Details

sample349.0ms

Algorithm

intervals

Results

90.0ms	67×	body	10240	exit
85.0ms	52×	body	1280	valid
61.0ms	311×	body	80	valid
42.0ms	54×	body	640	valid
31.0ms	11×	body	160	valid
11.0ms	21×	body	320	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: 32.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (* (- 1 eps) x)))
0.0b	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
0.0b	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
3.0b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 231

Calls

4 calls:

161.0ms	(exp (- (* (- 1 eps) x)))
490.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
535.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
2.4s	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series247.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (- (* (- 1 eps) x)))
42.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
29.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
149.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify3.2s

Counts

243 → 243

Iterations

Iter	Nodes
done	5000
2	4293
1	1351
0	440

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2 (* x x))
0.1b	(* (* 2/3 x) (* x x))
0.4b	(* 2/3 x)
7.0b	(+ (* (* 2/3 x) (* x x)) (- 2 (* x x)))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

25.0ms	(- 2 (* x x))
65.0ms	(* (* 2/3 x) (* x x))
12.0ms	(* 2/3 x)
316.0ms	(+ (* (* 2/3 x) (* x x)) (- 2 (* x x)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- 2 (* x x))
67.0ms	(* (* 2/3 x) (* x x))
15.0ms	(* 2/3 x)
59.0ms	(+ (* (* 2/3 x) (* x x)) (- 2 (* x x)))

simplify1.4s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	1602
1	472
0	146

prune394.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (posit16->real (real->posit16 (* 2/3 x))) (* x x))
0.4b	(* 2/3 x)
7.0b	(+ (* (posit16->real (real->posit16 (* 2/3 x))) (* x x)) (- 2 (* x x)))
60.3b	(posit16->real (real->posit16 (* 2/3 x)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
21×	`associate-r`
14×	`associate-l`
12×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
8×	`unswap-sqr`
6×	`distribute-lft-out`
4×	`swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `distribute-lft-out--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `flip-+` `remove-posit16`

Counts

4 → 88

Calls

4 calls:

47.0ms	(* (posit16->real (real->posit16 (* 2/3 x))) (* x x))
14.0ms	(* 2/3 x)
194.0ms	(+ (* (posit16->real (real->posit16 (* 2/3 x))) (* x x)) (- 2 (* x x)))
0.0ms	(posit16->real (real->posit16 (* 2/3 x)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (posit16->real (real->posit16 (* 2/3 x))) (* x x))
21.0ms	(* 2/3 x)
53.0ms	(+ (* (posit16->real (real->posit16 (* 2/3 x))) (* x x)) (- 2 (* x x)))
19.0ms	(posit16->real (real->posit16 (* 2/3 x)))

simplify3.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5003
3	3982
2	1059
1	336
0	117

prune684.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize84.0ms

Local error

Found 4 expressions with local error:

9.7b	(cbrt (+ (* (posit16->real (real->posit16 (* 2/3 x))) (* x x)) (- 2 (* x x))))
60.3b	(posit16->real (real->posit16 (* 2/3 x)))
60.3b	(posit16->real (real->posit16 (* 2/3 x)))
60.3b	(posit16->real (real->posit16 (* 2/3 x)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
9×	`cbrt-prod`
6×	`distribute-lft-out`
5×	`add-sqr-sqrt` `associate-l` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `distribute-lft-out--` `add-log-exp`
3×	`remove-posit16`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 47

Calls

4 calls:

165.0ms	(cbrt (+ (* (posit16->real (real->posit16 (* 2/3 x))) (* x x)) (- 2 (* x x))))
1.0ms	(posit16->real (real->posit16 (* 2/3 x)))
1.0ms	(posit16->real (real->posit16 (* 2/3 x)))
1.0ms	(posit16->real (real->posit16 (* 2/3 x)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (+ (* (posit16->real (real->posit16 (* 2/3 x))) (* x x)) (- 2 (* x x))))
28.0ms	(posit16->real (real->posit16 (* 2/3 x)))
18.0ms	(posit16->real (real->posit16 (* 2/3 x)))
17.0ms	(posit16->real (real->posit16 (* 2/3 x)))

simplify2.7s

Counts

59 → 59

Iterations

Iter	Nodes
done	5005
3	2680
2	625
1	202
0	89

prune568.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes116.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.2b

bsearch241.0ms

Steps

Iters	Range		Point
8	0.003724545156938161	2.2608459371195293	2.224816812712469

simplify9.0ms

Iterations

Iter	Nodes
done	44
2	44
1	42
0	28

end0.0ms

sample11.7s

Algorithm

intervals

Results

4.3s	1987×	body	10240	exit
2.5s	1758×	body	1280	valid
2.2s	9884×	body	80	valid
1.6s	1276×	body	640	valid
471.0ms	637×	body	320	valid
118.0ms	333×	body	160	valid