Details

sample392.0ms

Algorithm

intervals

Results

140.0ms	76×	body	10240	exit
68.0ms	333×	body	80	valid
67.0ms	48×	body	1280	valid
62.0ms	42×	body	640	valid
20.0ms	32×	body	320	valid
2.0ms	5×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
5	3313
4	892
3	314
2	124
1	49
0	19

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1 (/ 1 eps)) (exp (fma x eps x)))
0.0b	(exp (fma x eps x))
0.0b	(exp (- (* x eps) x))
4.4b	(fma (exp (- (* x eps) x)) (+ 1 (/ 1 eps)) (/ (- 1 (/ 1 eps)) (exp (fma x eps x))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
64×	`*-un-lft-identity` `times-frac`
30×	`difference-of-squares`
24×	`add-cube-cbrt`
18×	`exp-sum`
14×	`fma-udef`
11×	`associate-/l*`
10×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`exp-prod` `add-cbrt-cube` `div-inv`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff` `rem-exp-log`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `exp-diff` `diff-log` `div-sub` `div-exp` `flip--`

Counts

4 → 124

Calls

4 calls:

46.0ms	(/ (- 1 (/ 1 eps)) (exp (fma x eps x)))
2.0ms	(exp (fma x eps x))
19.0ms	(exp (- (* x eps) x))
0.0ms	(fma (exp (- (* x eps) x)) (+ 1 (/ 1 eps)) (/ (- 1 (/ 1 eps)) (exp (fma x eps x))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- 1 (/ 1 eps)) (exp (fma x eps x)))
16.0ms	(exp (fma x eps x))
20.0ms	(exp (- (* x eps) x))
130.0ms	(fma (exp (- (* x eps) x)) (+ 1 (/ 1 eps)) (/ (- 1 (/ 1 eps)) (exp (fma x eps x))))

simplify1.2s

Counts

136 → 136

Iterations

Iter	Nodes
3	2776
2	1010
1	466
0	233

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 2/3 x)
4.8b	(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)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(* 2/3 x)
47.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))

simplify1.4s

Counts

38 → 38

Iterations

Iter	Nodes
4	3647
3	711
2	210
1	103
0	53

prune362.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize56.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 2/3 x)
4.8b	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
5.0b	(posit16->real (real->posit16 (fma (* 2/3 x) (* x x) (- 2 (* x x)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `remove-posit16` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

11.0ms	(* 2/3 x)
0.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
1.0ms	(posit16->real (real->posit16 (fma (* 2/3 x) (* x x) (- 2 (* x x)))))

series125.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* 2/3 x)
39.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
57.0ms	(posit16->real (real->posit16 (fma (* 2/3 x) (* x x) (- 2 (* x x)))))

simplify2.2s

Counts

52 → 52

Iterations

Iter	Nodes
4	5571
3	842
2	249
1	119
0	64

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
10.2b	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))
10.2b	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))
10.2b	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

0.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
1.0ms	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))
1.0ms	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))
1.0ms	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma (* 2/3 x) (* x x) (- 2 (* x x)))
97.0ms	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))
107.0ms	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))
106.0ms	(cbrt (fma (* 2/3 x) (* x x) (- 2 (* x x))))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
4	4633
3	1244
2	400
1	163
0	77

prune630.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes162.0ms

Accuracy

95.8% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.7b

bsearch461.0ms

Steps

Iters	Range		Point
11	2.3824489835354504e-16	446233850.42817044	80.15112264149943

simplify5.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample12.3s

Algorithm

intervals

Results

3.6s	1950×	body	10240	exit
3.4s	1789×	body	1280	valid
2.6s	10087×	body	80	valid
1.3s	1259×	body	640	valid
894.0ms	628×	body	320	valid
155.0ms	291×	body	160	valid