Details

sample255.0ms

Algorithm

intervals

Results

107.0ms	78×	body	10240	exit
44.0ms	334×	body	80	valid
41.0ms	49×	body	1280	valid
28.0ms	49×	body	640	valid
7.0ms	19×	body	320	valid
2.0ms	8×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize60.0ms

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)))))

rewrite166.0ms

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

Counts

4 → 191

Calls

4 calls:

8.0ms	(exp (- (* (- 1 eps) x)))
49.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
55.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
49.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (- (* (- 1 eps) x)))
31.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
53.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
166.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.3s

Counts

203 → 203

Iterations

Iter	Nodes
done	2004
2	2004
1	1317
0	392

prune3.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`pow2` `expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

17.0ms	(* (* x x) x)
0.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (* x x) x)
63.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

simplify1.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	2000
4	2000
3	805
2	278
1	126
0	55

prune492.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`pow2` `expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

16.0ms	(* (* x x) x)
0.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

series117.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(* (* x x) x)
62.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	2000
4	2000
3	805
2	278
1	126
0	55

prune550.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `remove-posit16` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

40.0ms	(* (* x x) x)
0.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) (- 2 (* x x)))))
1.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (* x x) x)
52.0ms	(posit16->real (real->posit16 (fma 2/3 (* (* x x) x) (- 2 (* x x)))))
60.0ms	(fma 2/3 (* (* x x) x) (- 2 (* x x)))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	2012
4	2012
3	785
2	326
1	133
0	66

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes195.0ms

Accuracy

95.9% (0.7b remaining)

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

bsearch268.0ms

Steps

Iters	Range		Point
8	4.719180737436054	179479.52296690646	183.1502607165994

simplify41.0ms

Iterations

Iter	Nodes
done	57
3	57
2	55
1	46
0	30

end0.0ms

sample11.4s

Algorithm

intervals

Results

3.8s	2027×	body	10240	exit
2.5s	10015×	body	80	valid
2.2s	1680×	body	1280	valid
1.9s	1273×	body	640	valid
466.0ms	633×	body	320	valid
141.0ms	332×	body	160	valid