140
2	727
1	246
0	88

prune724.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* 2/3 (posit16->real (real->posit16 (* (* x x) x))))
6.2b	(+ (* 2/3 (posit16->real (real->posit16 (* (* x x) x)))) (- 2 (* x x)))
16.8b	(posit16->real (real->posit16 (* (* x x) x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus` `associate-r` `pow-prod-up`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`pow2` `associate-+r+` `sum-log` `pow-sqr` `*-commutative` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `pow3` `flip-+` `remove-posit16`

Counts

4 → 73

Calls

4 calls:

26.0ms	(* (* x x) x)
10.0ms	(* 2/3 (posit16->real (real->posit16 (* (* x x) x))))
12.0ms	(+ (* 2/3 (posit16->real (real->posit16 (* (* x x) x)))) (- 2 (* x x)))
0.0ms	(posit16->real (real->posit16 (* (* x x) x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* x x) x)
68.0ms	(* 2/3 (posit16->real (real->posit16 (* (* x x) x))))
60.0ms	(+ (* 2/3 (posit16->real (real->posit16 (* (* x x) x)))) (- 2 (* x x)))
43.0ms	(posit16->real (real->posit16 (* (* x x) x)))

simplify1.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	3095
2	772
1	236
0	97

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes132.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.4b

bsearch287.0ms

Steps

Iters	Range		Point
9	0.08974485042074802	5623247.098758675	307.0243008404694

simplify9.0ms

Iterations

Iter	Nodes
3	41
2	41
1	35
0	25

end0.0ms

sample12.0s

Algorithm

intervals

Results

3.9s	2015×	body	10240	exit
2.8s	1697×	body	1280	valid
2.7s	10189×	body	80	valid
1.6s	1316×	body	640	valid
494.0ms	615×	body	320	valid
113.0ms	302×	body	160	valid