Details

sample330.0ms

Algorithm

intervals

Results

86.0ms	49×	body	1280	valid
84.0ms	69×	body	10240	exit
55.0ms	323×	body	80	valid
31.0ms	42×	body	640	valid
11.0ms	22×	body	320	valid
2.0ms	6×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize45.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x))))
2.9b	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x)))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 22

Calls

2 calls:

0.0ms	(fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x))))
0.0ms	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x)))))

series262.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x))))
182.0ms	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x)))))

simplify1.6s

Counts

28 → 28

Iterations

Iter	Nodes
4	3111
3	865
2	309
1	127
0	64

prune404.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize33.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 2/3 x)
6.8b	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

rewrite13.0ms

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:

11.0ms	(* 2/3 x)
1.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

series60.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(* 2/3 x)
44.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

simplify1.5s

Counts

38 → 38

Iterations

Iter	Nodes
4	3450
3	744
2	212
1	100
0	53

prune334.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (* 2/3 x))
0.3b	(* 2/3 x)
0.6b	(log1p (expm1 (* 2/3 x)))
6.8b	(fma (* x x) (log1p (expm1 (* 2/3 x))) (- 2 (* x x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(expm1 (* 2/3 x))
10.0ms	(* 2/3 x)
0.0ms	(log1p (expm1 (* 2/3 x)))
1.0ms	(fma (* x x) (log1p (expm1 (* 2/3 x))) (- 2 (* x x)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(expm1 (* 2/3 x))
29.0ms	(* 2/3 x)
285.0ms	(log1p (expm1 (* 2/3 x)))
254.0ms	(fma (* x x) (log1p (expm1 (* 2/3 x))) (- 2 (* x x)))

simplify2.4s

Counts

68 → 68

Iterations

Iter	Nodes
4	4205
3	942
2	301
1	145
0	81

prune732.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.6b	(log1p (expm1 (* 2/3 x)))
0.6b	(log1p (expm1 (* 2/3 x)))
0.6b	(log1p (expm1 (* 2/3 x)))
6.8b	(fma (* x x) (* (* (cbrt (log1p (expm1 (* 2/3 x)))) (cbrt (log1p (expm1 (* 2/3 x))))) (cbrt (log1p (expm1 (* 2/3 x))))) (- 2 (* x x)))

rewrite2.0ms

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×	`log1p-udef` `log1p-expm1`
1×	`fma-udef`

Counts

4 → 47

Calls

4 calls:

0.0ms	(log1p (expm1 (* 2/3 x)))
0.0ms	(log1p (expm1 (* 2/3 x)))
0.0ms	(log1p (expm1 (* 2/3 x)))
0.0ms	(fma (* x x) (* (* (cbrt (log1p (expm1 (* 2/3 x)))) (cbrt (log1p (expm1 (* 2/3 x))))) (cbrt (log1p (expm1 (* 2/3 x))))) (- 2 (* x x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

252.0ms	(log1p (expm1 (* 2/3 x)))
257.0ms	(log1p (expm1 (* 2/3 x)))
240.0ms	(log1p (expm1 (* 2/3 x)))
255.0ms	(fma (* x x) (* (* (cbrt (log1p (expm1 (* 2/3 x)))) (cbrt (log1p (expm1 (* 2/3 x))))) (cbrt (log1p (expm1 (* 2/3 x))))) (- 2 (* x x)))

simplify1.1s

Counts

59 → 59

Iterations

Iter	Nodes
4	3158
3	550
2	177
1	66
0	39

prune778.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

regimes205.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch382.0ms

Steps

Iters	Range		Point
10	0.0042870261776910435	159184409.05021107	100.79533204800275

simplify10.0ms

Iterations

Iter	Nodes
2	30
1	30
0	27

end0.0ms

sample11.4s

Algorithm

intervals

Results

4.0s	1964×	body	10240	exit
2.5s	9993×	body	80	valid
2.3s	1767×	body	1280	valid
1.6s	1282×	body	640	valid
394.0ms	636×	body	320	valid
179.0ms	282×	body	160	valid