Details

sample365.0ms

Algorithm

intervals

Results

147.0ms	69×	body	10240	exit
71.0ms	54×	body	1280	valid
70.0ms	345×	body	80	valid
31.0ms	35×	body	640	valid
14.0ms	21×	body	320	valid
5.0ms	14×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	3307
4	836
3	312
2	122
1	47
0	19

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.3b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 eps) x)
0.0b	(* (- 1 eps) x)
0.0b	(exp (- (* (- 1 eps) x)))
3.6b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite74.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

13.0ms	(* (+ 1 eps) x)
19.0ms	(* (- 1 eps) x)
7.0ms	(exp (- (* (- 1 eps) x)))
28.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ 1 eps) x)
38.0ms	(* (- 1 eps) x)
29.0ms	(exp (- (* (- 1 eps) x)))
153.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.4s

Counts

180 → 180

Iterations

Iter	Nodes
2	3337
1	1274
0	389

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 2 (* x x))
0.1b	(* x (* x x))
5.6b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite46.0ms

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`
1×	`pow2` `sub-neg` `pow-plus` `flip3--` `diff-log` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

9.0ms	(- 2 (* x x))
35.0ms	(* x (* x x))
1.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(- 2 (* x x))
51.0ms	(* x (* x x))
41.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify14.9s

Counts

69 → 69

Iterations

Iter	Nodes
4	10454
3	1966
2	487
1	185
0	90

prune480.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

2.8b	(cbrt (* (* (fma 2/3 (* x (* x x)) (- 2 (* x x))) (fma 2/3 (* x (* x x)) (- 2 (* x x)))) (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
5.6b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
5.6b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
5.6b	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 46

Calls

4 calls:

19.0ms	(cbrt (* (* (fma 2/3 (* x (* x x)) (- 2 (* x x))) (fma 2/3 (* x (* x x)) (- 2 (* x x)))) (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
0.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (* (* (fma 2/3 (* x (* x x)) (- 2 (* x x))) (fma 2/3 (* x (* x x)) (- 2 (* x x)))) (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
63.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
39.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))
47.0ms	(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify535.0ms

Counts

58 → 58

Iterations

Iter	Nodes
4	2165
3	377
2	116
1	55
0	36

prune595.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2 (* x x))
0.1b	(* x (* x x))
5.6b	(fma 2/3 (* x (* x x)) (posit16->real (real->posit16 (- 2 (* x x)))))
14.9b	(posit16->real (real->posit16 (- 2 (* x x))))

rewrite43.0ms

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:

14.0ms	(- 2 (* x x))
27.0ms	(* x (* x x))
0.0ms	(fma 2/3 (* x (* x x)) (posit16->real (real->posit16 (- 2 (* x x)))))
1.0ms	(posit16->real (real->posit16 (- 2 (* x x))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- 2 (* x x))
68.0ms	(* x (* x x))
58.0ms	(fma 2/3 (* x (* x x)) (posit16->real (real->posit16 (- 2 (* x x)))))
69.0ms	(posit16->real (real->posit16 (- 2 (* x x))))

simplify11.2s

Counts

83 → 83

Iterations

Iter	Nodes
4	10041
3	1841
2	461
1	200
0	101

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

regimes204.0ms

Accuracy

95.7% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.6b

bsearch319.0ms

Steps

Iters	Range		Point
10	0.007550379505761139	462865523371709.2	245.97670246303022

simplify11.0ms

Iterations

Iter	Nodes
4	52
3	52
2	50
1	43
0	32

end0.0ms

sample11.2s

Algorithm

intervals

Results

3.8s	1880×	body	10240	exit
2.7s	1744×	body	1280	valid
2.2s	10040×	body	80	valid
1.6s	1251×	body	640	valid
389.0ms	594×	body	320	valid
170.0ms	318×	body	160	valid