Details

sample336.0ms

Algorithm

intervals

Results

93.0ms	78×	body	10240	exit
76.0ms	334×	body	80	valid
55.0ms	49×	body	1280	valid
49.0ms	19×	body	320	valid
38.0ms	49×	body	640	valid
2.0ms	8×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (- 1 eps) x)))
0.0b	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
0.0b	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
1.5b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

81×	`exp-neg` `frac-sub`
80×	`frac-times`
61×	`neg-sub0` `exp-diff`
40×	`associate-l/` `associate-r/`
31×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
28×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`un-div-inv`
19×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`exp-prod` `times-frac` `associate-r` `add-exp-log` `difference-of-squares`
4×	`insert-posit16`
3×	`difference-of-sqr-1`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr` `rem-exp-log`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `diff-log` `neg-log`

Counts

4 → 181

Calls

4 calls:

15.0ms	(exp (- (* (- 1 eps) x)))
34.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
77.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
53.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(exp (- (* (- 1 eps) x)))
36.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
36.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
173.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify2.1s

Counts

193 → 193

Iterations

Iter	Nodes
2	3071
1	1179
0	379

prune933.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x (* x x)) 2/3)
6.4b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
17×	`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` `pow-prod-up` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`associate-+l+` `sum-log` `*-commutative`
1×	`pow2` `+-commutative` `sub-neg` `flip3-+` `pow-plus` `diff-log` `cube-unmult` `pow-sqr` `associate-+l-` `flip-+` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

15.0ms	(* x (* x x))
62.0ms	(* (* x (* x x)) 2/3)
47.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

series187.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* x (* x x))
75.0ms	(* (* x (* x x)) 2/3)
65.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

simplify1.5s

Counts

72 → 72

Iterations

Iter	Nodes
3	3934
2	767
1	230
0	94

prune231.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x (* x x)) 2/3)
3.5b	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))
6.4b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

15.0ms	(* x (* x x))
45.0ms	(* (* x (* x x)) 2/3)
0.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))
51.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

series211.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* x (* x x))
54.0ms	(* (* x (* x x)) 2/3)
45.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))
51.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

simplify2.0s

Counts

84 → 84

Iterations

Iter	Nodes
3	4116
2	837
1	242
0	103

prune638.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (log (posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))))
3.5b	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))
6.4b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
9.7b	(log (posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(exp (log (posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))))
0.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))
46.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
11.0ms	(log (posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(exp (log (posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))))
63.0ms	(posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3))))
59.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
57.0ms	(log (posit16->real (real->posit16 (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
3	2717
2	704
1	245
0	106

prune584.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes97.0ms

Accuracy

95.9% (0.7b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.5b

bsearch206.0ms

Steps

Iters	Range		Point
8	4.719180737436054	179479.52296690646	183.1502607165994

simplify9.0ms

Iterations

Iter	Nodes
3	51
2	51
1	43
0	29

end0.0ms

sample11.2s

Algorithm

intervals

Results

3.7s	2027×	body	10240	exit
2.5s	10015×	body	80	valid
2.1s	1680×	body	1280	valid
2.0s	1273×	body	640	valid
406.0ms	633×	body	320	valid
142.0ms	332×	body	160	valid