Details

sample384.0ms

Algorithm

intervals

Results

129.0ms	70×	body	10240	exit
104.0ms	57×	body	1280	valid
64.0ms	315×	body	80	valid
40.0ms	42×	body	640	valid
15.0ms	25×	body	320	valid
5.0ms	12×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 eps) x)
0.0b	(exp (- (* (+ 1 eps) x)))
0.0b	(exp (- (* (- 1 eps) x)))
1.2b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3-+` `flip3--` `flip-+` `flip--`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

33.0ms	(* (+ 1 eps) x)
12.0ms	(exp (- (* (+ 1 eps) x)))
15.0ms	(exp (- (* (- 1 eps) x)))
57.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series265.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ 1 eps) x)
28.0ms	(exp (- (* (+ 1 eps) x)))
27.0ms	(exp (- (* (- 1 eps) x)))
167.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.4s

Counts

174 → 174

Iterations

Iter	Nodes
done	2000
2	2000
1	1277
0	377

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (* x x))
6.6b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

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

series109.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(* x (* x x))
45.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify945.0ms

Counts

44 → 44

Iterations

Iter	Nodes
done	2001
4	2001
3	905
2	277
1	108
0	56

prune180.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (* x x))
0.5b	(expm1 (log1p (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
6.6b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
10.9b	(log1p (fma (* x (* x x)) 2/3 (- 2 (* x x))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

29.0ms	(* x (* x x))
0.0ms	(expm1 (log1p (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
1.0ms	(log1p (fma (* x (* x x)) 2/3 (- 2 (* x x))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* x (* x x))
143.0ms	(expm1 (log1p (fma (* x (* x x)) 2/3 (- 2 (* x x)))))
58.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
60.0ms	(log1p (fma (* x (* x x)) 2/3 (- 2 (* x x))))

simplify1.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	2014
3	2014
2	700
1	257
0	123

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (* x x))
6.6b	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
18.9b	(posit16->real (real->posit16 (* x (* x x))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

29.0ms	(* x (* x x))
0.0ms	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
1.0ms	(posit16->real (real->posit16 (* x (* x x))))

series192.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* x (* x x))
59.0ms	(fma (posit16->real (real->posit16 (* x (* x x)))) 2/3 (- 2 (* x x)))
69.0ms	(posit16->real (real->posit16 (* x (* x x))))

simplify1.1s

Counts

58 → 58

Iterations

Iter	Nodes
done	2000
4	2000
3	1225
2	318
1	121
0	67

prune453.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes208.0ms

Accuracy

96.6% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.6b

bsearch299.0ms

Steps

Iters	Range		Point
10	1.4509785142153935e-08	32640636.358721357	158.8018617543875

simplify31.0ms

Iterations

Iter	Nodes
done	59
3	59
2	57
1	48
0	31

end0.0ms

sample12.6s

Algorithm

intervals

Results

3.7s	10022×	body	80	valid
3.3s	1869×	body	10240	exit
3.2s	1714×	body	1280	valid
1.4s	1241×	body	640	valid
506.0ms	650×	body	320	valid
170.0ms	336×	body	160	valid