Details

sample297.0ms

Algorithm

intervals

Results

94.0ms	47×	body	10240	exit
82.0ms	65×	body	1280	valid
55.0ms	288×	body	80	valid
34.0ms	42×	body	640	valid
11.0ms	21×	body	320	valid
1.0ms	3×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	1436
3	398
2	124
1	49
0	19

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize43.0ms

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
5×	`add-sqr-sqrt` `exp-prod` `*-un-lft-identity` `exp-sum` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-exp-log`
2×	`distribute-rgt-in` `distribute-lft-in` `exp-to-pow` `fma-udef`

Counts

4 → 56

Calls

4 calls:

2.0ms	(exp (fma eps x x))
5.0ms	(exp (* x (+ -1 eps)))
5.0ms	(exp (* x (+ -1 eps)))
0.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(exp (fma eps x x))
22.0ms	(exp (* x (+ -1 eps)))
23.0ms	(exp (* x (+ -1 eps)))
125.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (- (exp (* x (+ -1 eps))) (/ (- (/ 1 eps) 1) (exp (fma eps x x)))))

simplify1.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	2006
3	1381
2	451
1	185
0	92

prune446.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 2/3 x)
5.6b	(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:

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

series57.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(* 2/3 x)
41.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

simplify737.0ms

Counts

38 → 38

Iterations

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

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize40.0ms

Local error

Found 4 expressions with local error:

1.5b	(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)))

rewrite13.0ms

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:

12.0ms	(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)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(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)))))
40.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
43.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
49.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

simplify593.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	2001
3	540
2	152
1	63
0	36

prune314.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 2/3 x) (* x x) 2)
0.3b	(* 2/3 x)
4.1b	(posit16->real (real->posit16 (- (fma (* 2/3 x) (* x x) 2) (* x x))))
5.6b	(- (fma (* 2/3 x) (* x x) 2) (* x x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma (* 2/3 x) (* x x) 2)
10.0ms	(* 2/3 x)
0.0ms	(posit16->real (real->posit16 (- (fma (* 2/3 x) (* x x) 2) (* x x))))
12.0ms	(- (fma (* 2/3 x) (* x x) 2) (* x x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma (* 2/3 x) (* x x) 2)
16.0ms	(* 2/3 x)
64.0ms	(posit16->real (real->posit16 (- (fma (* 2/3 x) (* x x) 2) (* x x))))
57.0ms	(- (fma (* 2/3 x) (* x x) 2) (* x x))

simplify555.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	2001
2	496
1	196
0	94

prune708.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes144.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.3b

bsearch235.0ms

Steps

Iters	Range		Point
9	0.5242927222148749	19453700.538560145	41.6575809018513

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	28

end0.0ms

sample10.9s

Algorithm

intervals

Results

2.9s	1899×	body	10240	exit
2.9s	9973×	body	80	valid
2.7s	1743×	body	1280	valid
1.5s	1295×	body	640	valid
469.0ms	620×	body	320	valid
142.0ms	307×	body	160	valid