Details

sample398.0ms

Algorithm

intervals

Results

121.0ms	78×	body	10240	exit
107.0ms	49×	body	1280	valid
69.0ms	334×	body	80	valid
61.0ms	49×	body	640	valid
14.0ms	19×	body	320	valid
3.0ms	8×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize55.0ms

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)))))

rewrite181.0ms

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:

15.0ms	(exp (- (* (- 1 eps) x)))
30.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
86.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
41.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (- (* (- 1 eps) x)))
32.0ms	(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
55.0ms	(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
171.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.4s

Counts

203 → 203

Iterations

Iter	Nodes
2	3237
1	1273
0	392

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 2/3 (* (* x x) x) 2)
0.1b	(* (* x x) x)
6.4b	(- (fma 2/3 (* (* x x) x) 2) (* x x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
6×	`*-un-lft-identity` `pow-plus` `pow-prod-up` `add-cube-cbrt`
5×	`add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `pow3` `associate--l+` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`

Counts

3 → 65

Calls

3 calls:

0.0ms	(fma 2/3 (* (* x x) x) 2)
14.0ms	(* (* x x) x)
5.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))

series219.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(fma 2/3 (* (* x x) x) 2)
42.0ms	(* (* x x) x)
47.0ms	(- (fma 2/3 (* (* x x) x) 2) (* x x))

simplify4.9s

Counts

74 → 74

Iterations

Iter	Nodes
4	8331
3	1881
2	533
1	213
0	84

prune378.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) (fma 2/3 x -1) 2)
0.1b	(fma 2/3 x -1)
3.5b	(posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

3×	`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`
2×	`fma-udef`
1×	`remove-posit16`

Counts

3 → 33

Calls

3 calls:

0.0ms	(fma (* x x) (fma 2/3 x -1) 2)
0.0ms	(fma 2/3 x -1)
1.0ms	(posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma (* x x) (fma 2/3 x -1) 2)
65.0ms	(fma 2/3 x -1)
70.0ms	(posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))

simplify4.5s

Counts

42 → 42

Iterations

Iter	Nodes
5	7794
4	1331
3	394
2	152
1	76
0	48

prune788.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 2/3 x -1)
0.4b	(exp (log (posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))))
3.5b	(posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))
9.7b	(log (posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`log-pow`
1×	`rem-log-exp` `fma-udef` `remove-posit16` `rem-exp-log`

Counts

4 → 55

Calls

4 calls:

0.0ms	(fma 2/3 x -1)
3.0ms	(exp (log (posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))))
0.0ms	(posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))
1.0ms	(log (posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma 2/3 x -1)
40.0ms	(exp (log (posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))))
55.0ms	(posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2)))
73.0ms	(log (posit16->real (real->posit16 (fma (* x x) (fma 2/3 x -1) 2))))

simplify887.0ms

Counts

67 → 67

Iterations

Iter	Nodes
4	2372
3	837
2	366
1	172
0	95

prune616.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes109.0ms

Accuracy

95.9% (0.7b remaining)

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

bsearch246.0ms

Steps

Iters	Range		Point
8	4.719180737436054	179479.52296690646	183.1502607165994

simplify6.0ms

Iterations

Iter	Nodes
2	32
1	32
0	28

end0.0ms

sample10.9s

Algorithm

intervals

Results

3.3s	1680×	body	1280	valid
3.3s	2027×	body	10240	exit
2.5s	10015×	body	80	valid
1.0s	1273×	body	640	valid
382.0ms	633×	body	320	valid
109.0ms	332×	body	160	valid