Details

sample347.0ms

Algorithm

intervals

Results

137.0ms	69×	body	10240	exit
69.0ms	49×	body	1280	valid
62.0ms	323×	body	80	valid
36.0ms	42×	body	640	valid
12.0ms	22×	body	320	valid
2.0ms	6×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2010
5	2010
4	1436
3	398
2	124
1	49
0	19

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
40×	`associate-l/` `associate-r/`
31×	`flip3-+` `flip3--` `flip-+` `flip--`
28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`un-div-inv`
19×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`times-frac` `associate-r` `add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-def` `difference-of-sqr-1` `div-inv`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `sum-log` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 190

Calls

4 calls:

12.0ms	(+ 1 (/ 1 eps))
69.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
36.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
63.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ 1 (/ 1 eps))
53.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
36.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
168.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.2s

Counts

202 → 202

Iterations

Iter	Nodes
done	2001
2	2001
1	1304
0	382

prune2.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (* x x))
6.8b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

32.0ms	(* x (* x x))
1.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series97.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(* x (* x x))
46.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify882.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	2001
4	2001
3	905
2	277
1	108
0	56

prune364.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 2/3 x)
6.8b	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

6.0ms	(* 2/3 x)
0.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

series59.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(* 2/3 x)
38.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

simplify1.2s

Counts

38 → 38

Iterations

Iter	Nodes
done	2000
4	2000
3	985
2	257
1	108
0	53

prune415.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize53.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `remove-posit16` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

6.0ms	(* 2/3 x)
4.0ms	(posit16->real (real->posit16 (fma (* 2/3 x) (* x x) (- 2 (* x x)))))
0.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

series125.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* 2/3 x)
57.0ms	(posit16->real (real->posit16 (fma (* 2/3 x) (* x x) (- 2 (* x x)))))
47.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

simplify1.2s

Counts

52 → 52

Iterations

Iter	Nodes
done	2012
4	2012
3	1011
2	279
1	122
0	64

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes206.0ms

Accuracy

96.3% (0.6b remaining)

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

bsearch415.0ms

Steps

Iters	Range		Point
10	0.0042870261776910435	159184409.05021107	100.79533204800275

simplify13.0ms

Iterations

Iter	Nodes
done	38
2	38
1	32
0	24

end0.0ms

sample12.4s

Algorithm

intervals

Results

4.3s	1964×	body	10240	exit
2.8s	1767×	body	1280	valid
2.7s	9993×	body	80	valid
1.5s	1282×	body	640	valid
498.0ms	636×	body	320	valid
145.0ms	282×	body	160	valid