Details

sample189.0ms

Algorithm

intervals

Results

61.0ms	52×	body	1280	valid
37.0ms	292×	body	80	valid
35.0ms	45×	body	10240	exit
18.0ms	31×	body	640	valid
9.0ms	25×	body	320	valid
4.0ms	14×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1436
3	398
2	124
1	49
0	19

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma eps x x))
0.0b	(exp (* x (+ -1 eps)))
0.0b	(exp (* x (+ -1 eps)))
4.1b	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

308×	`add-sqr-sqrt`
241×	`times-frac`
233×	`*-un-lft-identity`
180×	`prod-diff`
123×	`add-cube-cbrt`
74×	`difference-of-squares`
47×	`exp-sum`
44×	`fma-udef`
36×	`difference-of-sqr-1`
25×	`distribute-lft-out--`
15×	`div-inv`
11×	`add-log-exp`
5×	`exp-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `rem-exp-log`
2×	`distribute-rgt-in` `distribute-lft-in` `exp-to-pow`
1×	`sub-neg` `flip3--` `diff-log` `div-sub` `associate--l+` `flip--` `associate--r-`

Counts

4 → 248

Calls

4 calls:

2.0ms	(exp (fma eps x x))
5.0ms	(exp (* x (+ -1 eps)))
9.0ms	(exp (* x (+ -1 eps)))
115.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (fma eps x x))
20.0ms	(exp (* x (+ -1 eps)))
22.0ms	(exp (* x (+ -1 eps)))
183.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

simplify2.3s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
2	3113
1	1224
0	486

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* x x))
0.2b	(fma 2/3 (* x (* x x)) 2)
6.2b	(- (fma 2/3 (* x (* x x)) 2) (* x x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
8×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow-prod-up` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`fma-udef`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `associate--l+` `pow-sqr` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

18.0ms	(* x (* x x))
0.0ms	(fma 2/3 (* x (* x x)) 2)
7.0ms	(- (fma 2/3 (* x (* x x)) 2) (* x x))

series238.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* x (* x x))
138.0ms	(fma 2/3 (* x (* x x)) 2)
61.0ms	(- (fma 2/3 (* x (* x x)) 2) (* x x))

simplify2.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2642
2	544
1	187
0	85

prune314.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x x))
0.2b	(fma 2/3 (* x (* x x)) 2)
4.8b	(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2)))
6.2b	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `remove-posit16` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

39.0ms	(* x (* x x))
0.0ms	(fma 2/3 (* x (* x x)) 2)
0.0ms	(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2)))
14.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* x (* x x))
122.0ms	(fma 2/3 (* x (* x x)) 2)
108.0ms	(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2)))
61.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))

simplify2.6s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
3	2021
2	507
1	194
0	95

prune638.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

4.8b	(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2)))
6.2b	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))
6.2b	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))
6.2b	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
9×	`fma-neg` `prod-diff`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`remove-posit16`

Counts

4 → 77

Calls

4 calls:

0.0ms	(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2)))
6.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))
7.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))
7.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2)))
58.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))
46.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))
50.0ms	(- (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) 2))) (* x x))

simplify2.6s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	1946
2	394
1	123
0	55

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

regimes154.0ms

Accuracy

94.4% (0.9b remaining)

Error of 1.5b against oracle of 0.5b and baseline of 17.1b

bsearch189.0ms

Steps

Iters	Range		Point
8	4.1750260115318935e-11	1.508099977930646e-06	1.4798868095701662e-06

simplify8.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.8s	1971×	body	10240	exit
2.0s	1717×	body	1280	valid
1.6s	1176×	body	640	valid
1.5s	10203×	body	80	valid
256.0ms	656×	body	320	valid
61.0ms	277×	body	160	valid